A nonlinear thermomechanical formulation for anisotropic volume and surface continua

Abstract

A thermomechanical, polar continuum formulation under finite strains is proposed for anisotropic materials using a multiplicative decomposition of the deformation gradient. First, the kinematics and conservation laws for three-dimensional, polar, and nonpolar continua are obtained. Next, these kinematics and conservation laws are connected to their corresponding counterparts for surface continua, based on Kirchhoff–Love assumptions. Then the shell material models are extracted from three-dimensional material models for finite-temperature problems using established connections. The weak forms are obtained for both three-dimensional nonpolar continua and Kirchhoff–Love shells. These formulations are expressed in tensorial form so that they can be used in both curvilinear and Cartesian coordinates. They can be used to model anisotropic crystals and soft biological materials.