Elastic-viscoplastic modeling of soft biological tissues using a mixed finite element formulation based on the relative deformation gradient

SUMMARYThe 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. A strongly objective integration scheme for proper evaluation of evolution equations and a new mixed finite element formulation are presented, which are particularly suitable for elastic‐viscoplastic modeling of soft biological tissues. As a challenging application of the model implementation within a user element UEL in Abaqus, experimental data from the mechanical characterization of facial skin tissue based on the suction method is used, to identify a set of model parameters for the Rubin and Bodner model. The corresponding inverse finite element problem is presented and constitutes a generally valid procedure for the identification of model parameters.