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  • 1.
    Kroon, Martin
    Royal Institute of Technology (KTH).
    A continuum mechanics framework and a constitutive model for remodelling of collagen gels and collagenous tissues2010In: Journal of the mechanics and physics of solids, ISSN 0022-5096, E-ISSN 1873-4782, Vol. 58, no 6, p. 918-933Article in journal (Refereed)
    Abstract [en]

    Collagen is a very important protein of the human body and is responsible for the structural stability of many body components. Furthermore, collagen fibre networks are able to grow and remodel themselves, which enables them to adjust to varying physiological conditions. This remodelling is accomplished by fibre-producing cells, such as fibroblasts. The ability to adjust to new physiological conditions is very important, for example in wound healing. In the present paper, a theoretical framework for modelling collagenous tissues and collagen gels is proposed. Continuum mechanics is employed to describe the kinematics of the collagen, and affine deformations of fibres are assumed. Biological soft tissues can be approximated as being hyperelastic, and the constitutive model for the collagen fabric is therefore formulated in terms of a strain energy function. This strain energy function includes a density function that describes the distribution of the collagen fibre orientation. The density function evolves according to an evolution law, where fibres tend to reorient towards the direction of maximum Cauchy stress. The remodelling of the collagen network is also assumed to include a pre-stretching of collagen fibres, accomplished by fibroblasts. The theoretical framework is applied to experiments performed on collagen gels, where gels were exposed to remodelling under both biaxial and uniaxial constraints. The proposed model was able to predict both the resulting collagen distribution and the resulting stress–strain relationships obtained for the remodelled collagen gels. The influence of the most important model parameters is demonstrated, and it appears that there is a fairly unique set of model parameters that gives an optimal fit to the experimental data.

  • 2.
    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.

  • 3.
    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.

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