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

Abstract

SUMMARYThe 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 intrastep 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.

m‐AGC tangent visco‐plastic operator with hardening/softening, and application to the visco‐plastic relaxation analysis of stable and unstable problems using fracture‐based geomechanical interfaces

“…The existing elastic perfect visco-plastic model developed by Aliguer et al 12 constitutes the starting point for the extended version proposed in this paper, which consists mainly of adding Hardening/Softening, to the original formulation. In this section, the main relevant aspects of the original perfect visco-plastic model are summarized.…”

Displacement‐based and hybrid formulations of zero‐thickness mortar/interface elements for unmatched meshes, with application to fracture mechanics

“…This is because strain-driven constitutive formulations provide directly the new stress and the new stiffness for prescribed strain values, and these are precisely the inputs required for the evaluation of integrals (10) or (25)- (27). By contrast, stress-driven constitutive equations (such as viscoplasticity, see for instance Aliguer et al 30 ) provide naturally strain and constitutive compliance for prescribed stress increments, which are the inputs required to calculate the reduced vector of mortar relative displacements and the reduced compliance (38).…”

“…By contrast, viscoplastic models would always seem adequate for hybrid formulations, since they may be always written to provide a consistent compliance matrix for the time increment. 30…”

“…Additional details of the constitutive model and results obtained in basic loading situations may be found in Carol et al 28 and Caballero et al 29 The "stress"-driven law, on its side, is a perfect viscoplastic model defined on the basis of the same hyperbolic loading surface. The theory and implementation details as well as simple examples of application may be found in Aliguer et al 30…”

“…This may be particularly useful in the case of fracturing solids or geomechanical domains with existing fractures or developing discontinuities. In this particular study, the elastoplastic geomechanical model for existing discontinuities, 27 or the for normal/shear cracking model based in fracture mechanics concepts, both in elastoplastic version 28,29 or viscoplastic version, 30 have been used in some of the examples presented.…”