OOF2: The Manual

Mechanical:Elasticity:LargeStrain:Anisotropic:TrigonalA
	6.4.1. Material Properties

Name

Mechanical:Elasticity:LargeStrain:Anisotropic:TrigonalA — Trigonal-A large-strain elasticity.

Details

Property Category: Elasticity
Parameters:

cijkl

Type: A TrigonalARank4TensorCij object.
Fields: Displacement
Fluxes: Stress

Discussion

The anisotropic large strain elasticity Properties specify that the Stress depends nonlinearly on the gradients of the Displacement, $u$ :

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

(6.27)

where $\sigma_{ij}$ is the Stress, $C_{ijkl}$ is the modulus cijkl, and

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

(6.28)

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

The crystal symmetry of the material is reflected in the symmetry of the modulus, cijkl. Materials containing an anisotropic elastic Property must also contain an orientation property.


Mechanical:Elasticity:LargeStrain:Anisotropic:Tetragonal		Mechanical:Elasticity:LargeStrain:Anisotropic:TrigonalB