Large viscoelastic deformation of hard-magnetic soft beams

Abstract

This work aims at developing a viscoelastic formulation for the time-dependent finite deformation analysis of beams made of hard-magnetic soft materials (HMSMs) under magnetic loading. After introducing the basic kinematic quantities, a viscoelasticity formulation for the analysis of HMSMs is developed, which is general in the sense that it can be used for 2D and 3D geometries beside the beam, plate, and shell-type structures. Next, the expression for the consistent fourth-order tangent tensors for 3D bodies and beams made of HMSMs are presented. Due to the highly nonlinear nature of the governing equations, a finite element formulation for the numerical solution of beam problems with various loading and boundary conditions is developed. To demonstrate the applicability of the developed formulation, several numerical examples are provided. It is observed that for the case of elastic deformations, the results of the present formulation are very close to those previously reported in the literature. For the case of viscoelastic deformations, the creep response of beams is simulated and the effect of viscoelastic parameters is studied. It is shown that the obtained results are qualitatively in agreement with the basic properties of viscoelastic deformations.