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On a relaxation‐based and time‐incremental approach to damage modeling
Author(s) -
Schwarz Stephan,
Hackl Klaus,
Junker Philipp
Publication year - 2018
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201800131
Subject(s) - finite element method , regularization (linguistics) , boundary value problem , regular polygon , mathematics , viscoplasticity , mathematical optimization , relaxation (psychology) , computer science , mathematical analysis , structural engineering , geometry , constitutive equation , engineering , psychology , social psychology , artificial intelligence
Damage models, which are characterized by softening effects, suffer from ill‐posed boundary value problems that result in mesh‐dependent finite‐element results. Regularization strategies counteract these problems by taking into account the non‐local behavior such as realized by the gradient‐enhanced formulation presented in [1]. Two variational equations are resulting at the expense of numerical effort but, however, mesh‐independent finite‐element results are provided. In contrast, we present a novel approach to the regularization of damage processes based on relaxed energies of two‐state models that are formulated in a time‐incremental way. The energies within each time step remain convex but the overall behavior is non‐coercive in order to maintain the characteristic stress‐behavior of damage models. Therefore, mesh‐independent results with less numerical effort are achieved.