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  • 51. Kroon, Martin
    Saccular Aneurysm Growth in a Human Middle Cerebral Aneurysm: Deformation and Stress Analysis2007In: Presented at 44th Annual Meeting of the Society of Engineering Science, 21-24 October, 2007, 2007Conference paper (Refereed)
  • 52.
    Kroon, Martin
    Royal Institute of Technology, (KTH).
    Simulation of cerebral aneurysm growth and prediction of evolving rupture risk2011In: Modelling and Simulation in Engineering, ISSN 1687-5591, E-ISSN 1687-5605, article id 289523Article in journal (Refereed)
    Abstract [en]

    Cerebral aneurysms are local expansions of blood vessel walls in the brain blood system. The rupture of an aneurysm is a very severe event associated with a high rate of mortality. When cerebral aneurysms are detected, clinicians need to decide if operation is required. The risk of aneurysm rupture is then compared to the risks associated with the medical intervention. In the present paper, a probabilistic framework for a mechanically based rupture risk assessment of cerebral aneurysms is proposed. The method is based on the assumption that the strength of aneurysmal tissues can be described by a statistical distribution. A structural analysis of the aneurysm in question is performed, and the maximum stress experienced by the aneurysm is compared to the strength distribution. The proposed model was compared with clinical results for ruptured aneurysms in terms of rupture density and accumulated rupture risk as a function of aneurysm size. The model was able to reproduce the clinical results well. The proposed framework may potentially be used under in vivo conditions to predict the risk of rupture for diagnosed aneurysms.

  • 53. Kroon, Martin
    Some aspects of crack propagation in rubber2015In: Presented at 5th B. Broberg Symposium, August 24-25, 2015, 2015Conference paper (Refereed)
  • 54.
    Kroon, Martin
    Royal Institute of Technology, (KTH).
    Steady-state Crack Growth in Rubber-like Solids2011In: International Journal of Fracture, ISSN 0376-9429, E-ISSN 1573-2673, Vol. 169, no 1, p. 49-60Article in journal (Refereed)
    Abstract [en]

    The fracture toughness of rubber-like materials depends on several factors. First there is the surface energy required to create new crack surface at the crack tip. Second, a significant amount of energy is dissipated through viscoelastic processes in the bulk material around the crack tip. Third, if the crack propagates very rapidly, inertia effects will come into play and contribute to the fracture toughness. In the present study, a computational framework for studying high-speed crack growth in rubber-like solids under conditions of steady-state is proposed. Effects of inertia, viscoelasticity and finite strains are included. The main purpose of the study is to study the contribution of viscoelastic dissipation to the total work of fracture required to propagate a crack in a rubber-like solid. The model was fully able to predict experimental results in terms of the local surface energy at the crack tip and the total energy release rate at different crack speeds. In addition, the predicted distributions of stress and dissipation around the propagating crack tip are presented.

  • 55. Kroon, Martin
    Strengthening and Remodelling of Collagenous Networks2009In: Presented at 7th Euromech Solid Mechanics Conference, 7-11 September, 2009, 2009Conference paper (Refereed)
  • 56. Kroon, Martin
    Transiently cross-linked actin networks2012In: Presented at 10th World Congress on Computational Mechanics, 8-13 July, 2012, 2012Conference paper (Refereed)
  • 57.
    Kroon, Martin
    et al.
    Linnaeus University, Faculty of Technology, Department of Mechanical Engineering.
    Andreasson, E.
    Tetra Pak, Sweden;Blekinge Institute of Technology, Sweden.
    Persson Jutemar, E.
    Tetra Pak, Sweden.
    Petersson, V.
    Tetra Pak, Sweden.
    Persson, L.
    Tetra Pak, Sweden.
    Dorn, Michael
    Linnaeus University, Faculty of Technology, Department of Building Technology.
    Olsson, P.A.T.
    Malmö University, Sweden.
    Anisotropic elastic-viscoplastic properties of at finite strains of of injection-moulded low-density polyethylene2018In: Experimental mechanics, ISSN 0014-4851, E-ISSN 1741-2765, Vol. 58, no 1, p. 75-86Article in journal (Refereed)
    Abstract [en]

    Injection-moulding is one of the most common manufacturing processes used for polymers. In many applications, the mechanical properties of the product is of great importance. Injection-moulding of thin-walled polymer products tends to leave the polymer structure in a state where the mechanical properties are anisotropic, due to alignment of polymer chains along the melt flow direction. The anisotropic elastic-viscoplastic properties of low-density polyethylene, that has undergone an injection-moulding process, are therefore examined in the present work. Test specimens were punched out from injection-moulded plates and tested in uniaxial tension. Three in-plane material directions were investigated. Because of the small thickness of the plates, only the in-plane properties could be determined. Tensile tests with both monotonic and cyclic loading were performed, and the local strains on the surface of the test specimens were measured using image analysis. True stress vs. true strain diagrams were constructed, and the material response was evaluated using an elastic-viscoplasticity law. The components of the anisotropic compliance matrix were determined together with the direction-specific plastic hardening parameters.

