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Elastic–viscoplastic modeling of soft biological tissues using a mixed finite element formulation based on the relative deformation gradient
Author(s) -
Weickenmeier J.,
Jabareen M.
Publication year - 2014
Publication title -
international journal for numerical methods in biomedical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.741
H-Index - 63
eISSN - 2040-7947
pISSN - 2040-7939
DOI - 10.1002/cnm.2654
Subject(s) - viscoplasticity , finite element method , deformation (meteorology) , mechanics , materials science , constitutive equation , structural engineering , physics , engineering , composite material
SUMMARY The characteristic highly nonlinear, time‐dependent, and often inelastic material response of soft biological tissues can be expressed in a set of elastic–viscoplastic constitutive equations. The specific elastic–viscoplastic model for soft tissues proposed by Rubin and Bodner (2002) is generalized with respect to the constitutive equations for the scalar quantity of the rate of inelasticity and the hardening parameter in order to represent a general framework for elastic–viscoplastic models. A strongly objective integration scheme and a new mixed finite element formulation were developed based on the introduction of the relative deformation gradient—the deformation mapping between the last converged and current configurations. The numerical implementation of both the generalized framework and the specific Rubin and Bodner model is presented. As an example of a challenging application of the new model equations, the mechanical response of facial skin tissue is characterized through an experimental campaign based on the suction method. The measurement data are used for the identification of a suitable set of model parameters that well represents the experimentally observed tissue behavior. Two different measurement protocols were defined to address specific tissue properties with respect to the instantaneous tissue response, inelasticity, and tissue recovery. Copyright © 2014 John Wiley & Sons, Ltd.