OOF2: The Manual

Mechanical:Elasticity:LargeStrain:Isotropic
	6.4.1. Material Properties

Name

Mechanical:Elasticity:LargeStrain:Isotropic — Isotropic large-strain elasticity.

Details

Property Category: Elasticity
Parameters:

cijkl

Type: An object of the IsotropicRank4Tensor class.
Fields: Displacement
Fluxes: Stress

Discussion

The isotropic large strain elasticity Property specifies that the Stress depends nonlinearly on the gradients of the Displacement, $u$ :

$\sigma_{ij} = C_{ijkl}\epsilon_{kl}$

(6.19)

where $\sigma_{ij}$ is the Stress, $C_{ijkl}$ is an isotropic fourth rank tensor given by the modulus cijkl, and $\epsilon$ is the nonlinear geometric strain,

$\epsilon_{ij} = \frac12\left( \frac{\partial u_i}{\partial x_j} + \frac{\partial u_j}{\partial x_i} + \frac{\partial u_k}{\partial x_i}\frac{\partial u_k}{\partial x_j} \right).$

(6.20)

This form of the geometric strain is invariant under rigid rotations, unlike its linear variant, Eq. (6.2).


Mechanical:Elasticity:Anisotropic:Triclinic		Mechanical:Elasticity:LargeStrain:Anisotropic:Cubic