  • 58.
    Kroon, Martin
    et al.
    Linnaeus University, Faculty of Technology, Department of Mechanical Engineering.
    Andreasson, Eskil
    Tetra Pak.
    Modeling of damage and crack growth in semi-crystalline polymers2017In: Proceedings of NSCM 30: The 30th Nordic Seminar on Computational Mechanics, 25-27 October, 2017 / [ed] J. Høgsberg. N.L. Pedersen, DTU Mechanical Engineering , 2017, p. 108-108Conference paper (Refereed)
    Abstract [en]

    t. Crack growth in semi-crystalline polymers, represented by polyethylene, is considered. The material considered comes in plates that had been created through an injection-molding process. Hence, the material was taken to be orthotropic. Material directions were identified as MD: molding direction, CD: transverse direction, TD: thickness direction. Uniaxial tensile testing was performed in order to establish the direction-specific elastic-plastic behaviour of the polymer. In addition, the fracture mechanics properties of the material was determined by performing fracture mechanics testing on plates with side cracks of different lengths. The fracture mechanics tests were filmed using a video camera. Based on this information, the force vs. load-line displacement could be established for the fracture mechanics tests, in which also the current length of the crack was indicated, since crack growth took place. In parallel to the experimental testing, an anisotropic plasticity model for finite strains was developed, which accounts for orthotropic elasticity and orthotropic plastic yielding and hardening. That plasticity model was implemented as a user subroutine in Abaqus. The crack growth experiments were then simulated using Abaqus, using the implemented plasticity model in combination with a damage model. Different types of crack initiation and growth criteria were explored, and the force-displacement-crack length data from the experiments could be well reproduced. Furthermore, the direction-specific work of fracture had been established from the experiments and these energies could be compared to the values of the J-integral from the simulations for the different crack lengths.

  • 59.
    Kroon, Martin
    et al.
    Linnaeus University, Faculty of Technology, Department of Mechanical Engineering.
    Andreasson, Eskil
    Tetra Pak.
    Olsson, Pär
    Malmö University.
    Assessment of fracture energy of polyethylene2017In: Svenska mekanikdagar 2017 Uppsala 12-13 juni, Uppsala universitet, 2017, p. 49-49Conference paper (Refereed)
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  • 60.
    Kroon, Martin
    et al.
    Linnaeus University, Faculty of Technology, Department of Mechanical Engineering.
    Andreasson, Eskil
    Tetra Pak.
    Olsson, Pär
    Malmo University.
    Modelling of Damage and Crack Growth in Semi-crystalline Polymers2018In: Presented at International Conference on Plasticity, Damage and Fracture 2018, Puerto Rico, Neat press , 2018Conference paper (Refereed)
    Abstract [en]

    Crack growth in semi-crystalline polymers, represented by polyethylene, is considered. The material considered comes in plates that had been created through an injection-molding process. Hence, the material was taken to be orthotropic. Material direction were identified as MD: molding direction, CD: transverse direction, TD: thickness direction. Uniaxial tensile testing was performed in order to establish the direction-specific elastic-plastic behaviour of the polymer. In addition, the fracture mechanics properties of the material was determined by performing fracture mechanics testing on plates with side cracks of different lengths. The fracture mechanics tests were filmed using a video camera. Based on this information, the force vs. load-line displacement could be established for the fracture mechanics tests, in which also the current length of the crack was indicated, since crack growth took place. In parallel to the experimental testing, an anisotropic plasticity model for finite strains was developed, which accounts for orthotropic elasticity and orthotropic plastic yielding and hardening. That plasticity model was implemented as a user subrouting in Abaqus. The crack growth experiments were then simulated using Abaqus, using the implemented plasticity model in combination with a damage model. Different types of crack initiation and growth criteria were explored, and the force-displacement-crack length data from the experiments could be well reproduced. Furthermore, the direction-specific work of fracture had been established from the experiments and these energies could be compared to the values of the J-integral from the simulations for the different crack lengths.

  • 61.
    Kroon, Martin
    et al.
    Linnaeus University, Faculty of Technology, Department of Mechanical Engineering.
    Andreasson, Eskil
    Tetra pak;Blekinge Technical University.
    Petersson, Viktor
    Tetra pak.
    Olsson, Pär
    Malmö University;Lund University.
    Experimental and numerical assessment of the work of fracture in injection-moulded low-density polyethylene2018In: Engineering Fracture Mechanics, ISSN 0013-7944, E-ISSN 1873-7315, Vol. 192, p. 1-11Article in journal (Refereed)
    Abstract [en]

    The fracture mechanics properties of injection-moulded low-density polyethylene (LDPE) sheets were investigated both experimentally and numerically. The total work of fracture was determined experimentally, by means of fracture mechanics testing of sheets of injection-moulded LDPE with side cracks of different lengths. A multi-specimen method, proposed by Kim and Joe (1987), was employed. The total work of fracture was estimated to 13 kJ/m(2). The experiments were simulated numerically using the finite element method. Crack growth was enabled by inclusion of a cohesive zone, and the constitutive response of this zone was governed by a traction-separation law. The local (or essential) work of fracture was estimated through numerical analyses, where the initiation of crack growth was simulated and the outcome was compared to the experimental results. The local (i.e. essential) work of fracture was estimated to 1.7 kJ/m(2), which is consistent with previous experimental measurements for the material in question. The total work of fracture, retrieved from the present experiments, agreed well with the far field values of the J-integral in the numerical analyses.

