Existence results for energetic models for rate-independent systems

By Andreas Mainik, Alexander Mielke. 2005

222 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/3155c2cb7eaf7138f4ab6dffbe4eb6b092e42e75

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In Control and Systems Engineering

In Statistical and Nonlinear Physics

Citations in the corpus

Quasistatic Crack Growth in Nonlinear Elasticity (2005, background): “This definition fits the general scheme of the continuous-time energetic formulation of rate-independent processes developed in [27, 28, 25].”
BV SOLUTIONS AND VISCOSITY APPROXIMATIONS OF RATE-INDEPENDENT SYSTEMS ∗ (2009, background): “Furthermore, as shown in [29,32], it is amenable to analysis in very general ambient spaces, even with no underlying linear structure.”
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 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.”
Chapter 6 – Evolution of Rate-Independent Systems (2005, unknown): “In [MM04a] the slightly stronger assumption yk = (φk, zk) ∈ S(t) and zk Z → z =⇒ φk F → φ (5.”
Existence results for a class of rate-independent material models with nonconvex elastic energies (2006, background): “As mentioned in the introduction, the proof puts the new ideas of a similar existence result for quasi-static brittle fracture evolution [11], [14] into the more general context of abstract rate-independent models, as studied in [25].”
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 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”
An asymmetric Arzelà–Ascoli theorem (2007, background): “In the realms of applied mathematics and materials science we find many recent applications of asymmetric metric spaces; for example, in rate-independent models for plasticity [6], shape-memory alloys [8], and models for material failure [12].”