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Deformation gradient

rajan_prithivi's picture

How does abaqus calculate deformation gradient in presence of thermal expansion

When 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

Deformation Gradient from a deformed mesh - 4 node solid elements

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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. 

Deformation gradient in VUMAT of ABAQUS

Dear 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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