  • 62.
    Kroon, Martin
    et al.
    Malmö University.
    Faleskog, Jonas
    A J2-J3-dependent constitutive model for porous plasticity2016In: Presented at International Symposium on Plasticity, Big Island, Hawaii, January 3-9, 2016, 2016Conference paper (Refereed)
  • 63.
    Kroon, Martin
    et al.
    Royal Institute of Technology.
    Faleskog, Jonas
    Royal Institute of Technology.
    A probabilistic model for cleavage fracture with a length scale: influence of material parameters and constraint2002In: International Journal of Fracture, ISSN 0376-9429, E-ISSN 1573-2673, Vol. 118, no 2, p. 99-118Article in journal (Refereed)
    Abstract [en]

    A probabilistic model for the cumulative probability of failure by cleavage fracture with a material related length scale is developed in this study. The model aims at describing the random nature of fracture in ferritic steels in the brittle-to-ductile transition temperature region. The model derives from use of an exponential function to describe the distribution of microstructural entities eligible to take part in the fracture initiation process, where also a dependence on effective plastic strain is incorporated. A nonlocal stress measure, calculated as the average stress in a spherical volume, drives the contribution to failure probability of an infinitesimal material volume. The radius of the spherical volume enters as the material length in this model. This length has a significant influence on failure probability predictions in geometries exposed to strong stress gradients as found ahead of cracks. The material length is associated with a fracture toughness threshold value. In a fracture application three model parameters need to be estimated based on testing; a parameter directly related to the mean fracture toughness, a parameter that primarily is related to crack-tip constraint effects and the material length parameter. The model is explored in a parametric study showing model features in concord with typical features found in toughness distributions from fracture mechanics testing in the transition region.

  • 64.
    Kroon, Martin
    et al.
    Royal Institute of Technology.
    Faleskog, Jonas
    Royal Institute of Technology.
    Influence of crack deflection into the carbide/ferrite interface on cleavage fracture initiation in ferritic steels2008In: Mechanics of materials (Print), ISSN 0167-6636, E-ISSN 1872-7743, Vol. 40, no 8, p. 695-707Article in journal (Refereed)
    Abstract [en]

    In this and a companion study (Kroon, M., Faleskog, J., 2005. Micromechanics of cleavage fracture initiation in ferritic steels by carbide cracking. J. Mech. Phys. Solids 53, 171–196), the initiation of cleavage fracture in ferritic steels is studied. The initiation is modelled explicitly in the form of a microcrack, which nucleates in a brittle carbide and propagates into the surrounding ferrite. The carbide is modelled as an elastic cylinder and the ferrite as an elastic viscoplastic material. The crack growth is modelled using a cohesive surface, in which the tractions are governed by a modified exponential cohesive law. The advancing microcrack, which has nucleated in the carbide, may either continue into the ferrite or deflect into the interface between the carbide and the ferrite. Special attention is given to the influence of the mode mixity factor ββ, which is defined as the ratio between the shear and tensile strength of the interface between the carbide and the ferrite. Crack growth in the interface occurs in shear mode and is driven by a fibre loading mechanism. For mode mixity values β⩽0.2β⩽0.2, the crack deflects into the interface. The results indicate that crack growth in the interface can have a profound influence on the macroscopic fracture toughness of ferritic steels.

  • 65.
    Kroon, Martin
    et al.
    Royal Institute of Technology.
    Faleskog, Jonas
    Royal Institute of Technology.
    Micromechanics of cleavage fracture initiation in ferritic steels by carbide cracking2005In: Journal of the mechanics and physics of solids, ISSN 0022-5096, E-ISSN 1873-4782, Vol. 53, no 1, p. 171-196Article in journal (Refereed)
    Abstract [en]

    Cleavage fracture in ferritic steels is often initiated in brittle carbides randomly distributed in the material. The carbides break as a result of a fibre loading mechanism in which the stress levels in the carbides are raised, as the surrounding ferrite undergoes plastic deformation. The conditions in the vicinity of the nucleated micro-crack will then determine whether the crack will penetrate or be arrested by the ferrite. The ferrite is able to arrest nucleated cracks through the presence of mobile dislocations, which blunt and shield the microcrack and thus lowers the stresses at the crack tip. Hence, the macroscopic toughness of the material directly depends on the ability of the ferrite to arrest nucleated micro-cracks and in turn on the plastic rate sensitivity of the ferrite. The initiation of cleavage fracture is here modelled explicitly in the form of a micro-crack, which nucleates in a brittle carbide and propagates into the surrounding ferrite. The carbide is modelled as an elastic cylinder or in a few cases an elastic sphere and the ferrite as an elastic viscoplastic material. The crack growth is modelled using a cohesive surface, where the tractions are governed by a modified exponential cohesive law. It is shown that the critical stress, required to propagate a microcrack from a broken carbide, increases with decreasing plastic rate sensitivity of the ferrite. The results also show that a low stress triaxiality and a high aspect ratio of the carbide promote the initiation of cleavage fracture from a broken carbide.

  • 66.
    Kroon, Martin
    et al.
    Royal Institute of Technology, (KTH).
    Faleskog, Jonas
    Royal Institute of Technology, (KTH).
    Numerical implementation of a J2- and J3-dependent plasticity model based on a spectral decomposition of the stress deviator2013In: Computational Mechanics, ISSN 0178-7675, E-ISSN 1432-0924, Vol. 52, no 5, p. 1059-1070Article in journal (Refereed)
    Abstract [en]

    A new plasticity model with a yield criterion that depends on the second and third invariants of the stress deviator is proposed. The model is intended to bridge the gap between von Mises’ and Tresca’s yield criteria. An associative flow rule is employed. The proposed model contains one new non-dimensional key material parameter, that quantifies the relative difference in yield strength between uniaxial tension and pure shear. The yield surface is smooth and convex. Material strain hardening can be ascertained by a standard uniaxial tensile test, whereas the new material parameter can be determined by a test in pure shear. A fully implicit backward Euler method is developed and presented for the integration of stresses with a tangent operator consistent with the stress updating scheme. The stress updating method utilizes a spectral decomposition of the deviatoric stress tensor, which leads to a stable and robust updating scheme for a yield surface that exhibits strong and rapidly changing curvature in the synoptic plane. The proposed constitutive theory is implemented in a finite element program, and the influence of the new material parameter is demonstrated in two numerical examples.

