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Kroon, Martin, Professor
Publications (10 of 104) Show all publications
Stoltz, B., Lindvall, M. & Kroon, M. (2024). A modified neo-Hookean model for semi-crystalline thermoplastics assessed by relaxation and zero-stress creep tests of recycled polypropylene and polyoxymethylene. Mechanics of time-dependant materials, 28, 43-63
Open this publication in new window or tab >>A modified neo-Hookean model for semi-crystalline thermoplastics assessed by relaxation and zero-stress creep tests of recycled polypropylene and polyoxymethylene
2024 (English)In: Mechanics of time-dependant materials, ISSN 1385-2000, E-ISSN 1573-2738, Vol. 28, p. 43-63Article in journal (Refereed) Published
Abstract [en]

The mechanical behavior of thermoplastics is strongly rate-dependent, and oftentimes it is difficult to find constitutive models that can accurately describe their behavior in the small to moderate strain regime. In this paper, a hyperelastic network model (modified neo-Hookean) and a set of experiments are presented. The testing consists of monotonic tensile loading as well as stress relaxation and zero stress creep. Two materials were tested, polyoxymethylene (POM) and recycled polypropylene (rPP), representing one more rigid and brittle and one softer and more ductile semi-crystalline polymer. The model contains two main novelties. The first novelty is that the stiffness is allowed to vary with the elastic deformation (in contrast to a standard neo-Hookean model). The second novelty is that the exponent governing viscous relaxation is allowed to vary with the viscous deformation. The basic features of the new model are illustrated, and the model was fitted to the experimental data. The model proved to be able to describe the experimental results well.

Place, publisher, year, edition, pages
Springer, 2024
Keywords
Recycled polypropylene, Polyoxymethylene, Relaxation, Network model, Viscoelasticity, Viscoplasticity
National Category
Applied Mechanics
Research subject
Technology (byts ev till Engineering), Mechanical Engineering
Identifiers
urn:nbn:se:lnu:diva-124637 (URN)10.1007/s11043-023-09631-x (DOI)001058321300002 ()2-s2.0-85169843576 (Scopus ID)
Available from: 2023-09-15 Created: 2023-09-15 Last updated: 2024-04-03Bibliographically approved
Kroon, M., Gortz, J., Islam, S., Andreasson, E., Petersson, V. & Jutemar, E. P. (2024). Experimental and theoretical study of stress relaxation in high-density polyethylene. Acta Mechanica
Open this publication in new window or tab >>Experimental and theoretical study of stress relaxation in high-density polyethylene
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2024 (English)In: Acta Mechanica, ISSN 0001-5970, E-ISSN 1619-6937Article in journal (Refereed) Epub ahead of print
Abstract [en]

Stress relaxation of high-density polyethylene is addressed both experimentally and theoretically. Two types of stress relaxation testing are carried out: uniaxial tensile testing at constant test specimen length and compression testing of a 3D structure producing inhomogeneous deformation fields and relaxation. A constitutive model for isotropic, semi-crystalline polymers is also proposed. The model has the ability to model stress relaxation at different time scales. The developed model was implemented as a user subroutine in Abaqus (UMAT). The implicit integration scheme including an algorithmic tangent modulus is described in detail. The material model is calibrated by use of the uniaxial tensile tests, and the model is then validated by simulating the compression tests of the 3D structure. The model is able to describe the uniaxial tension tests well, and the comparison between the simulations and experimental testing of the 3D structure shows very good agreement.

Place, publisher, year, edition, pages
Springer, 2024
National Category
Textile, Rubber and Polymeric Materials
Research subject
Technology (byts ev till Engineering), Mechanical Engineering
Identifiers
urn:nbn:se:lnu:diva-127674 (URN)10.1007/s00707-024-03851-z (DOI)001149549300001 ()2-s2.0-85183408279 (Scopus ID)
Available from: 2024-02-14 Created: 2024-02-14 Last updated: 2024-03-15
Kroon, M., Andreasson, E., Petersson, V. & Jutemar Persson, E. (2024). Numerical and experimental analysis of inelastic and rate-dependent buckling of thin injection-moulded high-density polyethylene structure. International Journal of Solids and Structures, 290, Article ID 112673.
Open this publication in new window or tab >>Numerical and experimental analysis of inelastic and rate-dependent buckling of thin injection-moulded high-density polyethylene structure
2024 (English)In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 290, article id 112673Article in journal (Refereed) Published
Abstract [en]

Semi-crystalline polymers is an important group of materials that is used in a vast array of products. In this study, the rate-dependent properties of high-density polyethylene (HDPE) are investigated, both experimentally and theoretically. Experimental compression testing of a three-dimensional HDPE structure is performed and analysed numerically by use of the finite element method. In addition, an Eulerian constitutive material model for isotropic, semi-crystalline polymers is proposed. The model is able to account for such essential phenomena as strain-rate dependence, work hardening, pressure-dependence of inelastic deformations, and damage. The proposed material model was implemented in Abaqus as a VUMAT, which is an explicit implementation. The material model was calibrated by use of uniaxial tensile tests performed on HDPE dog-bone shaped samples, and the model was further explored by applying the VUMAT implementation to the compression tests of the HDPE structure. The simulation model was able to reproduce the experimental results well, both the uniaxial tests and the compression tests. In particular, the friction present in the compression tests seems to play an important role in determining the buckling mode of the structure.

