# Hyperelastic Umat

Hi All,

Just wondering could anyone define DDSDDE in terms of d2W/dFdF where W is the strain energy density function and F is the deformation gradient, (i.e the second derivative of the strain energy density function). It is difficult to figure out exactly what DDSDDE is from abaqus documentation. Do any papers/books define it exactly?

Thanks for the help,

creanea

[QUOTE=creanea,5916]Hi All,

Just wondering could anyone define DDSDDE in terms of d2W/dFdF where W is the strain energy density function and F is the deformation gradient, (i.e the second derivative of the strain energy density function). It is difficult to figure out exactly what DDSDDE is from abaqus documentation. Do any papers/books define it exactly?

Thanks for the help,

creanea[/QUOTE]

There are lots of books besides papers:

For derivation you might want to skip the following,

Nonlinear Continuum Mechanics for Finite Element Analysis of Bonnet and Wood.

DDSDDE may need a small correction depending on the selected objective rate and its compatibility with Jaumann.

Also you might want to look Simo and Hughes Computational Inelasticity.

Kumar

Thanks Kumar,

Currently my model is purely Hyperelastic and I am defining cauchy stress as (1/J)*F*Transpose(dW/df). I basically want to describe DDSDDE with another straight forward equation that I could use for any strain energy density function. I had thought that it would be simply related to the elasticity tensor, Aijkl = d2W/dFdF?

Any ideas?

Also I know I could be using a UHYPER instead of a UMAT but I will eventually need to use a UMAT so thats why Im working with it at the moment.

Thanks

[QUOTE=creanea,5919]Thanks Kumar,

Currently my model is purely Hyperelastic and I am defining cauchy stress as (1/J)*F*Transpose(dW/df). I basically want to describe DDSDDE with another straight forward equation that I could use for any strain energy density function. I had thought that it would be simply related to the elasticity tensor, Aijkl = d2W/dFdF?

Any ideas?

Also I know I could be using a UHYPER instead of a UMAT but I will eventually need to use a UMAT so thats why Im working with it at the moment.

Thanks[/QUOTE]

Youre correct. However DDSDDE simply stands for the material tangent

for the Jaumann rate, thus your form which has a certain tensorial expression in a general way just should be modified again in a general way.

- default mat41 is used in LS-Dyna8 months ago
- Abaqus Larc05 subroutine10 months ago
- Low Cycle Fatigue in Abaqus1 year ago
- Orthotropic viscoelastic material model validation1 year ago
- Urgent HELP! USDFLD problem2 years ago

Latest Post: Exercises for the Mechanics of Solid Polymers Book Our newest member: djhirenearme Recent Posts Unread Posts Tags

Forum Icons: Forum contains no unread posts Forum contains unread posts

Topic Icons: Not Replied Replied Active Hot Sticky Unapproved Solved Private Closed