  • 67.
    Kroon, Martin
    et al.
    Royal Institute of Technology.
    Faleskog, Jonas
    Royal Institute of Technology.
    Öberg, Hans
    Royal Institute of Technology.
    A probabilistic model for cleavage fracture with a length scale: parameter estimation and predictions of growing crack experiments2008In: Engineering Fracture Mechanics, ISSN 0013-7944, E-ISSN 1873-7315, Vol. 75, no 8, p. 2398-2417Article in journal (Refereed)
    Abstract [en]

    A probabilistic model for the cumulative probability of failure by cleavage fracture was applied to experimental results where cleavage fracture was preceded by ductile crack growth. The model, introduced by Kroon and Faleskog [Kroon M, Faleskog J. A probabilistic model for cleavage fracture with a length scale – influence of material parameters and constraint. Int J Fract 2002;118:99–118], includes a non-local stress with an associated material related length scale, and it also includes a strain measure to account for the number of nucleated cleavage initiation sites. The experiments were performed on single edge cracked bend test specimens with three different crack lengths at the temperature 85 °C, which is in the upper transition region for the steel in question. The ductile rupture process is modelled using the cell model for nonlinear fracture mechanics. The original cleavage fracture model had to be modified in order to account for the substantial number of cleavage initiators being consumed by the ductile process. With this modification, the model was able to accurately capture the experimental failure probability distribution.

  • 68.
    Kroon, Martin
    et al.
    Royal Institute of Technology.
    Faleskog, Jonas
    Royal Institute of Technology.
    Öberg, Hans
    Royal Institute of Technology.
    A probabilistic model for cleavage fracture with a length scale: parameter estimation and predictions of stationary crack experiments2004In: Engineering Fracture Mechanics, ISSN 0013-7944, E-ISSN 1873-7315, Vol. 71, no 1, p. 57-79Article in journal (Refereed)
    Abstract [en]

    This study presents a large experimental investigation in the transition temperature region on a modified A508 steel. Tests were carried out on single-edge-notch-bend specimens with three different crack depth over specimen width ratios to capture the strong constraint effect on fracture toughness. Three test temperatures were considered, covering a range of 85 °C. All specimens failed by cleavage fracture prior to ductile tearing. A recently proposed probabilistic model for the cumulative failure by cleavage was applied to the comprehensive sets of experimental data. This modified weakest link model incorporates a length scale, which together with a threshold stress reduce the scatter in predicted toughness distributions as well as introduces a fracture toughness threshold value. Model parameters were estimated by a robust procedure, which is crucial in applications of probabilistic models to real structures. The conformity between predicted and experimental toughness distributions, respectively, were notable at all the test temperatures.

  • 69.
    Kroon, Martin
    et al.
    Royal Institute of Technology.
    Holzapfel, Gerhard
    Graz University of Technology, Austria.
    A model for saccular cerebral aneurysm growth by collagen fibre remodelling2007In: Journal of Theoretical Biology, ISSN 0022-5193, E-ISSN 1095-8541, Vol. 247, p. 775-787Article in journal (Refereed)
    Abstract [en]

    The first structural model for saccular cerebral aneurysm growth is proposed. It is assumed that the development of the aneurysm isaccompanied by a loss of the media, and that only collagen fibres provide load-bearing capacity to the aneurysm wall. The aneurysm ismodelled as an axisymmetric multi-layered membrane, exposed to an inflation pressure. Each layer is characterized by an orientationangle, which changes between different layers. The collagen fibres and fibroblasts within a specific layer are perfectly aligned. The growthand the morphological changes of the aneurysm are accomplished by the turnover of collagen. Fibroblasts are responsible for collagenproduction, and the related deformations are assumed to govern the collagen production rate. There are four key parameters in themodel: a normalized pressure, the number of layers in the wall, an exponent in the collagen mass production rate law, and the pre-stretchunder which the collagen is deposited. The influence of the model parameters on the aneurysmal response is investigated, and a stabilityanalysis is performed. The model is able to predict clinical observations and mechanical test results, for example, in terms of predictedaneurysm size, shape, wall stress and wall thickness.

  • 70.
    Kroon, Martin
    et al.
    Royal Institute of Technology.
    Holzapfel, Gerhard
    Royal Institute of Technology ; Graz University of Technology, Austria.
    A new constitutive model for multi-layered collagenous tissues2008In: Journal of Biomechanics, ISSN 0021-9290, E-ISSN 1873-2380, Vol. 41, no 12, p. 2766-2771Article in journal (Refereed)
    Abstract [en]

    Collagenous tissues such as the aneurysmal wall or the aorta are multi-layered structures with the mean fibre alignments distinguishing one layer from another. A constitutive representation of the multiple collagen layers is not yet developed, and hence the aim of the present study. The proposed model is based on the constitutive theory of finite elasticity and is characterized by an anisotropic strain-energy function which takes the material structure into account. The passive tissue behaviour is modelled and the related mechanical response is assumed to be dominated by elastin and collagen. While elastin is modelled by the neo-Hookean material the constitutive response of collagen is assumed to be transversely isotropic for each individual layer and based on an exponential function. The proposed constitutive function is polyconvex which ensures material stability. The model has five independent material parameters, each of which has a clear physical interpretation: the initial stiffnesses of the collagen fabric in the two principal directions, the shear modulus pertaining to the non-collagenous matrix material, a parameter describing the level of nonlinearity of the collagen fabric, and the angle between the principal directions of the collagen fabric and the reference coordinate system. An extension-inflation test of the adventitia of a human femoral artery is simulated by means of the finite element method and an error function is minimized by adjusting the material parameters yielding a good agreement between the model and the experimental data.

