Engineering Mechanics Institute Conference 2013

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Efficient Numerical Integration of Perzyna viscoplasticity, with Application to Zero-Thickness Interface Elements

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Ignacio Carol
UPC, Barcelona
Spain

Stein Sture
University of Colorado - Boulder
United States

Ignasi Aliguer
UPC, Barcelona
Spain

Abstract:
Viscoplasticity has been widely used for engineering materials with (physical) time-dependent behaviour
over a threshold stress level(1), or in the context of viscoplastic relaxation strategies to obtain the
stationary solution of an inviscid problem via a fictitious (not physical) pseudo-time(2). In either case, the
rate-type infinitesimal viscoplastic formulation requires a time integration strategy to a) discretize time in
increments and b) evaluate a linearized relation between stress and strain increments for each time step
and, possibly some residual force calculation and iterative strategy. A variety of such algorithms has been
proposed, from the original constant stiffness and constant stress procedures to more recent and
sophisticated contributions(3). However, while for Duvaut-Lyons formulations a good compromise
between complexity and cost has been reached via quasi-linear exponential algorithms(4), for Perzyna-type
viscoplasticity there seems to be no equivalent approach.
In this paper, such an approach is proposed. Perzyna-type viscoplastic rate equations are integrated for a
time step considering the step as a stress-driven problem. Depending on how the increment of stress is
imposed (constant, linear, etc), different strategies arise, with a new linearized expression reminiscent of
the standard tangential stiffness in elasto-plasticity.
In the context of the Finite Element Method and using zero-thickness interface elements for slope and
stability problems with discontinuities, simple numerical examples are presented with comparison
between the various strategies, in order to illustrate the advantages of the new algorithm developed.

 

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