An efficient numerical approach to the micromorphic hyperelasticity

Abstract

A computationally efficient numerical strategy called as variational differential quadrature-finite element method (VDQFEM) is developed herein for the nonlinear analysis of hyperelastic micromorphic continua. To this end, a novel formulation including microstructure effects is proposed in which high-order tensors are written in equivalent matrix or vector forms, and is then discretized in an efficient way. This feature is utilized in the coding process of numerical method. For the solution purpose, the domain is first transformed into a number of finite elements. Thereafter, a variational discretization technique called as VDQ is applied within each element. In order to employ the VDQ method, the irregular domain of the element is transformed into the regular one using the mapping technique. Finally, the assemblage procedure is performed. This approach can be used for the analysis of bodies with arbitrary geometries. By considering several numerical examples, it is revealed that the presented size-dependent formulation and numerical solution approach have a good performance to study the large deformations of hyperelastic micromorphic bodies with complex geometries. © 2019, Springer-Verlag GmbH Germany, part of Springer Nature.