Energetic formulation of multiplicative elasto-plasticity using dissipation distances

By Alexander Mielke. 2003

197 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/d805009c8e06c1a09b0b231717c5083ee1d8ea1b

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In Biomedical Engineering

In Mechanics of Materials

Citations in the corpus

Modeling solutions with jumps for rate-independent systems on metric spaces (2008, background): “Furthermore, Q may even lack a linear structure (in these cases we will denote it by the calligraphic letter Q), like for finite-strain elastoplasticity [19, 18] or for quasistatic evolution of fractures [7].”
On the relation between the principle of maximum dissipation and inelastic evolution given by dissipation potentials (2008, methodology): “Related approaches and results are given in Ortiz & Repetto (1999), Miehe & Lambrecht (2003), Miehe et al. (2004) and Mielke (2003).”
Nonsmooth analysis of doubly nonlinear evolution equations (2011, background): “In fact, state-dependent dissipations naturally occur in various plasticity models, see for example [31, 30, 5].”
On the Relation between Gradient Flows and the Large-Deviation Principle, with Applications to Markov Chains and Diffusion (2013, unknown): “…evolution; this can be seen from writing the evolution as ˙ z t = D ξ Ψ ∗ z t , − D S ( z t ) . concerning Finally, the symmetry of Ψ: this property is natural in many systems, in which forward and backward velocities lead to the same dissipation (exceptions arise e.g. in plasticity [Mie03, Sect.”
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”
Existence results for a class of rate-independent material models with nonconvex elastic energies (2006, background): “In many situations the above described model is intractable, either because the suitable tools are not yet developed or because the model is badly behaved resulting in the formation of microstructure, see [6], [7], [28], [29], [33], [39].”
Chapter 6 – Evolution of Rate-Independent Systems (2005, background): “It was first proposed in [Mie03a] to study a version of the incremental problem, where global minimization is replaced by a local one, namely inside a ball in the d-distance of small radius δ > 0:”
BV SOLUTIONS AND VISCOSITY APPROXIMATIONS OF RATE-INDEPENDENT SYSTEMS ∗ (2009, unknown): “Published December 23, 2010.”
A Vanishing Viscosity Approach to Quasistatic Evolution in Plasticity with Softening (2006, background): “Among the papers which are closest in spirit to our approach we quote [25], [26], [21], and [22].”
A metric approach to a class of doubly nonlinear evolution equations and applications (2008, background): “Rate-independent models indeed occur, for instance, in elastoplasticity [29, 30, 31, 32, 19, 20, 24], in damage [39], in the quasistatic evolution of fractures [21, 28], in shape memory alloys [40, 41, 38], and in several other contexts, see the survey [33] and the references therein.”
Existence results for energetic models for rate-independent systems (2005, methodology): “See [ Mie03a ] for a general setup for rate-independent material models in the framework of “standard generalized materials”.”