3D finite element analysis of micromorphic hyperelastic structures considering finite deformations: Two-point formulation

Abstract

The purpose of this article is to introduce a novel finite element (FE) approach for investigating the large deformations of three-dimensional (3D) micromorphic hyperelastic continua that have an arbitrary geometry. The 3D micromorphic hyperelasticity formulation is initially presented in a general form. To facilitate the procedure of coding, the vector-matrix counterparts of the aforementioned relations are also provided, which can be conveniently employed in numerical methods. Afterwards, an FE approach is implemented to investigate the large deformations of micromorphic hyperelastic structures under static loading. This is achieved via the user element (UEL) subroutine utilized by the commercial ABAQUS software. Problems with complex domains can be solved using this FE approach. Solving some test problems, including bending of a beam, Cook's membrane under bending load, a cracked spherical shell under external pressure point load and a cracked cylindrical shell under stretching load, demonstrates the fast convergence rate, simple implementation, accuracy and efficiency of the method. In addition, the influences of internal length and scale-transition parameters and geometrical properties on the finite deformation of considered micromorphic hyperelastic structures are evaluated.