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MECHANICS OF COHESIVE-FRICTIONAL MATERIALS Mech. Cohes.-Frict. Mater. 2000; 5:87}112

Mech. Cohes.-Frict. Mater. 2000; 5:87}112
Adaptivity based on error estimation for viscoplastic
softening materials
Pedro DmHez, Marino Arroyo and Antonio Huerta*
Departamento de MatemaH tica Aplicada III, E.T.S. Ingenieros de Caminos, Universitat Polite` cnica de Catalunya, Spain
This paper focuses on the numerical simulation of strain softening mechanical problems. Two problems
arise: (1) the constitutive model has to be regular and (2) the numerical technique must be able to capture the
two scales of the problem (the macroscopic geometrical representation and the microscopic behaviour in the
localization bands). The Perzyna viscoplastic model is used in order to obtain a regularized softening model
allowing to simulate strain localization phenomena. This model is applied to quasistatic examples. The
viscous regularization of quasistatic processes is also discussed: in quasistatics, the internal length associated
with the obtained band width is no longer only a function of the material parameters but also depends on the
boundary value problem (geometry and loads, specially loading velocity).
An adaptive computation is applied to softening viscoplastic materials showing strain localization. As the
key ingredient of the adaptive strategy, a residual-type error estimator is generalized to deal with such highly
non-linear material model.
In several numerical examples the adaptive process is able to detect complex collapse modes that are not
captured by a "rst, even if "ne, mesh. Consequently, adaptive strategies are found to be essential to detect the


Source: Arroyo, Marino - Departament de Matemàtica Aplicada III, Universitat Politècnica de Catalunya


Collections: Engineering; Materials Science