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G. Hofstetter, J.C. Simo, R.L. Taylor:
"A Modified Cap-Model: Closest Point Solution Algorithms";
Computers and Structures, 46 (1993), 2; 203 - 214.

An application of the return mapping algorithm for the inviscid two invariant cap model, originally proposed by DiMaggio and Sandler, is presented. This cap model serves as an example for nonsmooth multisurface plasticity. Precise conditions for discrete loading in all possible models are derived from the discrete Kuhn-Tucker conditions and new unconditionally stable closest point projection algorithms are presented. These are characterized by reducing local iterations in the constitutive equations to the solution of one nonlinear scalar equation for each of the different modes of the cap model. Tangent operators, consistent with the integration algorithm are derived, thus preserving the quadratic rate of convergence in a Newton solution procedure. It is shown that the original cap model does not obey the principle of maximum plastic dissipation, because the hardening law for the cap is nonassiciative, which leads to the undesirable feature of unsymmetric consistent tangent moduli. To overcome this drawback an associative hardening law is proposed for a restricted class of problems.

http://dx.doi.org/10.1016/0045-7949(93)90185-G