Corotational formulation for 3d solids. An analysis of geometrically nonlinear foam deformation

TL;DR

This paper develops a co-rotational finite element formulation for 3D structures that handles large rotations with small strains, enabling efficient analysis of nonlinear deformation, stability, and fracture in complex materials.

Contribution

It introduces a new best fit rotator and spin filter within the co-rotational framework, applicable to various discretization methods for nonlinear 3D solid analysis.

Findings

Efficient formulation for nonlinear 3D deformation analysis.

Applicable to stability, fracture, and dynamic problems.

Versatile methodology for different discretization techniques.

Abstract

This paper presents theory for the Lagrange co-rotational (CR) formulation of finite elements in the geometrically nonlinear analysis of 3D structures. In this paper strains are assumed to be small while the magnitude of rotations from the reference configuration is not restricted. A new best fit rotator and consistent spin filter are derived. Lagrange CR formulation is applied with Hybrid Trefftz Stress elements, although presented methodology can be applied to arbitrary problem formulation and discretization technique, f.e. finite volume methods and lattice models, discreet element methods. Efficiency of CR formulation can be utilized in post-buckling stability analysis, damage and fracture mechanics, modelling of dynamic fragmentation of bodies made from quasi-brittle materials, solid fluid interactions and analysis of post-stressed structures, discreet body dynamics.