Book ChapterDOI
Variational models for microstructure and phase transitions
Stefan Müller
- pp 85-210
About:
The article was published on 1999-01-01. It has received 641 citations till now. The article focuses on the topics: Young measure & Quasiconvex function.read more
Citations
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Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications
TL;DR: In this paper, a review of continuum-based variational formulations for describing the elastic-plastic deformation of anisotropic heterogeneous crystalline matter is presented and compared with experiments.
Journal ArticleDOI
Regularity of minima: an invitation to the Dark Side of the Calculus of Variations
TL;DR: A survey of regularity results for both minima of variational integrals and solutions to non-linear elliptic, and sometimes parabolic, systems of partial differential equations can be found in this article.
Journal ArticleDOI
A polyconvex framework for soft biological tissues. Adjustment to experimental data
TL;DR: In this paper, a simple method for constructing transversely isotropic polyconvex functions suitable for the description of biological soft tissues is presented, where only a few parameters are necessary to approximate a variety of stress-strain curves and to satisfy the condition of a stress-free reference configuration a priori in the framework of polyconcaveity.
Journal ArticleDOI
A Variational Formulation of Rate-Independent Phase Transformations Using an Extremum Principle
TL;DR: In this paper, a rate-independent mesoscopic model for the hysteretic evolution of phase transformations in shape-memory alloys is proposed, using the deformation and phase-indicator function as basic unknowns and the potentials for the elastic energy and for the dissipation as constitutive laws.
Journal ArticleDOI
A variational approach for materially stable anisotropic hyperelasticity
TL;DR: In this article, an anisotropic stored energy function which satisfies a priori the Legendre-Hadamard condition was proposed, which is strongly related to the material stability of the constitutive equations.
References
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Journal ArticleDOI
The Determination of the Elastic Field of an Ellipsoidal Inclusion, and Related Problems
TL;DR: In this paper, it is shown that to answer several questions of physical or engineering interest, it is necessary to know only the relatively simple elastic field inside the ellipsoid.
Book
Geometric Measure Theory
TL;DR: In this article, Grassmann algebras of a vectorspace have been studied in the context of the calculus of variations, and a glossary of some standard notations has been provided.
Book
Measure theory and fine properties of functions
TL;DR: In this article, the authors define and define elementary properties of BV functions, including the following: Sobolev Inequalities Compactness Capacity Quasicontinuity Precise Representations of Soboleve Functions Differentiability on Lines BV Function Differentiability and Structure Theorem Approximation and Compactness Traces Extensions Coarea Formula for BV Functions isoperimetric inequalities The Reduced Boundary The Measure Theoretic Boundary Gauss-Green Theorem Pointwise Properties this article.
BookDOI
Multiple integrals in the calculus of variations
TL;DR: In this paper, a variational method in the theory of harmonic integrals has been proposed to solve the -Neumann problem on strongly pseudo-convex manifolds and parametric Integrals two-dimensional problems.