# A nonlinear thermomechanical formulation for anisotropic volume and surface continua

## TL;DR

This paper develops a comprehensive thermomechanical formulation for anisotropic materials, integrating volume and surface continua with finite strains, suitable for complex materials like crystals and biological tissues.

## Contribution

It introduces a unified tensorial framework connecting 3D and surface continua, extending thermomechanical modeling to anisotropic and multi-physics materials.

## Key findings

- Formulation applicable to anisotropic crystals and biological materials
- Derived weak forms for 3D and shell continua in tensor form
- Framework adaptable to thermo-electro-magneto-mechanical modeling

## 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 non-polar continua are obtained. Next, these kinematics are connected to their corresponding counterparts for surface continua based on Kirchhoff-Love kinematics. Likewise, the conservation laws for Kirchhoff-Love shells are derived from their three dimensional counterparts. From this, the weak forms are obtained for three dimensional non-polar 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, and they can be extended to other field equations, like Maxwell's equations to model thermo-electro-magneto-mechanical materials.