Crack Propagation by Cohesive Element
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Hi everyone,
I've been working on crack propagation problem by cohesive elements in Abaqus.
I have a sandwich struture where adhesive bonds two steels together. And I've attached part of my input file in the following.
I can have the stress and strain distribution, but I really expect the crack will propagate in the midplane of the adhesives. I don't know whether I have to preset a line in the middle of adhesive as existing crac, or I can set some crack interaction to get the crack growth result.
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relation between the Euler-Lagrange strain tensor and the 2nd Piola-Kirchhoff stress tensor
At finite deformations, the 2nd Piola-Kirchhoff stress tensor S_{IJ} is work-conjugate to the Euler-Lagrange strain tensor E_{IJ}, i.e. the work done by the stress S_{IJ} at developing a strain E_{IJ} per unit volume in the reference configuration is
W = 1/2 S_{IJ} E_{IJ} (Einstein summation over repeated indices implied)
I would like to express this in the same form as used in linear elasticity, i.e. to write S_{IJ} = M_{IJKL} E_{KL}, which would give me
W = 1/2 M_{IJKL} E_{IJ} E_{KL}
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