## Hyperelastic Material Models for Stress Analysis (B2000++ Pro)

Hyperelastic materials models are provided with B2000++ Pro and are supported by 2D and 3D elements.

## 1. Mooney-Rivlin Material Model

The nonlinear hyperelastic Mooney-Rivlin material model is suited for finite strain analysis of rubber-like isotropic materials. The elastic potential includes a hydrostatic work term. This material model is supported by 3D elements.

material id type mooney_rivlin   c1 v   [c2 v]   kappa v   [alpha v]   [failure ... end]   [density v] end

The following parameters are specified:

c1|c2 v

Specifies the Mooney-Rivlin material constants. If c2 is not specified, it will be assumed 0, in which case a Neo-Hookean material is described.

kappa v

Specifies the bulk modulus.

alpha v

Specifies the thermal expansion coefficient. Default is 0.

failure ... end

Specifies a failure criterion (optional).

density v

Specifies the material density. Default is 0.

Alternatively, the elastic modulus e and Poisson's ratio nu may be specified instead of the Mooney-Rivlin coefficients c1, c2, and kappa. In this case, the Mooney-Rivlin material constants will be calculated from e and nu.

## 2. Generalised Blatz-Ko Material Model

The nonlinear hyperelastic generalised Blatz-Ko material model is suited for finite strain analysis of foam-rubber materials. The elastic potential includes a hydrostatic work term. This material model is supported by 3D elements.

material id type blatz_ko   g v   kappa v   [f v]   [alpha v]   [failure ... end]   [density v] end

The following parameters are specified:

g v

Specifies the shear modulus.

kappa v

Specifies the bulk modulus.

f v

Specifies the volume-fraction of voids in the foam-rubber material. Default is 0.5.

alpha v

Specifies the thermal expansion coefficient. Default is 0.

failure ... end

Specifies a failure criterion (optional).

density v

Specifies the material density. Default is 0.

Alternatively, the elastic modulus e and Poisson's ratio nu may be specified instead of the shear modulus g and the bulk modulus kappa.