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

Hello,

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.

My idea is that through nodal displacements with a bi-linear interpolation - moving least square algorithm, I should be able to set up u(x,y) and v(x,y). Can anyone suggest any good example how it can be calculated in matlab or any pertinent code I can refer to?

Thanks,

Jay Patel

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### F is given by

F is given by

F = I + partial_u/partial_x ; (u, x are vectors here)

You said, you already have a 4 noded element for which the shape functions would already be available.

So,

u = N1*u1 + N2*u2 + . . .

You may take the partial of the above to get F.

You may refer to any UMAT to see how it is initialized and updated, Abaqus directly calculates the deformation gradients ( look at dfgrd0 and dfgrd1). 