When rank-one convexity meets polyconvexity: an algebraic approach to elastic binodal
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Publication:2633558
DOI10.1007/s00332-018-9485-7zbMath1411.74012OpenAlexW2884658347WikidataQ129501272 ScholiaQ129501272MaRDI QIDQ2633558
Yury Grabovsky, L. M. Truskinovskij
Publication date: 9 May 2019
Published in: Journal of Nonlinear Science (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00332-018-9485-7
Sensitivity, stability, well-posedness (49K40) Structured surfaces and interfaces, coexistent phases (74A50) Energy minimization in equilibrium problems in solid mechanics (74G65) Variational principles of physics (49S05)
Related Items (6)
Numerical approaches for investigating quasiconvexity in the context of Morrey's conjecture ⋮ Morrey's conjecture for the planar volumetric-isochoric split: least rank-one convex energy functions ⋮ A class of nonlinear elasticity problems with no local but many global minimizers ⋮ Explicit relaxation of a two-well Hadamard energy ⋮ The quasiconvex envelope of conformally invariant planar energy functions in isotropic hyperelasticity ⋮ Sharp rank-one convexity conditions in planar isotropic elasticity for the additive volumetric-isochoric split
Cites Work
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- Legendre-Hadamard conditions for two-phase configurations
- Marginal material stability
- Normality condition in elasticity
- A partial differential equation for the rank one convex envelope
- Two-phase deformations of elastic solids
- Roughening instability of broken extremals
- Finite deformation by mechanical twinning
- Quasiconvexity and relaxation of nonconvex problems in the calculus of variations
- Dilatationally nonlinear elastic materials. I: Some theory
- Dilatationally nonlinear elastic materials. II: An example illustrating stress concentration reduction
- Linear \(\Gamma \)-limits of multiwell energies in nonlinear elasticity theory
- Continuum theory of dilatant transformation toughening in ceramics
- Fine phase mixtures as minimizers of energy
- Nilpotent energies in liquid crystal theory
- Regularization of optimal design problems for bars and plates. I
- The relaxation of a double-well energy
- Equilibrium of bars
- On the non-locality of quasiconvexity
- Phase transformations surfaces and exact energy lower bounds
- Quadratic extremality conditions for broken extremals in the general problem of the calculus of variations
- Correction to: ``Derivation of a linearised elasticity model from singularly perturbed multiwell energy functionals
- On the existence of solutions to some problems of optimal design for bars and plates
- Regularity of quasiconvex envelopes
- The null set of the Euler-Lagrange operator
- The relaxation of two-well energies with possibly unequal moduli
- Quasi-convexity and the lower semicontinuity of multiple integrals
- Bounds and extremal microstructures for two-component composites: a unified treatment based on the translation method
- Proposed experimental tests of a theory of fine microstructure and the two-well problem
- Numerical Computation of Rank-One Convex Envelopes
- The Theory of Composites
- On conditions for polyconvexity
- From nonlinear to linearized elasticity via Γ-convergence: The case of multiwell energies satisfying weak coercivity conditions
- The mayer-bolza problem for multiple integrals and the optimization of the performance of systems with distributed parameters
- Plane elastic waves of finite amplitude. Hadamard materials and harmonic materials
- Quasi-Convexity and Lower Semi-Continuity of Multiple Variational Integrals of Any Order
- Direct methods in the calculus of variations
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