  • 71.
    Kroon, Martin
    et al.
    Royal Institute of Technology.
    Holzapfel, Gerhard
    Graz University of Technology, Austria.
    Estimation of the distributions of the anisotropic, elastic properties and wall stresses of saccular cerebral aneurysms by inverse analysis2008In: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, E-ISSN 1471-2946, Vol. 464, no 2092, p. 807-825Article in journal (Refereed)
    Abstract [en]

    A new method is proposed for estimating the elastic properties of the inhomogeneous and anisotropic structure of saccular cerebral aneurysms by inverse analysis. The aneurysm is modelled as a membrane and the constitutive response of each individual layer of the passive tissue is characterized by a transversely isotropic strain energy function of exponential type. The collagen fibres in the aneurysm wall are assumed to govern the mechanical response. Four parameters characterize the constitutive behaviour of the tissue: two initial stiffnesses of the collagen fabric in the two in-plane principal directions, one parameter describing the degree of nonlinearity that the collagen fibres exhibit and the other structural parameter, i.e. the angle which defines the orientation of the collagen fibres. The parameter describing the fibre nonlinearity is assumed to be constant, while all others are assumed to vary continuously over the aneurysm surface. Two model aneurysms, with the same initial geometry, boundary and loading conditions, constitutive behaviour and finite-element discretization, are defined: a ‘reference model’ with known distributions of material and structural properties and an ‘estimation model’ whose properties are to be estimated. An error function is defined quantifying the deviations between the deformations from the reference and the estimation models. The error function is minimized with respect to the unknown parameters in the estimation model, and in this way the reference parameter distributions are re-established. In order to achieve a robust parameter estimation, a novel element partition method is employed. The accordance between the estimated and the reference distributions is satisfactory. The deviations of the maximum stress distributions between the two models are below 1%. Consequently, the wall stresses in the cerebral aneurysm estimated by inverse analysis are accurate enough to facilitate the assessment of the risk of aneurysm rupture.

  • 72.
    Kroon, Martin
    et al.
    Royal Institute of Technology .
    Holzapfel, Gerhard
    Royal Institute of Technology ; Graz University of Technology, Austria.
    Modelling of saccular aneurysm growth in a human middle cerebral artery2008In: Journal of Biomechanical Engineering, ISSN 0148-0731, E-ISSN 1528-8951, Vol. 130, no 5, article id 051012Article in journal (Refereed)
    Abstract [en]

    Saccular aneurysm growth in a human middle cerebral artery is modeled. The aneurysm growth model was presented in a companion paper by Kroon and Holzapfel ("A Model for Saccular Cerebral Aneurysm Growth by Collagen Fibre Remodelling," J. Theor. Biol., in press) and was assessed there for axisymmetric growth. The aneurysm growth model is now evaluated for a more realistic setting. The middle cerebral artery is modeled as a two-layered cylinder, where the layers correspond to the media and the adventitia. An instant loss of the media in a region of the artery wall initiates the growth of the saccular aneurysm. The aneurysm wall is assumed to be a development of the adventitia of the original healthy artery, and collagen is assumed to be the only load-bearing constituent in the adventitia and in the aneurysm wall. The collagen is organized in a number of distinct layers where fibers in a specific layer are perfectly aligned in a certain fiber direction. The production of new collagen is taken to depend on the stretching of the aneurysm wall, and the continuous remodeling of the collagen fibers is responsible for the aneurysm growth. The general behavior of the growth model is investigated and also the influence of the structural organization of the collagen fabric. The analysis underlines the fact that the material behavior of aneurysmal tissue cannot be expected to be isotropic. The model predictions agree well with clinical and experimental results, for example, in terms of aneurysm size and shape, wall stress levels, and wall thickness.

  • 73.
    Kroon, Martin
    et al.
    Royal Institute of Technology (KTH).
    Holzapfel, Gerhard A.
    Royal Institute of Technology (KTH) ; Graz University of Technology, Austria.
    A theoretical model for fibroblast-controlled growth of saccular cerebral aneurysms2009In: Journal of Theoretical Biology, ISSN 0022-5193, E-ISSN 1095-8541, Vol. 257, no 1, p. 73-83Article in journal (Refereed)
    Abstract [en]

    A new theoretical model for the growth of saccular cerebral aneurysms is proposed by extending the recent constitutive framework of Kroon and Holzapfel [2007a. A model for saccular cerebral aneurysm growth by collagen fibre remodelling. J. Theor. Biol. 247, 775–787]. The continuous turnover of collagen is taken to be the driving mechanism in aneurysmal growth. The collagen production rate depends on the magnitude of the cyclic deformation of fibroblasts, caused by the pulsating blood pressure during the cardiac cycle. The volume density of fibroblasts in the aneurysmal tissue is taken to be constant throughout the growth process. The growth model is assessed by considering the inflation of an axisymmetric membranous piece of aneurysmal tissue, with material characteristics representative of a cerebral aneurysm. The diastolic and systolic states of the aneurysm are computed, together with its load-free state. It turns out that the value of collagen pre-stretch, that determines growth speed and stability of the aneurysm, is of pivotal importance. The model is able to predict aneurysms with typical berry-like shapes observed clinically, and the predicted wall stresses correlate well with the experimentally obtained ultimate stresses of this type of tissue. The model predicts that aneurysms should fail when reaching a size of about 1.2–3.6 mm, which is smaller than what has been clinically observed. With some refinements, the model may, however, be used to predict future growth of diagnosed aneurysms.