Place, publisher, year, edition, pages
Elsevier, 2024
National Category
Mechanical Engineering
Research subject
Technology (byts ev till Engineering), Mechanical Engineering
Identifiers
urn:nbn:se:lnu:diva-127834 (URN)10.1016/j.ijsolstr.2024.112673 (DOI)001169812900001 ()2-s2.0-85183577353 (Scopus ID)
Available from: 2024-02-18 Created: 2024-02-18 Last updated: 2024-03-26Bibliographically approved
Kroon, M. & Rubin, M. B. (2023). An Eulerian constitutive model for the inelastic finite strain behaviour of isotropic semi-crystalline polymers. European journal of mechanics. A, Solids, 100, Article ID 105004.
Open this publication in new window or tab >>An Eulerian constitutive model for the inelastic finite strain behaviour of isotropic semi-crystalline polymers
2023 (English)In: European journal of mechanics. A, Solids, ISSN 0997-7538, E-ISSN 1873-7285, Vol. 100, article id 105004Article in journal (Refereed) Published
Abstract [en]

A constitutive model for isotropic, semi-crystalline polymers is proposed. The model is Eulerian in the sense that it is independent of measures of total deformation and plastic/inelastic deformations. It is able to account for such essential phenomena as strain-rate dependence, work hardening, stress relaxation, volumetric inelastic deformations, and damage. The model was applied to uniaxial tension tests performed on polyoxymethylene (POM), which is a semi-crystalline polymer widely used in the industry. Three types of tests were conducted: monotonic tests at different strain rates, stress relaxation tests, and loading-unloading tests. The model was able to reproduce the experimental results well. The proposed model was also implemented as a VUMAT in Abaqus, and the deformation of a 3D geometry was simulated.

Place, publisher, year, edition, pages
Elsevier, 2023
National Category
Mechanical Engineering
Research subject
Technology (byts ev till Engineering), Mechanical Engineering
Identifiers
urn:nbn:se:lnu:diva-120432 (URN)10.1016/j.euromechsol.2023.105004 (DOI)001054242800001 ()2-s2.0-85153211620 (Scopus ID)
Available from: 2023-04-25 Created: 2023-04-25 Last updated: 2023-09-07Bibliographically approved
Kroon, M. (2023). An Eulerian formulation of orthotropic elasticity and inelasticity. In: International Conference on Plasticity, Damage, and Fracture, January 3-9, 2023: Barcelo Bavaro Punta Cana, Dominican Republic. Paper presented at International Conference on Plasticity, Damage, and Fracture, January 3-9, 2023, Barcelo Bavaro Punta Cana, Dominican Republic.
Open this publication in new window or tab >>An Eulerian formulation of orthotropic elasticity and inelasticity
2023 (English)In: International Conference on Plasticity, Damage, and Fracture, January 3-9, 2023: Barcelo Bavaro Punta Cana, Dominican Republic, 2023Conference paper, Oral presentation with published abstract (Refereed)
National Category
Applied Mechanics
Research subject
Technology (byts ev till Engineering), Mechanical Engineering
Identifiers
urn:nbn:se:lnu:diva-120070 (URN)
Conference
International Conference on Plasticity, Damage, and Fracture, January 3-9, 2023, Barcelo Bavaro Punta Cana, Dominican Republic
Note

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Available from: 2023-04-03 Created: 2023-04-03 Last updated: 2023-05-10Bibliographically approved
Kroon, M. & Rubin, M. (2023). Modelling Large Inelastic Dilatational and Distortional Deformations in Semi-crystalline Polymers Using an Eulerian Framework. In: USNCCM17: Book of Abstracts. Paper presented at 17th U. S. National Congress on Computational Mechanics, Albuquerque, New Mexico, July 23-27, 2023. USACM
Open this publication in new window or tab >>Modelling Large Inelastic Dilatational and Distortional Deformations in Semi-crystalline Polymers Using an Eulerian Framework
2023 (English)In: USNCCM17: Book of Abstracts, USACM , 2023Conference paper, Oral presentation with published abstract (Refereed)
Abstract [en]

