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If the study step is geometrically linear, the strain ε is the engineering strain. The stress σ could in principle be any of the stress measures, as they all converge to the same engineering stress in this case.
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If the study step is geometrically nonlinear, the variation of strain δε is taken from the displacement gradient, and the stress conjugate σ is the first Piola–Kirchhoff stress. The integration is done in the undeformed configuration.
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