MAT4

Material Property ElementMAT4 lets you define a hyper-elastic material model for NLFE elements based on the Mooney-Rivlin material model.

Format

<MAT4
       id       = "integer"
       mu01     = "real"
       mu10     = "real"        
       nu       = "real"
       rho      = "real"
       YS       = "real"
/> 

Attributes

id
Unique material property identification number.
mu01
Material constant ( μ 01 ).
mu10
Material constant ( μ 10 ).
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 MAT4 element.

<MAT4 id="1" mu01="8e+3"  mu10="2e+3" nu="0.499" rho="7.810e-6" YS="0.125"/>

Comments

  1. This material element defines a hyper-elastic material that follows the Mooney-Rivlin material model law for the strain energy density function:

    U = μ 10 ( I ¯ 1 3 ) + μ 01 ( I ¯ 2 3 ) + k 2 ( J 1 ) 2

    where

    μ = 2 ( μ 01 + μ 10 ) is the shear modulus

    k = 2 μ ( 1 + v ) 3 ( 1 2 v ) is the bulk modulus

    v is the Poisson's ratio

    I ¯ 1 = J 2 3 I 1 , I ¯ 2 = J 4 3 I 2

    I 1 = t r ( C ) = r x T r x + r y T r y + r z T r z

    I 2 = 1 2 ( ( t r ( C ) ) 2 ( t r ( C 2 ) ) )

    J = det ( J ) = r x T ( r y × r z )

    Each element must have a unique material identification number.

  2. This material model can only be used with a fully parameterized element (BEAM12, QUAD12, TRIA12 and solid elements).
  3. mu10 and mu10 are material constants. mu10 can be determined using a tension or compression tests, however, mu01 should be determined using a biaxial test.
  4. 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.