  • 74.
    Kroon, Martin
    et al.
    Royal Institute of Technology (KTH).
    Holzapfel, Gerhard A.
    Royal Institute of Technology (KTH) ; Graz University of Technology, Austria.
    Elastic properties of anisotropic vascular membranes examined by inverse analysis2009In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 198, no 45-46, p. 3622-3632Article in journal (Refereed)
    Abstract [en]

    An inverse method for estimating the distributions of the nonlinear elastic properties of inhomogeneous and anisotropic vascular membranes such as cerebral aneurysms is proposed. The material description of the membrane is based on a versatile structural model able to represent multiple collagen layers and the passive response of the vascular wall. Each individual layer is assumed to behave transversely isotropic following exponential stiffening with increasing loading. The model includes four parameters to be explainable physically: two initial stiffnesses of the collagen fabric, a parameter related to the nonlinearity of the collagen fabric, angle between the principal directions of the collagen fabric and a reference coordinate system. For this finite deformation problem a finite element framework for membranous structures considering pressure boundary loading is outlined, i.e. the principle of virtual work, its linearisation and the related spatial discretisation. The estimation procedure consists of the following three steps: (i) in vivo or in vitro approaches record the mechanical responses of membranous structures whose properties are to be determined; (ii) define a corresponding finite element model; (iii) minimise an error function (regarding the unknown parameters) that quantifies the deviation of the numerical prediction from the recorded data. To achieve a robust parameter estimation, an element partition method is employed. The outcome of the procedure is affected by the number of nodes defined on the membrane surface and the number of load steps. In a numerical example, the proposed procedure is assessed by reestablishing given reference distributions in a reference membrane. The deviations of the estimated material parameter distributions from the related reference fields are within just a few percent. In most of the investigated cases the standard deviation for the resulting maximum principal stress was even below 1%, which is accurate enough for rupture risk assessment of vascular membranes.

  • 75.
    Kroon, Martin
    et al.
    Malmo University.
    Olsson, Pär
    Andreasson, Eskil
    An Anisotropic Lagrangian Plasticity Model for Semi-crystalline Polymers2017In: International Conference on Plasticity, Damage, and Fracture, Puerto Vallarta, Mexico, Jan 3-9, 2017, 2017Conference paper (Refereed)
  • 76.
    Kroon, Martin
    et al.
    Linnaeus University, Faculty of Technology, Department of Mechanical Engineering.
    Rubin, M. B.
    Technion Israel Inst Technol, Israel.
    Influence of thermal recovery on predictions of the residual mechanical state during melting and solidification2020In: Mechanics of materials (Print), ISSN 0167-6636, E-ISSN 1872-7743, Vol. 141, p. 1-12, article id 103258Article in journal (Refereed)
    Abstract [en]

    A thermomechanically consistent Eulerian plasticity model with work hardening is adopted for studying the residual mechanical state resulting from loading at elevated temperatures. The isotropic plasticity model includes the standard effect of thermal softening as well as specific modeling of thermal recovery. The model parameters and functions were calibrated to data for an austenitic stainless steel 316L. The model is applied in two numerical examples: a case of uniaxial tension and a circular disk that is exposed to a temperature load. The influence of thermal recovery is examined for each example by comparing the response of the complete model with thermal recovery to that when thermal recovery is omitted. The results of the second example indicate the importance of modeling thermal recovery for accurate prediction of residual stresses for problems dealing with melting and solidification.

  • 77.
    Murtada, Sae-Il
    et al.
    Royal Institute of Technology (KTH).
    Kroon, Martin
    Royal Institute of Technology (KTH).
    Holzapfel, Gerhard A.
    Graz University of Technology, Austria ; Royal Institute of Technology (KTH).
    A calcium-driven mechanochemical model for prediction of force generation in smooth muscle.2010In: Biomechanics and Modeling in Mechanobiology, ISSN 1617-7959, E-ISSN 1617-7940, Vol. 9, no 6, p. 749-762Article in journal (Refereed)
    Abstract [en]

    A new model for the mechanochemical response of smooth muscle is presented. The focus is on the response of the actin–myosin complex and on the related generation of force (or stress). The chemical (kinetic) model describes the cross-bridge interactions with the thin filament in which the calcium-dependent myosin phosphorylation is the only regulatory mechanism. The new mechanical model is based on Hill’s three-component model and it includes one internal state variable that describes the contraction/relaxation of the contractile units. It is characterized by a strainenergy function and an evolution law incorporating only a few material parameters with clear physical meaning. The proposed model satisfies the second law of thermodynamics. The results of the combined coupled model are broadly consistent with isometric and isotonic experiments on smooth muscle tissue. The simulations suggest that the matrix in which the actin–myosin complex is embedded does have a viscous property. It is straightforward for implementation into a finite element program in order to solve more complex boundary-value problems such as the control of short-term changes in lumen diameter of arteries due to mechanochemical signals.

