High-performance geometric nonlinear analysis with the unsymmetric 4-node, 8-DOF plane element US-ATFQ4

A recent unsymmetric 4-node, 8-DOF plane element US-ATFQ4, which exhibits excellent precision and distortion-resistance for linear elastic problems, is extended to geometric nonlinear analysis. Since the original linear element US-ATFQ4 contains the analytical solutions for plane pure bending, how to modify such formulae into incremental forms for nonlinear applications and design an appropriate updated algorithm become the key of the whole job. First, the analytical trial functions should be updated at each iterative step in the framework of updated Lagrangian formulation that takes the configuration at the beginning of an incremental step as the reference configuration during that step. Second, an appropriate stress update algorithm in which the Cauchy stresses are updated by the Hughes-Winget method is adopted to estimate current stress fields. Numerical examples show that the new nonlinear element US-ATFQ4 also possesses amazing performance for geometric nonlinear analysis, no matter whether regular or distorted meshes are used. It again demonstrates the advantages of the unsymmetric finite element method with analytical trial functions

Application of a geometrically nonlinear elastoplastic gradient-enhanced damage model with incremental potential to composite microstructures

The prediction of inelastic processes like plastic deformations and cracks within the microstructure of modern man-made materials by realistic, yet simple and efficient continuum models remains a major task in material modelling. For this purpose, gradient-extended standard dissipative solids represent one of the most promising model classes, which is also formulated and applied in this work to investigate microscopic failure mechanisms in three exemplary three-dimensional composite microstructures. The model combines geometrically nonlinear isotropic elastoplasticity with an isotropic damage model with gradient-extension. For the numerical treatment, a variational constitutive update algorithm based on the exponential map is applied. The model is used to provide insight into the microscopic failure of a brittle woven composite material, a particle-reinforced plastic and a carbon fiber reinforced composite. The influence of different microstructural and material parameters on the overall failure behavior is characterized. Adaptive meshing is used to enable a refined numerical resolution of the cracked regions