Large Deformation Analysis of Arbitrary-Shaped Micromorphic Hyperelastic Structures: A Finite Element Approach

Abstract

The aim of this paper is to propose a novel finite element (FE) approach for studying the large deformations of structures with arbitrary geometry in the context of micromorphic hyperelasticity. The 3D micromorphic hyperelasticity is first formulated in a general form based on novel constitutive relations within a Lagrangian framework. In order to implement in the coding procedure, the vector–matrix counterparts of presented relations are also given, which can be used in numerical approaches readily. In the next step, a finite element method is developed to compute large deformations in arbitrary-shaped structures under static loading. The correctness and reliability of the approach are illustrated by solving some test problems. Additionally, the effects of Young's modulus, internal length, and scale-transition parameters on the large deformation behavior of considered micromorphic hyperelastic structures are analyzed. © 2025 John Wiley & Sons Ltd.