1.4. Conventions

Overview

Conventions used through out Matmodlab2 are described.

Dimension

Material models are always called with full 3D tensors.

Vector Storage

Vector components are stored as

\[v_i = \{v_x, v_y, v_z\}\]

Tensor Storage

Second-order symmetric tensors are stored as 6x1 arrays with the following component ordering

(1)\[A_{ij} = \{A_{xx}, A_{yy}, A_{zz}, A_{xy}, A_{yz}, A_{xz}\}\]

Nonsymmetric, second-order tensors are stored as 9x1 arrays in row major ordering, i.e.,

\[B_{ij} = \{B_{xx}, B_{xy}, B_{xz}, B_{yx}, B_{yy}, B_{yz}, B_{zx}, B_{zy}, B_{zz}\}\]

Engineering Strains

The shear components of strain-like tensors are sent to the material model as engineering strains, i.e.

\[\epsilon_{ij} = \{\epsilon_{xx}, \epsilon_{yy}, \epsilon_{zz}, 2\epsilon_{xy}, 2\epsilon_{yz}, 2\epsilon_{xz}\} = \{\epsilon_{xx}, \epsilon_{yy}, \epsilon_{zz}, \gamma_{xy}, \gamma_{yz}, \gamma_{xz}\}\]