Continuum-kinematics-inspired peridynamics: Thermo-mechanical problems

Abstract

The recently proposed continuum-kinematics-inspired peridynamics (CPD) is extended to account for thermo-mechanical coupling at large deformations. The key features of CPD are that it is geometrically exact and is built upon multi-neighbour interactions. The bond-based interactions of the original PD formalism are equivalent to one-neighbour interactions of CPD. Two- and three-neighbour interactions, however, are fundamentally different from state-based PD in that the basic elements of continuum kinematics are preserved exactly. We elaborate on thermodynamic restrictions on the interaction energies and derive thermodynamically consistent constitutive laws through a Coleman–Noll-like procedure. Notably, we show that various choices for temperature, or coldness, satisfy the dissipation inequality and provide meaningful temperature, or coldness, evolution equations together with Fourier-like conduction relations.