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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.