Dynamic analysis of 2D micromorphic hyperelastic continua considering finite deformation: A novel numerical approach

Abstract

In this paper, a numerical method named as variational differential quadrature-finite element method (VDQ-FEM) is proposed to study the dynamic response of hyperelastic structures with finite deformation in the context of 2D micromorphic theory. Continuum micromorphic hyperelasticity relations are first written in a novel vector-matrix form, which are then discretized using the method of VDQ-FEM. In the next step, the resulting relations are discretized on time domain using Newmark's method in order to study the time response. The presented matricized formulation can be exploited in the coding procedure of numerical techniques. Moreover, VDQ-FEM is capable of addressing problems with irregular domains. Simple implementation, absence of locking problem, fast convergence rate and computational efficiency are the main benefits of proposed numerical approach. Three test problems are solved to show the accuracy and efficiency of developed numerical approach. It is revealed that VDQ-FEM in conjunction with Newmark's method is capable of predicting the dynamic response of micromorphic hyperelastic continua with large deformations in an efficient way. The influences of internal length parameter, density and micro-inertia on the responses of considered micromorphic hyperelastic structures are also analyzed. © 2025 Elsevier Inc.