  • 78.
    Murtada, Sae-Il
    et al.
    Royal Institute of Technology, (KTH).
    Kroon, Martin
    Royal Institute of Technology, (KTH).
    Holzapfel, Gerhard A.
    Graz University of Technology, Austria ; Royal Institute of Technology (KTH).
    Modeling the dispersion effects of contractile fibers in smooth muscles2010In: Journal of the mechanics and physics of solids, ISSN 0022-5096, E-ISSN 1873-4782, Vol. 58, no 12, p. 2065-2082Article in journal (Refereed)
    Abstract [en]

    Micro-structurally based models for smooth muscle contraction are crucial for a better understanding of pathological conditions such as atherosclerosis, incontinence and asthma. It is meaningful that models consider the underlying mechanical structure and the biochemical activation. Hence, a simple mechanochemical model is proposed that includes the dispersion of the orientation of smooth muscle myofilaments and that is capable to capture available experimental data on smooth muscle contraction. This allows a refined study of the effects of myofilament dispersion on the smooth muscle contraction. A classical biochemical model is used to describe the cross-bridge interactions with the thin filament in smooth muscles in which calcium-dependent myosin phosphorylation is the only regulatory mechanism. A novel mechanical model considers the dispersion of the contractile fiber orientations in smooth muscle cells by means of a strain-energy function in terms of one dispersion parameter. All model parameters have a biophysical meaning and may be estimated through comparisons with experimental data. The contraction of the middle layer of a carotid artery is studied numerically. Using a tube the relationships between the internal pressure and the stretches are investigated as functions of the dispersion parameter, which implies a strong influence of the orientation of smooth muscle myofilaments on the contraction response. It is straightforward to implement this model in a finite element code to better analyze more complex boundary-value problems.

  • 79.
    Olsson, P. A. T.
    et al.
    Malmö University.
    Kese, K.
    Studsvik Nuclear Corporation.
    Kroon, Martin
    Malmö University ; Royal Institute of Technology.
    Holston, A-M Alvarez
    Studsvik Nuclear Corporation.
    Ab initio-based fracture toughness estimates and transgranular traction-separation modelling of zirconium hydrides2015In: Modelling and Simulation in Materials Science and Engineering, ISSN 0965-0393, E-ISSN 1361-651X, Vol. 23, no 4, article id 045015Article in journal (Refereed)
    Abstract [en]

    In this work we report the results of an ab initio study of the transgranular fracture toughness and cleavage of brittle zirconium hydrides. We use the Griffith–Irwin relation to assess the fracture toughness using calculated surface energy and estimated isotropic Voigt–Reuss–Hill averages of the elastic constants. The calculated fracture toughness values are found to concur well with experimental data, which implies that fracture is dominated by cleavage failure. To investigate the cleavage energetics, we model the decohesion process. To describe the interplanar interaction we adopt Rose's universal binding energy relation, which is found to reproduce the behaviour accurately. The modelling shows that the work of fracture and ductility decreases with increasing hydrogen content.

  • 80.
    Olsson, Pär A. T.
    et al.
    Malmö University ; Lund University.
    Hyldgaard, Per
    Chalmers University of Technology.
    Schröder, Elsebeth
    Chalmers University of Technology.
    Jutemar, Elin Persson
    Tetra Pak.
    Andreasson, Eskil
    Tetra Pak ; Blekinge Institute of Technology.
    Kroon, Martin
    Linnaeus University, Faculty of Technology, Department of Mechanical Engineering.
    Ab initio investigation of monoclinic phase stability and martensitic transformation in crystalline polyethylene2018In: Physical Review Materials, E-ISSN 2475-9953, Vol. 2, no 7, article id 075602Article in journal (Refereed)
    Abstract [en]

    We study the phase stability and martensitic transformation of orthorhombic and monoclimic polyethylene by means of density functional theory using the nonempirical consistent-exchange vdW-DF-cx functional [Phys. Rev. B 89, 035412 (2014)]. The results show that the orthorhombic phase is the most stable of the two. Owing to the occurrence of soft librational phonon modes, the monoclimic phase is predicted not to be stable at zero pressure and temperature, but becomes stable when subjected to compressive transverse deformations that pin the chains and prevent them from wiggling freely. This theoretical characterization, or prediction, is consistent with the fact that the monoclimic phase is only observed experimentally when the material is subjected to mechanical loading. Also, the estimated threshold energy for the combination of lattice deformation associated with the T1 and T2 transformation paths (between the orthorhombic and monoclimic phases) and chain shuffling is found to be sufficiently low for thermally activated back transformations to occur. Thus, our prediction is that the crystalline part can transform back from the monoclimc to the orthorhombic phase upon unloading and/or annealing, which is consistent with experimental observations. Finally, we observe how a combination of such phase transformations can lead to a fold-plane reorientation from {110} to {100} type in a single orthorhombic crystal.

