Gradient theory from the thermomechanics point of view

This work demonstrates how gradients of internal state variables can be used in a set of internal variables when the thermomechanics of internal state variables is utilised. This is done by introducing a thermal internal variable called specific dissipative entropy. The gradient term in a material model can be used to avoid localisation. A material model showing Hookean deformation and creep is evaluated. Damage affects the Hookean response. The damage evolution equation contains a Laplacian of damage being introduced to avoid localisation of damage and mesh-dependence of a finite element solution. The material model satisfies the Clausius–Duhem inequality.