A Variational Formulation of¶Rate-Independent Phase Transformations¶Using an Extremum Principle

By Alexander Mielke, Florian Theil, V. Levitas. 2002

309 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/513102427277a261bcbaebaa395b326775f9cf77

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In Civil and Structural Engineering

In Materials Chemistry

Citations in the corpus

Existence results for a class of rate-independent material models with nonconvex elastic energies (2006, background): “[36]); for magnetism the appropriate choice is Z 1⁄4 S 1 (cf.”
Gradient flows of non convex functionals in Hilbert spaces and applications (2006, methodology): “[22, 26, 30]), and has been proposed (in an even more general formulation) as a possible general method to study Gradient Flows in [19] (see also the lecture notes [1, 3]).”
Nonsmooth analysis of doubly nonlinear evolution equations (2011, background): “Note that we follow the ideas in [26, 38], where W (·, z) is considered to be a polyconvex relaxation, under given volume fractions of the different phases.”
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”
A Vanishing Viscosity Approach to Quasistatic Evolution in Plasticity with Softening (2006, background): “According to the energetic approach to rate-independent processes developed in [24], [18], [23], the variational formulation of the quasistatic evolution problem consists in finding functions u(t, x), e(t, x), p(t, x), and z(t, x) satisfying the following conditions: (vf1) global stability: for ever”
Γ-limits and relaxations for rate-independent evolutionary problems (2008, background): “[14,25,27, 32,34]), there is still a need to develop a theory for parameter dependence and for numerical approximation properties.”
A robust model of pseudoelasticity in shape memory alloys (2013, unknown): “, [28, 29, 30, 31, 32, 33, 34], including modelling of SMA single crystals, e.”
Chapter 6 – Evolution of Rate-Independent Systems (2005, methodology): “However, the case with only two phases (m = 2) has been treated in [MTL02] under the additional assumption that the elastic behavior is linear and both phases have the same elastic tensor.”