Guide

Modules

• Nonlinear deformation: AlgoDeforNonlinearModule (algorithms), FEMMDeforNonlinearModule, MatDeforNonlinearModule, MatDeforNeohookeanModule (hyperelastic material models).

Nonlinear deformation FEM machines

For the base machine for nonlinear deformation, FEMMDeforNonlinearBase, assumes standard isoparametric finite elements. It evaluates the interior integrals:

• The stiffness matrix, the geometric stiffness matrix, the loading corresponding to prescribed nonzero displacement.

• The load vector corresponding to restoring forces due to deformation of the material.

The nonlinear deformation package FinEtoolsDeforNonlinear is dependent on the linear deformation package, FinEtoolsDeforLinear.

Material and Material Orientation

Materials for nonlinear deformation analysis

The module MatDeforNonlinearModule defines the interface for nonlinear materials (based upon the model-reduction type, 3-D, 2-D, or 1-D) are provided.

Currently there are material types for hyper elastic materials. The user may add additional material types by deriving from AbstractMatDeforNonlinear and equipping them with two methods: (1) compute the tangent moduli, and (2) update the material state.

The material model assumes that the strains are provided in the local, material-attached coordinate system. The stresses (and the tangent moduli) also need to be output in this local coordinate system.

For full generality, material types should implement these methods for fully three-dimensional, plane strain and plane stress, 2D axially symmetric, and one-dimensional deformation models.

Algorithms

Nonlinear deformation algorithms

There are algorithms for

• Nonlinear static analysis.