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W. Liu, G. Meschke:
"A re-formulation of the exponential algorithm for finite strain plasticity in terms of Cauchy stresses.";
Computer Methods in Applied Mechanics and Engineering, 173 (1999), 167 - 187.

The role of the stress measure to be chosen as the argument in the definition of the yield function is discussed in the context of finite strain plasticity theory. Motivated by physical arguments, the exponential algorithm for multiplicative finite strain plasticity is revisited such that Cauchy stresses are adopted as arguments in the yield function. using logarithmic strain measures, the return map algorithm is formulated in principal axes. The algorithmic tangent moduli are obtained in a slightly modified, unsymmetric format compared to the standard formulation in terms of Kirchhoff stresses. However, the global structure of the exponential algorithm is unchanged. The algorithm is applied to the re-formulation of the Cam-Clay model in terms of Cauchy stresses. The typical calibration procedure of the Cam-Clay model based on Cauchy stresses is demonstrated. As an alternative, a modification of the Cam-Clay model, which allows re-calibration of Cauchy stress-based test data to be used within the framework of a Kirchhoff-based finite strain model is also discussed. The relevance of the adequate choice of the stress measure is illustrated by means of selected numerical analyses.

http://dx.doi.org/10.1016/S0045-7825(98)00267-9