Isotropic Elasticity

In isotropic elasticity, the stress-strain relationship is given by

{\begin{matrix} ε_{11} \\ ε_{22} \\ ε_{33} \\ γ_{12} \\ γ_{13} \\ γ_{23} \end{matrix}} = [\begin{matrix} 1 / E & - ν / E & - ν / E & 0 & 0 & 0 \\ □ & 1 / E & - ν / E & 0 & 0 & 0 \\ □ & □ & 1 / E & 0 & 0 & 0 \\ □ & □ & □ & 1 / G & 0 & 0 \\ □ & s y m & □ & □ & 1 / G & 0 \\ □ & □ & □ & □ & □ & 1 / G \end{matrix}] {\begin{matrix} σ_{11} \\ σ_{22} \\ σ_{33} \\ σ_{12} \\ σ_{13} \\ σ_{23} \end{matrix}} = D^{e l} {\begin{matrix} ε_{11} \\ ε_{22} \\ ε_{33} \\ γ_{12} \\ γ_{13} \\ γ_{23} \end{matrix}} .

The elastic properties are completely defined by giving the Young's modulus,

E

, and the Poisson's ratio,

ν

. The shear modulus,

G

, can be expressed in terms of

E

and

E

G = E / 2 (1 + ν)

. These parameters can be given as functions of temperature and of other predefined fields, if required.

The stability criterion requires that $E > 0$ and $- 1 < ν < 0.5$ . Values of Poisson's ratio approaching 0.5 result in nearly incompressible behavior. Except for plane stress cases (including membranes and shells) or beams and trusses, such values require the use of “hybrid” elements in implicit analyses and generate high frequency noise and result in excessively small stable time increments in explicit simulations.

Parameters


Input Data	Description
Young's Modulus	$E > 0$ .
Poisson's Ratio	$- 1 < ν < 0.5$ .
Use temperature-dependent data	Specifies material parameters that depend on temperature. A Temperature field appears in the data table. For more information, see Specifying Material Data as a Function of Temperature and Independent Field Variables.
Number of field variables	Specifies material parameters that depend on field variables. Field columns appear in the data table for each field variable you add. For more information, see Specifying Material Data as a Function of Temperature and Independent Field Variables.