Calculating the deformation gradient for a 3D surface

Question

Amin Kassab-Bachi 2022-1-15

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https://ww2.mathworks.cn/matlabcentral/answers/1629600-calculating-the-deformation-gradient-for-a-3d-surface

评论： Amin Kassab-Bachi 2022-1-15

I'm trying to calculate strain from deformation field, for which I need the deformation gradient. What I have is the x,y,z displacements of the nodes, and I found that the the deformation gradient F = I + ∇u , but I don't understand how the gradient function is applied (i.e. what the input (u) should look like).

I tried using this function [Grad] = gradient(u), Where u is the [x,y,z] disaplacment of the size (#nodes x 3).

is this the correct way for using this function in this case?

Thanks.

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Answer 1

Friedel Hartmann 2022-1-15

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You can calculate the gradient of the displacement field u (3 components), which is a function of (x,y,z) and which is an expansion in terms of the shape functions of the mesh. The nodal displacements cannot be differentiated, they are vectors, they are the value of the displacement field at the nodes.

So, you must understand how the displacement field is defined, which shape functions the program uses.

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Amin Kassab-Bachi 2022-1-15

Thanks for the answer. My understanding is that the displacement field is just the nodal displacements as defined here. I probably also need to input the points' x,y,z spacings.

What I'm trying to do is based on spam python package

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