A constitutive model for isotropic, semi-crystalline polymers is proposed. The model is Eulerian in the sense that it is independent of measures of total deformation, plastic/inelastic deformations, and all state variables are defined in the current state of the material. The deformation state of the material is represented by a unimodular tensor, characterizing elastic distortional deformation, and an elastic dilatation. The model is able to account for such essential phenomena as strain-rate dependence, work hardening, stress relaxation, volumetric inelastic deformations, and damage. Uniaxial tension tests were performed on polyoxymethylene (POM), which is a semi-crystalline polymer widely used in the industry. Three types of tests were conducted: monotonic loading tests at different strain rates, stress relaxation tests, and loading-unloading tests. These tests produced large elastic and inelastic deformations which were reproduced well by the model. The model was also implemented as a VUMAT in Abaqus, and the deformation of a 3D geometry was simulated. Specifically, a simple structure of the POM material was deformed and then unloaded. Thenresulting elastic spring-back and residual stress state was investigated. 

Place, publisher, year, edition, pages
USACM, 2023
National Category
Mechanical Engineering
Research subject
Technology (byts ev till Engineering), Mechanical Engineering
Identifiers
urn:nbn:se:lnu:diva-127835 (URN)
Conference
17th U. S. National Congress on Computational Mechanics, Albuquerque, New Mexico, July 23-27, 2023
Available from: 2024-02-18 Created: 2024-02-18 Last updated: 2024-02-20Bibliographically approved
Kroon, M. & Rubin, M. (2023). Modelling of rate-dependent and volumetric inelasticity of semi-crystalline polymers using an Eulerian framework. In: 17th International Conference on Computational Plasticity (COMPLAS 2023), Barcelona, Spain, September 2023: . Paper presented at 17th International Conference on Computational Plasticity (COMPLAS 2023), Barcelona, Spain, September 2023. International Center for Numerical Methods in Engineering (CIMNE)
Open this publication in new window or tab >>Modelling of rate-dependent and volumetric inelasticity of semi-crystalline polymers using an Eulerian framework
2023 (English)In: 17th International Conference on Computational Plasticity (COMPLAS 2023), Barcelona, Spain, September 2023, International Center for Numerical Methods in Engineering (CIMNE), 2023Conference paper, Oral presentation with published abstract (Refereed)
Abstract [en]

A constitutive model for isotropic, semi-crystalline polymers is proposed. The model is Eulerian in the sense that it is independent of measures of total deformation and plastic/inelastic deformations. Hence, all state variables are defined in the current state of the material. It is able to account for such essential phenomena as strain-rate dependence, work hardening, stress relaxation, volumetric inelastic deformations, and damage. The model includes 15 model parameters and was applied to uniaxial tension tests performed on polyoxymethylene (POM), which is a semi-crystalline polymer widely used in the industry. Three types of tests were conducted: monotonic tests at different strain rates, stress relaxation tests, and loading-unloading tests. The model was able to reproduce the experimental results well. The proposed model was also implemented as a VUMAT in Abaqus. The deformation of a 3D geometry was simulated. The 3D geometry consisted of a “tooth” that was deformed by a rigid block, causing permanent deformation and spring-back of the tooth. The elastic spring-back and relaxation of the tooth is demonstrated and also the residual state in the tooth after the inelastic deformation.

Place, publisher, year, edition, pages
International Center for Numerical Methods in Engineering (CIMNE), 2023
National Category
Mechanical Engineering
Research subject
Technology (byts ev till Engineering), Mechanical Engineering
Identifiers
urn:nbn:se:lnu:diva-127837 (URN)
Conference
17th International Conference on Computational Plasticity (COMPLAS 2023), Barcelona, Spain, September 2023
Available from: 2024-02-18 Created: 2024-02-18 Last updated: 2024-02-20Bibliographically approved
Abelen, A. & Kroon, M. (2023). Modelling of rate-dependent inelasticity and damage in semi-crystalline polymers using an Eulerian framework. International Journal of Engineering Science, 193, Article ID 103945.
Open this publication in new window or tab >>Modelling of rate-dependent inelasticity and damage in semi-crystalline polymers using an Eulerian framework
2023 (English)In: International Journal of Engineering Science, ISSN 0020-7225, E-ISSN 1879-2197, Vol. 193, article id 103945Article in journal (Refereed) Published
Abstract [en]

The present paper concerns the mechanical response of semi-crystalline polymers during cyclic loading, and it includes both modelling and experimental testing. The model is Eulerian in the sense that it is independent of measures of total deformation and plastic/inelastic deformations. It is able to account for such essential phenomena as strain-rate dependence, work hardening, and damage. The model was applied to uniaxial tension tests performed on high-density polyethylene (HDPE), which is a semi-crystalline polymer widely used in the industry. Two types of tests were conducted: monotonic tests, and loading-unloading tests. The model was able to reproduce the experimental results very well. The proposed model was also implemented as a UMAT in Abaqus, including an analytic tangent. The UMAT was used for simulating two 3D geometries. The implementation seems to be robust, and no convergence problems were observed.

