A 3D Cosserat point element (CPE) for nonlinear orthotropic solids: Generalization for an initially distorted mesh and an arbitrary orientation of material orthotropy

Abstract

Summary The objective of the present paper is to develop a Cosserat point element (CPE) formulation for the numerical solution of three‐dimensional problems of general hyperelastic orthotropic materials under finite deformations with initially distorted element shapes. Generally speaking, the accuracy of the CPE depends on the constitutive coefficients of the strain energy function that controls the inhomogeneous deformations. In the present study, a new methodology for the determination of the constitutive coefficients is presented, which allows the CPE to model any elastic material including isotropic, orthotropic, and anisotropic materials and with initially distorted element geometry. A number of example problems are considered, which verify and compare the performance of the developed CPE with other 3D brick elements that exist in the commercial finite element package ABAQUS. These examples demonstrate that the developed CPE is accurate, robust, free of hourglass instabilities, and can be used for modeling both 3D and thin structures that undergo large deformations. Copyright © 2015 John Wiley & Sons, Ltd.

The Cosserat Point Element as an Accurate and Robust Finite Element Formulation for Implicit Dynamic Simulations

“…So far, the 3D brick Cosserat point element was applied to solve the nonlinear static response of structures [Nadler and Rubin (2003); Rubin (2007b, 2008); Jabareen et al (2012); Jabareen and Mtanes (2016)]. In the present study, the 3D brick Cosserat point is further extended and applied to obtain the nonlinear dynamic response of solid structures that undergo finite deformations.…”

“…Recently, a three-dimensional (3D) brick element based on the Cosserat point theory was developed [Nadler and Rubin (2003); Rubin (2007b, 2008); Jabareen et al (2012); Jabareen and Mtanes (2016)]. This brick element was referred to as Cosserat point element (CPE) and was applied in modeling the finite deformation of solids including both thick and thin structures under static loading.…”

Extension of the unsymmetric 8‐node hexahedral solid element US‐ATFH8 to 3D hyper‐elastic finite deformation analysis

“…A mean-strain brick element including stabilizing technique was developed by Krysl 33 for hyper-elastic material. For 3D hyper-elastic problems, Jabareen et al 34,35 developed a Cosserat point element method as well. The higher order mixed formulation was constructed by Zdunek and Rachowicz 36 for compressible hyper-elastic material with transversely isotropy.…”