MAT2

Material Property ElementMAT2 lets you define a hyper-elastic material model for NLFE elements that follows the incompressible Neo-Hookean material law.

Format

<MAT2
       id       = "integer"
       mu       = "real"       
       nu       = "real"
       rho      = "real"
       YS       = "real"
/>

Attributes

id: Unique material property identification number.
mu: Shear modulus for the element.
nu: Poisson's ratio for the element. Default is 0.49.
rho: Element density.
YS: An elastic limit for strain. Default is 0.0.; YS >= 0.0

Example

The example demonstrates the definition of a MAT2 element.

<MAT2 id="1" mu="1.906036" nu="0.499" rho="2.150e-6" YS="0.125"/>

Comments

This material element defines a hyper-elastic material that obeys the incompressible Neo-Hookean law for the strain energy density function:
$U = \frac{μ}{2} ({\bar{I}}_{1} - 3) + \frac{k}{2} {(J - 1)}^{2}$

where

$μ$ is the shear modulus; $μ = N K T$ , where N is the number of polymer chains per unit volume, K is the Boltzmann constant, and T is temperature

$k = \frac{2 μ (1 + v)}{3 (1 - 2 v)}$ is the bulk modulus

$v$ is the Poisson's ratio

${\bar{I}}_{1} = J^{\frac{- 2}{3}} I_{1}$ , $I_{1} = t r (C) = r_{x}^{T} r_{x} + r_{y}^{T} r_{y} + r_{z}^{T} r_{z}$

$J = \det (J) = r_{x}^{T} (r_{y} \times r_{z})$

Each element must have a unique material identification number.
This material model can only be used with a fully parameterized element (BEAM12, QUAD12, TRIA12 and solid elements).
YS lets you specify a maximum limit on the elastic strain that the component is allowed. If, during the simulation, the component strain (at any element in the component) exceeds this value, MotionSolve issues a warning message.