Place, publisher, year, edition, pages
Elsevier, 2023
Keywords
Semi-crystalline, HDPE, Eulerian, Damage, Viscoplasticity, Viscoelasticity, Implicit
National Category
Applied Mechanics
Research subject
Technology (byts ev till Engineering), Mechanical Engineering
Identifiers
urn:nbn:se:lnu:diva-125191 (URN)10.1016/j.ijengsci.2023.103945 (DOI)001072628300001 ()2-s2.0-85169977087 (Scopus ID)
Available from: 2023-10-20 Created: 2023-10-20 Last updated: 2023-11-07Bibliographically approved
Kroon, M. & Rubin, M. (2023). Regularization of damage and failure using a non-local hardening variable in an Eulerian formulation of inelasticity. In: 15th International Conference on Fracture (ICF15)June 11-16, 2023 Atlanta, GA USA: . Paper presented at 15th International Conference on Fracture (ICF15) June 11-16, 2023 Atlanta, GA USA.
Open this publication in new window or tab >>Regularization of damage and failure using a non-local hardening variable in an Eulerian formulation of inelasticity
2023 (English)In: 15th International Conference on Fracture (ICF15)June 11-16, 2023 Atlanta, GA USA, 2023Conference paper, Oral presentation with published abstract (Refereed)
Abstract [en]

It is known that damage or inelastic softening can cause an ill-posed problem leading to localization and mesh-dependence in finite element simulations. Here, a nonlocal hardening variable is introduced in a finite deformation Eulerian formulation of inelasticity. This nonlocal variable is defined over an Eulerian region of nonlocality, which is a sphere with radius equal to a characteristic length, defined in the current deformed geometry of the material. The influence of the nonlocal hardening variable is studied using an example of a plate that is loaded by a prescribed boundary displacement causing formation of a shear band. Predictions of the applied load vs. displacement curves and contour plots of the total distortional deformation of the plate and the hardening variable are studied. It is shown that the characteristic material length controls the structure of the shear band developed in the plate.

National Category
Mechanical Engineering
Research subject
Technology (byts ev till Engineering), Mechanical Engineering
Identifiers
urn:nbn:se:lnu:diva-127836 (URN)
Conference
15th International Conference on Fracture (ICF15) June 11-16, 2023 Atlanta, GA USA
Available from: 2024-02-18 Created: 2024-02-18 Last updated: 2024-02-20Bibliographically approved
Kroon, M. & Rubin, M. B. (2022). An Eulerian model for orthotropic elasticity and inelasticity applied to injection-moulded low-density polyethylene. Mechanics of materials, 167, Article ID 104239.
Open this publication in new window or tab >>An Eulerian model for orthotropic elasticity and inelasticity applied to injection-moulded low-density polyethylene
2022 (English)In: Mechanics of materials, ISSN 0167-6636, E-ISSN 1872-7743, Vol. 167, article id 104239Article in journal (Refereed) Published
Abstract [en]

Anisotropic elasticity and inelasticity is of relevance in many practical applications. The Eulerian formulation for anisotropic elastic and inelastic response based on microstructural vectors is used here to model an injection-moulded low-density polyethylene. In contrast with Lagrangian models of inelasticity, the Eulerian formulation is insensitive to arbitrariness of the reference and intermediate configurations as well as to measures of total and inelastic deformations. A specific strain-space-type anisotropic yield function is proposed that depends on anisotropic measures of elastic deformation and anisotropic hardening variables. Use is also made of a rate-independent model with a smooth elastic-inelastic transition. The material parameters were calibrated to reproduce uniaxial test data for loading in three directions in the moulding plane. In addition, a strongly objective numerical implementation is presented and used to simulate stretching of a plate with a circular hole. In contrast with metals, this polyethylene experiences elastic deformations of about 10%. Although the inelastic spin rate could not be determined by the available test data, simulations of loadings in different material directions yield observable influences of inelastic spin rate.

Place, publisher, year, edition, pages
Elsevier, 2022
Keywords
Anisotropic, Orthotropic, Plasticity, Polyethylene, Plastic spin
National Category
Applied Mechanics
Research subject
Technology (byts ev till Engineering), Mechanical Engineering
Identifiers
urn:nbn:se:lnu:diva-110867 (URN)10.1016/j.mechmat.2022.104239 (DOI)000761008300004 ()2-s2.0-85124463943 (Scopus ID)2022 (Local ID)2022 (Archive number)2022 (OAI)
Available from: 2022-03-18 Created: 2022-03-18 Last updated: 2024-01-17Bibliographically approved
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