2D analysis in the context of micromorphic thermo-hyperelasticity: a two-point formulation

Abstract

This paper develops a finite element method (FEM) to study the dynamic behavior of two-dimensional (2D) micromorphic thermo-hyperelastic solids with finite deformations. For this purpose, a two-point formulation is derived using energy functions including mechanical, thermal and coupling (due to thermal expansion) between thermal and mechanical parts. The vector–matrix representation of this formulation is also given which can be exploited in the coding procedure of numerical methods. FEM, utilizing the Newton–Raphson and Newmark techniques, has been employed to solve nonlinear time-dependent micromorphic thermo-hyperelastic governing equations. Some test problems are solved to demonstrate the accuracy and reliability of the approach. Furthermore, the influences of internal length parameter, thermal expansion and heat flux on the dynamic behavior of the micromorphic thermo-hyperelastic structures are examined. © The Author(s), under exclusive licence to Springer-Verlag GmbH Austria, part of Springer Nature 2025.