Stress-driven integration strategies and m-AGC tangent operator for Perzyna viscoplasticity and viscoplastic relaxation: application to geomechanical interfaces

This is the peer reviewed version of the following article: [Aliguer, I., Carol, I., and Sture, S. (2017) Stress-driven integration strategies and m-AGC tangent operator for Perzyna viscoplasticity and viscoplastic relaxation: application to geomechanical interfaces. Int. J. Numer. Anal. Meth. Geomech., 41: 918–939. doi: 10.1002/nag.2654.], which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/nag.2654/abstract. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.The paper proposes a stress-driven integration strategy for Perzyna-type viscoplastic constitutive models, which leads also to a convenient algorithm for viscoplastic relaxation schemes. A generalized trapezoidal rule for the strain increment, combined with a linearized form of the yield function and flow rules, leads to a plasticity-like compliance operator that can be explicitly inverted to give an algorithmic tangent stiffness tensor also denoted as the m-AGC tangent operator. This operator is combined with the stress-prescribed integration scheme, to obtain a natural error indicator that can be used as a convergence criterion of the intra-step iterations (in physical viscoplasticity), or to a variable time-step size in viscoplastic relaxation schemes based on a single linear calculation per time step. The proposed schemes have been implemented for an existing zero-thickness interface constitutive model. Some numerical application examples are presented to illustrate the advantages of the new schemes proposed.Peer Reviewe