  • 81.
    Olsson, Pär A. T.
    et al.
    Malmö University;Lund University.
    in't Veld, Pieter J.
    BASF SE, Germany.
    Andreasson, Eskil
    Tetra Pak, Lund.
    Bergvall, Erik
    Tetra Pak, Lund;Blekinge Institute of Technology.
    Jutemar, Elin Persson
    Tetra Pak, Lund.
    Petersson, Viktor
    Tetra Pak, Lund.
    Rutledge, Gregory C.
    MIT, USA.
    Kroon, Martin
    Linnaeus University, Faculty of Technology, Department of Mechanical Engineering.
    All-atomic and coarse-grained molecular dynamics investigation of deformation in semi-crystalline lamellar polyethylene2018In: Polymer, ISSN 0032-3861, E-ISSN 1873-2291, Vol. 153, p. 305-316Article in journal (Refereed)
    Abstract [en]

    In the present work we have performed classical molecular dynamics modelling to investigate the effects of different types of force-fields on the stress-strain and yielding behaviours in semi-crystalline lamellar stacked linear polyethylene. To this end, specifically the all-atomic optimized potential for liquid simulations (OPLS-AA) and the coarse-grained united-atom (UA) force-fields are used to simulate the yielding and tensile behaviour for the lamellar separation mode. Despite that the considered samples and their topologies are identical for both approaches, the results show that they predict widely different stress-strain and yielding behaviours. For all UA simulations we obtain oscillating stress-strain curves accompanied by repetitive chain transport to the amorphous region, along with substantial chain slip and crystal reorientation. For the OPLS-AA modelling primarily cavitation formation is observed, with small amounts of chain slip to reorient the crystal such that the chains align in the tensile direction. This force-field dependence is rooted in the lack of explicit H-H and C-H repulsion in the UA approach, which gives rise to underestimated ideal critical resolved shear stress. The computed critical resolved shear stress for the OPLS-AA approach is in good agreement with density functional theory calculations and the yielding mechanisms resemble those of the lamellar separation mode. The disparate energy and shear stress barriers for chain slip of the different models can be interpreted as differently predicted intrinsic activation rates for the mechanism, which ultimately are responsible for the observed diverse responses of the two modelling approaches.

  • 82.
    Olsson, Pär A. T.
    et al.
    Malmö University, Sweden.
    Schroder, Elsebeth
    Chalmers University of Technology, Sweden.
    Hyldgaard, Per
    Malmö University, Sweden;Chalmers University of Technology, Sweden.
    Kroon, Martin
    Linnaeus University, Faculty of Technology, Department of Mechanical Engineering.
    Andreasson, Eskil
    Tetra Pak, Sweden;Blekinge Institute of Technology, Sweden.
    Bergvall, Erik
    Tetra Pak, Sweden.
    Ab initio and classical atomistic modelling of structure and defects in crystalline orthorhombic polyethylene: Twin boundaries, slip interfaces, and nature of barriers2017In: Polymer, ISSN 0032-3861, E-ISSN 1873-2291, Vol. 121, p. 234-246Article in journal (Refereed)
    Abstract [en]

    We study the stability of twin boundaries and slip in crystalline orthorhombic polyethylene by means of density functional theory (DFT), using a nonempirical, truly nonlocal density function, and by means of classical molecular dynamics (MD). The results show that, in accordance with experimental observations, there is a clear preference to chain slip over transverse slip for all considered slip planes. The activation energy for pure chain slip lies in the range 10-20 mJ/m(2) while that for transverse slip corresponds to 40-280 mJ/m(2). For the (110)-slip plane the energy landscape is non-convex with multiple potential energy minima, indicating the presence of stable stacking faults. This suggests that dissociation of perfect dislocations into partials may occur. For the two low-energy twin boundaries considered in this work, {110} and {310}, we find that the former is more stable than the latter, with ground state energies corresponding to 8.9 and 28 mJ/m2, respectively. We have also evaluated how well the empirical MD simulations with the all-atom optimized potential for liquid MD simulations (OPLS-AA) and the coarsegrained united atom (UA) potential concur with the DFT results. It is found that an all-atom potential is necessary to partially capture the gamma-surface energy landscapes obtained from the DFT calculations. The OPLS-AA predicts chain slip activation energies comparable with DFT data, while the transverse slip energy thresholds are low in comparison, which is attributed to weak close ranged monomer repulsion. Finally, we find that the H-H interaction dominates the slip activation. While not explicitly represented in the UA potential, its key role is revealed by correlating the DFT energy landscape with changes in the electron distributions and by MD simulations in which components of the OPLS-AA intermolecular potential are selectively silenced. (C) 2017 Elsevier Ltd. All rights reserved.

  • 83.
    Olsson, Pär A.T.
    et al.
    Malmö University.
    Mrovec, Matous
    b Fraunhofer Institute for Mechanics of Materials (IWM), Germany ; Karlsruhe Institute of Technology, Germany .
    Kroon, Martin
    Linnaeus University, Faculty of Technology, Department of Mechanical Engineering. Malmö University ; Royal Institute of Technology, (KTH).
    First principles characterisation of brittle transgranular fracture of titanium hydrides2016In: Acta Materialia, ISSN 1359-6454, E-ISSN 1873-2453, Vol. 118, p. 362-373Article in journal (Refereed)
    Abstract [en]

    In this work we have studied transgranular cleavage and the fracture toughness of titanium hydrides by means of quantum mechanical calculations based on density functional theory. The calculations show that the surface energy decreases and the unstable stacking fault energy increases with increasing hydrogen content. This is consistent with experimental findings of brittle behaviour of titanium hydrides at low temperatures. Based on Griffith-Irwin theory we estimate the fracture toughness of the hydrides to be of the order of 1 MPa⋅m1/2, which concurs well with experimental data. To investigate the cleavage energetics, we analyse the decohesion at various crystallographic planes and determine the traction-separation laws based on the Rose's extended universal binding energy relation. The calculations predict that the peak stresses do not depend on the hydrogen content of the phases, but it is rather dependent on the crystallographic cleavage direction. However, it is found that the work of fracture decreases with increasing hydrogen content, which is an indication of hydrogen induced bond weakening in the material.

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