Quasistatic Evolution Problems for Linearly Elastic–Perfectly Plastic Materials

By Gianni Dal Maso, Antonio DeSimone, Maria Giovanna Mora. 2004

227 citations recorded by the source corpus.

The problem of quasistatic evolution in small strain associative elastoplasticity is studied in the framework of the variational theory for rate-independent processes. Existence of solutions is proved through the use of incremental variational problems in spaces of functions with bounded deformation. This approach provides a new approximation result for the solutions of the quasistatic evolution problem, which are shown to be absolutely continuous in time. Four equivalent formulations of the problem in rate form are derived. A strong formulation of the flow rule is obtained by introducing a precise definition of the stress on the singular set of the plastic strain.

Subfields: Biomedical Engineering, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/dcf223e63d6f9fc5ac9516889e256bc6ab19397a

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In Biomedical Engineering

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

WELL-POSEDNESS AND LONG-TIME BEHAVIOR FOR A CLASS OF DOUBLY NONLINEAR EQUATIONS (2006, background): “1) stem in connection with phase change phenomena [14, 17, 23, 32, 46, 47], gas flow through porous media [68], damage [15, 16, 30, 31, 54], and, in the specific case α(λr) = α(r) for all λ > 0 and r ∈ R (which is however not included in the present analysis), elastoplasticity [25, 50, 51, 52], brit”
Coupling damage and plasticity for a phase-field regularisation of brittle, cohesive and ductile fracture: One-dimensional examples (2017, unknown): “For perfect plasticity, p can localise and, consequently, induce similar singularities on u ′ , [33,37,38,64] .”
Quasistatic evolution for Cam-Clay plasticity: a weak formulation via viscoplastic regularization and time rescaling (2011, background): “The former is similar to the energy-dissipation balance of perfect plasticity [5] with two main differences: first, the set K , and hence the plastic dissipation, depend now on ζ◦(s, x); second, there is an additional dissipative term, ∫ S”