A thermo-electro-mechanically coupled cohesive zone formulation for predicting interfacial damage

Material interfaces can occur at different material length scales. Understanding the properties and the behaviour of interfaces is of utmost importance because interfaces can significantly influence the effective constitutive response of the material under consideration. Based on the fundamentals of electro-mechanically coupled cohesive zone formulations for electrical conductors and on the associated finite element framework proposed in Kaiser and Menzel(2021), a thermo-electro-mechanically coupled cohesive zone formulation is established in this article. To this end, the governing equations of continuum thermodynamics for materials with interfaces under combined mechanical, thermal, and electrical loads are derived. A damage variable is introduced to account for the evolution of interface damage in a thermodynamically consistent way. Motivated by deformation-induced property changes, the effective thermal and electrical conductivities are moreover assumed to be functions of the damage variable. Finally, analytical solutions are derived to validate the finite element formulation, and representative boundary value problems are studied so as to reveal key properties of the proposed cohesive-zone framework.