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Hyperelastic Umat


kirde
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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

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lynx
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 lynx
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[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

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kirde
Posts: 10
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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

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lynx
Posts: 59
 lynx
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Joined: 13 years ago

[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.

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