Numerical stability enhancement of modeling hyperelastic materials. Duong, M., T., Nguyen, N., H., & Staat, M. In Eberhardsteiner, J., Böhm, H., J., & Rammerstorfer, F., G., editors, Proceedings European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012) Vienna, Austria, September 10-14, 2012, pages 4794-4808, 9, 2012.
Numerical stability enhancement of modeling hyperelastic materials [link]Website  abstract   bibtex   
Besides the capability of representing the material behavior of biological soft tissue accurately, constitutive equations must also ensure numerical stability in simulations. Biomechanical models of composite materials, such as arteries, ureter, intestine, etc., which combine an isotropic term and an anisotropic term, may generally show Strongly Directional Behavior (SDB). This can lead to unphysical response in numerical simulation known as “fibre rotation”. However, based on mathematical reasoning and numerical analysis, a plausible argument proves that this unrealistic behavior is due to a large difference between the isotropic strain energy and the anisotropic strain energy, resulting in an ill-conditioned constitutive matrix. Furthermore, this paper shows that the SDB dominating over the isotropic behavior can, in general, cause unphysical responses along non-fibrous directions, which was proven for a Transversely Isotropic Model (TIM). Different from the solution developed in literature, this paper proposes a model implemented in a finite element program which can solve or alleviate the instability problem at large strains regardless of determining the histological structure of tissue. The proposed material model comprising a new strain energy component can mitigate some restrictions of mechanical response of the model in the literature. Though it was mathematically formulated for dealing with the numerical problem, however, good performance is still achieved. Pure shear, biaxial tests, and additional tension tests were carried out to validate the proposed formulation and analyze comprehensively the numerical problems. The numerical results show reasonable stability and convergence of the proposed model and its significant effect on the mechanical behavior at larger strains as well as its capability of modeling soft tissue.
@inproceedings{
 title = {Numerical stability enhancement of modeling hyperelastic materials},
 type = {inproceedings},
 year = {2012},
 keywords = {Holzapfel model,hyperelastic model,numerical instability,strongly directional behavior},
 pages = {4794-4808},
 websites = {https://www.scopus.com/record/display.uri?eid=2-s2.0-84871639018&origin=inward&txGid=3242fda8b10367fbcb86133a8618d38f},
 month = {9},
 institution = {European Community on Computational Methods in Applied Sciences (ECCOMAS)},
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 abstract = {Besides the capability of representing the material behavior of biological soft tissue accurately, constitutive equations must also ensure numerical stability in simulations. Biomechanical models of composite materials, such as arteries, ureter, intestine, etc., which combine an isotropic term and an anisotropic term, may generally show Strongly Directional Behavior (SDB). This can lead to unphysical response in numerical simulation known as “fibre rotation”. However, based on mathematical reasoning and numerical analysis, a plausible argument proves that this unrealistic behavior is due to a large difference between the isotropic strain energy and the anisotropic strain energy, resulting in an ill-conditioned constitutive matrix. Furthermore, this paper shows that the SDB dominating over the isotropic behavior can, in general, cause unphysical responses along non-fibrous directions, which was proven for a Transversely Isotropic Model (TIM). Different from the solution developed in literature, this paper proposes a model implemented in a finite element program which can solve or alleviate the instability problem at large strains regardless of determining the histological structure of tissue. The proposed material model comprising a new strain energy component can mitigate some restrictions of mechanical response of the model in the literature. Though it was mathematically formulated for dealing with the numerical problem, however, good performance is still achieved. Pure shear, biaxial tests, and additional tension tests were carried out to validate the proposed formulation and analyze comprehensively the numerical problems. The numerical results show reasonable stability and convergence of the proposed model and its significant effect on the mechanical behavior at larger strains as well as its capability of modeling soft tissue.},
 bibtype = {inproceedings},
 author = {Duong, M T and Nguyen, N H and Staat, Manfred},
 editor = {Eberhardsteiner, Josef and Böhm, Helmut J. and Rammerstorfer, Franz G.},
 booktitle = {Proceedings European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012) Vienna, Austria, September 10-14, 2012}
}

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