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# Deformation gradient

## How does abaqus calculate deformation gradient in presence of thermal expansion

Fri, 2017-04-21 17:05 - rajan_prithiviWhen we only have mechanical loading, I understand that abaqus calculates the total deformation gradient using F = I + partial_U/partial_X and U = N_i*U_i where U_i is the displacement at the nodes and N is the shape function .

If I use a thermal expansion in addition to mechanical loading , Does abaqus give the total deformation gradient incorporating both mechanical loading and thermal expansion ?

F = I + partial_Utot/partial_X ; Utot = U_mechanical + U_thermal

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## Deformation Gradient from a deformed mesh - 4 node solid elements

Thu, 2015-12-17 15:34 - pateljay26Hello,

I have a 2D mesh that has 4 node solid elements. I am aware that to determine the components of deformation gradient tensor F, I will require displacement functions, u(x,y) and v(x,y) in a current configuration. Taking a partial derivative with respect to x and y respectively yields components of def. gradient tensor F.

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## Stupid Question Regarding Deformation Gradient

Wed, 2011-07-06 08:53 - gnoij- Read more about Stupid Question Regarding Deformation Gradient
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## Deformation gradient in VUMAT of ABAQUS

Thu, 2008-10-02 16:16 - zhpengDear All,

In ABAQUS manual, it is said for hyperelastic material, it is better to define it by stretch tensor U. But if I need to use deformation gradient F in the material model directly, I need to rotate the stress back to corotational frame. How should I do that? Should I make a polar decomposition of F=R*U first, and then apply Rt*S*R? or I can use the relative spin increment already provided to do that? If so, how?

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