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A penetration-based finite element method for hyperelastic 3D biphasic tissues in contact. Part II: finite element simulations.
J Biomech Eng. 2006 Dec; 128(6):934-42.JB

Abstract

The penetration method allows for the efficient finite element simulation of contact between soft hydrated biphasic tissues in diarthrodial joints. Efficiency of the method is achieved by separating the intrinsically nonlinear contact problem into a pair of linked biphasic finite element analyses, in which an approximate, spatially and temporally varying contact traction is applied to each of the contacting tissues. In Part I of this study, we extended the penetration method to contact involving nonlinear biphasic tissue layers, and demonstrated how to derive the approximate contact traction boundary conditions. The traction derivation involves time and space dependent natural boundary conditions, and requires special numerical treatment. This paper (Part II) describes how we obtain an efficient nonlinear finite element procedure to solve for the biphasic response of the individual contacting layers. In particular, alternate linearization of the nonlinear weak form, as well as both velocity-pressure, v-p, and displacement-pressure, u-p, mixed formulations are considered. We conclude that the u-p approach, with linearization of both the material law and the deformation gradients, performs best for the problem at hand. The nonlinear biphasic contact solution will be demonstrated for the motion of the glenohumeral joint of the human shoulder joint.

Authors+Show Affiliations

Department of Biomedical Engineering and Scientific Computation Research Center, Rensselaer Polytechnic Institute, Troy, NY 12180-3590, USA.No affiliation info available

Pub Type(s)

Journal Article

Language

eng

PubMed ID

17154696

Citation

Un, Kerem, and Robert L. Spilker. "A Penetration-based Finite Element Method for Hyperelastic 3D Biphasic Tissues in Contact. Part II: Finite Element Simulations." Journal of Biomechanical Engineering, vol. 128, no. 6, 2006, pp. 934-42.
Un K, Spilker RL. A penetration-based finite element method for hyperelastic 3D biphasic tissues in contact. Part II: finite element simulations. J Biomech Eng. 2006;128(6):934-42.
Un, K., & Spilker, R. L. (2006). A penetration-based finite element method for hyperelastic 3D biphasic tissues in contact. Part II: finite element simulations. Journal of Biomechanical Engineering, 128(6), 934-42.
Un K, Spilker RL. A Penetration-based Finite Element Method for Hyperelastic 3D Biphasic Tissues in Contact. Part II: Finite Element Simulations. J Biomech Eng. 2006;128(6):934-42. PubMed PMID: 17154696.
* Article titles in AMA citation format should be in sentence-case
TY - JOUR T1 - A penetration-based finite element method for hyperelastic 3D biphasic tissues in contact. Part II: finite element simulations. AU - Un,Kerem, AU - Spilker,Robert L, PY - 2006/12/13/pubmed PY - 2007/3/1/medline PY - 2006/12/13/entrez SP - 934 EP - 42 JF - Journal of biomechanical engineering JO - J Biomech Eng VL - 128 IS - 6 N2 - The penetration method allows for the efficient finite element simulation of contact between soft hydrated biphasic tissues in diarthrodial joints. Efficiency of the method is achieved by separating the intrinsically nonlinear contact problem into a pair of linked biphasic finite element analyses, in which an approximate, spatially and temporally varying contact traction is applied to each of the contacting tissues. In Part I of this study, we extended the penetration method to contact involving nonlinear biphasic tissue layers, and demonstrated how to derive the approximate contact traction boundary conditions. The traction derivation involves time and space dependent natural boundary conditions, and requires special numerical treatment. This paper (Part II) describes how we obtain an efficient nonlinear finite element procedure to solve for the biphasic response of the individual contacting layers. In particular, alternate linearization of the nonlinear weak form, as well as both velocity-pressure, v-p, and displacement-pressure, u-p, mixed formulations are considered. We conclude that the u-p approach, with linearization of both the material law and the deformation gradients, performs best for the problem at hand. The nonlinear biphasic contact solution will be demonstrated for the motion of the glenohumeral joint of the human shoulder joint. SN - 0148-0731 UR - https://www.unboundmedicine.com/medline/citation/17154696/A_penetration_based_finite_element_method_for_hyperelastic_3D_biphasic_tissues_in_contact__Part_II:_finite_element_simulations_ L2 - https://asmedigitalcollection.asme.org/biomechanical/article-lookup/doi/10.1115/1.2354203 DB - PRIME DP - Unbound Medicine ER -