In this paper we investigate a three-dimensional finite-strain phenomenological constitutive model and propose an efficient solution algorithm by properly defining the variables and by avoiding extensively-used regularization schemes which increase the solution time. We define a nucleation-completion criterion and modify the regularized solution algorithm. Implementation of the proposed integration algorithm within a user-defined subroutine UMAT in the commercial nonlinear finite element software ABAQUS has made possible the solution of boundary value problems. The obtained results show the efficiency of the proposed solution algorithm and confirm the improved efficiency (in terms of solution CPU time) when a nucleation-completion criterion is used instead of regularization schemes.

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