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

Computational inelasticity at different scales - FE technology and beyond

The necessity to provide physically reasonable and mathematically sound descriptions of mechanical behaviour at different scales is without discussion. Nevertheless, for engineering design quick estimations of important quantities such as stresses and strain are needed. This is not even enough. At a larger scale, information about the overall behaviour of complex systems has to be supplied. For this reason, we need to develop computational methods which on the one hand enable a detailed material description, on the other hand allow the bridging to coarser scales without losing too much information. In the present contribution, methods such as the phase field method are combined with FE technology, and, FE technology is combined with model reduction in order to reach this goal

On the computation of the exact overall consistent algorithmic tangent moduli for non-linear finite strain homogenization problems using six finite perturbations

This work is concerned with the development of a numerically robust two-scale computational approach for the prediction of the local and overall mechanical behavior of heterogeneous materials with non-linear constitutive behavior at finite strains. Assuming scale separation, the macroscopic constitutive behavior is determined by the mean response of the underlying microstructure which is attached to each macroscopic integration point in the form of a periodic unit cell. The algorithmic formulation and numerical solution of the two locally-coupled boundary value problems is based on the FE-FFT method (e.g. [14, 17]). In particular, a numerically robust algorithmic formulation for the computation of the overall consistent algorithmic tangent moduli is presented. The underlying concept is a perturbation method. In contrast to existing numerical tangent computation algorithms the proposed method yields the exact tangent using only six (instead of nine) perturbations (3 in 2d). As an example, the micromechanical fields and effective material behavior of elasto-viscoplastic polycrystals are predicted for representative simulation examples. copyright © Crown copyright (2018).All right reserved