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Dynamic finite element implementation of nonlinear, anisotropic hyperelastic biological membranes.

Abstract

We present a novel method for the implementation of hyperelastic finite strain, non-linear strain-energy functions for biological membranes in an explicit finite element environment. The technique is implemented in LS-DYNA but may also be implemented in any suitable non-linear explicit code. The constitutive equations are implemented on the foundation of a co-rotational uniformly reduced Hughes-Liu shell. This shell is based on an updated-Lagrangian formulation suitable for relating Cauchy stress to the rate-of-deformation, i.e. hypo-elasticity. To accommodate finite deformation hyper-elastic formulations, a co-rotational deformation gradient is assembled over time, resulting in a formulation suitable for pseudo-hyperelastic constitutive equations that are standard assumptions in biomechanics. Our method was validated by comparison with (1) an analytic solution to a spherically-symmetric dynamic membrane inflation problem, incorporating a Mooney-Rivlin hyperelastic equation and (2) with previously published finite element solutions to a non-linear transversely isotropic inflation problem. Finally, we implemented a transversely isotropic strain-energy function for mitral valve tissue. The method is simple and accurate and is believed to be generally useful for anyone who wishes to model biologic membranes with an experimentally driven strain-energy function.

Authors+Show Affiliations

Department of Bioengineering, University of Washington, Seattle, WA, USA.No affiliation info availableNo affiliation info availableNo affiliation info availableNo affiliation info available

Pub Type(s)

Comparative Study
Evaluation Studies
Journal Article
Validation Studies

Language

eng

PubMed ID

12623436

Citation

Einstein, D R., et al. "Dynamic Finite Element Implementation of Nonlinear, Anisotropic Hyperelastic Biological Membranes." Computer Methods in Biomechanics and Biomedical Engineering, vol. 6, no. 1, 2003, pp. 33-44.
Einstein DR, Reinhall P, Nicosia M, et al. Dynamic finite element implementation of nonlinear, anisotropic hyperelastic biological membranes. Comput Methods Biomech Biomed Engin. 2003;6(1):33-44.
Einstein, D. R., Reinhall, P., Nicosia, M., Cochran, R. P., & Kunzelman, K. (2003). Dynamic finite element implementation of nonlinear, anisotropic hyperelastic biological membranes. Computer Methods in Biomechanics and Biomedical Engineering, 6(1), pp. 33-44.
Einstein DR, et al. Dynamic Finite Element Implementation of Nonlinear, Anisotropic Hyperelastic Biological Membranes. Comput Methods Biomech Biomed Engin. 2003;6(1):33-44. PubMed PMID: 12623436.
* Article titles in AMA citation format should be in sentence-case
TY - JOUR T1 - Dynamic finite element implementation of nonlinear, anisotropic hyperelastic biological membranes. AU - Einstein,D R, AU - Reinhall,P, AU - Nicosia,M, AU - Cochran,R P, AU - Kunzelman,K, PY - 2003/3/8/pubmed PY - 2003/9/27/medline PY - 2003/3/8/entrez SP - 33 EP - 44 JF - Computer methods in biomechanics and biomedical engineering JO - Comput Methods Biomech Biomed Engin VL - 6 IS - 1 N2 - We present a novel method for the implementation of hyperelastic finite strain, non-linear strain-energy functions for biological membranes in an explicit finite element environment. The technique is implemented in LS-DYNA but may also be implemented in any suitable non-linear explicit code. The constitutive equations are implemented on the foundation of a co-rotational uniformly reduced Hughes-Liu shell. This shell is based on an updated-Lagrangian formulation suitable for relating Cauchy stress to the rate-of-deformation, i.e. hypo-elasticity. To accommodate finite deformation hyper-elastic formulations, a co-rotational deformation gradient is assembled over time, resulting in a formulation suitable for pseudo-hyperelastic constitutive equations that are standard assumptions in biomechanics. Our method was validated by comparison with (1) an analytic solution to a spherically-symmetric dynamic membrane inflation problem, incorporating a Mooney-Rivlin hyperelastic equation and (2) with previously published finite element solutions to a non-linear transversely isotropic inflation problem. Finally, we implemented a transversely isotropic strain-energy function for mitral valve tissue. The method is simple and accurate and is believed to be generally useful for anyone who wishes to model biologic membranes with an experimentally driven strain-energy function. SN - 1025-5842 UR - https://www.unboundmedicine.com/medline/citation/12623436/Dynamic_finite_element_implementation_of_nonlinear_anisotropic_hyperelastic_biological_membranes_ L2 - http://www.tandfonline.com/doi/full/10.1080/1025584021000048983 DB - PRIME DP - Unbound Medicine ER -