oa Updated Lagrange Formulation Of Internally Balanced Compressible Hyperelastic Materials

Nonlinear continuum mechanics is commonly used to study the response of highly de- formable materials. Nowadays, the proposed material models often include internal ma- terial variables in order to capture realistic engineering behavior. The theoretical back- ground is mature and its implementation in the frame of nite element method is well established. Solely, these material constitutive models are expressed in terms of defor- mation gradient F, its derived quantities, and various multiplicative decompositions such as F = ^F F (1) This multiplicative decomposition serves to pertain particular portions of F to specic parts of the material response. The usual scheme is then that ^F models elastic response and it is associated to the rules of variational calculus. The F portion then models inelastic response, usually by means of a time dependent evolution law. Recently, the arguments of variational calculus have been applied to both portions of the deformation gradient decomposition for incompressible hyperelastic material [1]. The decomposition itself is then determined by an additional internal balance equation that is generated by such a variational treatment. The internally balanced compressible hyperelastic material response is presented in [2]. Fundamental studies of this type are key to better physics-based modeling of complex biomechanical processes in soft tissue, including long time scale processes of growth, and short time scale processes of wound healing. The FE formulation of this internal balance multiplicative decomposition is naturally achieved by linearizing the weak form that is obtained by the variation with respect to both portions of the multiplicative decomposition. In this work, we would like to present the Updated Lagrange Formulation. This formulation will be implemented into com- mercial nite element package FEAP that will facilitate in future studying engineering application in the eld of biomechanics. The correctness of implementation will be ex- amined by simulating homogeneous deformations such as uniaxial loading, dilatation and simple shear. References [1] H. Demirkoparan, T. J. Pence, and H. Tsai. Hyperelastic internal balance by multi- plicative decomposition of the deformation gradient. Archive for Rational Mechanics and Analysis, 2014. DOI: 10.1007/s00205-014-0770-9. [2] A. Hadoush, H. Demirkoparan, and T.J. Pence. Modeling of soft materials via mul- tiplicative decomposition of deformation gradient. In USNCTAM, 2014.