MAT5

Material Property ElementMAT5 lets you define a hyper-elastic material model for NLFE elements based on the Yeoh material model.

Format

<MAT5
       id       = "integer"
       C10      = "real"
       C20      = "real"        
       C30      = "real"
       nu       = "real"
       rho      = "real" 
       YS       = "real"
/> 

Attributes

id
Unique material property identification number.
C10
Material constant ( C 10 ).
C20
Material constant ( C 20 ).
C30
Material constant ( C 30 ).
nu
Poisson's ratio for the element. Default is 0.49.
rho
Element density.
An elastic limit for strain. Default is 0.0.
YS >= 0.0

Example

The example demonstrates the definition of a MAT5 element.

<MAT5 id="1" C10="1e+4"  C20="5e+3" C30="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 Yeoh material model law for the strain energy density function:
    U = C 10 ( I ¯ 1 3 ) + C 20 ( I ¯ 1 3 ) 2 + C 30 ( I ¯ 1 3 ) 3 + k 2 ( J 1 ) 2

    where

    C 10 , C 20 , C 30 are the material properties.

    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 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 × r z )

    Each element must have a unique material identification number.

  2. The constants C10, C20 and C30 denote material parameters of shear modulus that are usually determined experimentally.
  3. 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.