A polycrystal plasticity model based on the mechanical threshold S. Kok, A.J. Beaudoin*, D.A. Tortorelli Department of Mechanical and Industrial Engineering, University of Illinois at Urbana Champaign, 354 Mechanical Engineering Building, 1206 West Green Street, Urbana, IL 61801, USA Received in final revised form 14 September 2000 Abstract A temperature and rate-dependent viscoplastic polycrystalmodel is presented.It uses a sin- gle crystal constitutive response that is based on the isotropic Mechanical Threshold Stress continuum model. This combination gives us theability to relate the constitutive model para- meters between the polycrystaland continuum models. The individual crystal response is used to obtain themacroscopic response through the extended Taylor hypothesis. A Newton-Raph- sonalgorithm is used to solve the set of fully implicit nonlinear equations for each crystal. The analysis also uses a novel state variable integration method which renders the analysis time step size independent for constant strain rate simulations. Material parameter estimates are obtained through an identification study, where the error between experimental and computed stress response is minimized. The BFGS method, which is used to solve theidentification problem, requires first-order gradients. These gradients arecomputed efficiently via the direct method of design sensitivity analysis.Texture augmentation is performed in a second identifi- cation study by changing crystal weights (volume fractions). # 2002 Elsevier Science Ltd. All rights reserved. Keywords: B. Crystal plasticity; B. Viscoplastic material; C. Optimization 1. Introduction One of the first attempts to model the plastic behavior of polycrystalline metals, based on dislocation glide on slip systems of single crystals, was made by Taylor (1938). This pioneering work has been extended by numerous authors (Bishop and International Journal of Plasticity 18 (2002) 715–741 www.elsevier.com/locate/ijplas 0749-6419/01/$ - see front matter # 2002 Elsevier Science Ltd. All rights reserved. PII: S0749-6419(01)00051-1 * Corresponding author. Tel.: +1-217-244-9094; fax: +1-217-244-6534. E-mail address: abeaudoin@uiuc.edu (A.J. Beaudoin).