Homogenization of nonlinearly elastic materials, microscopic bifurcation and macroscopic loss of rank-one convexity
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Publication:684420
DOI10.1007/BF00380256zbMath0801.73008OpenAlexW2021965384MaRDI QIDQ684420
Giuseppe Geymonat, Nicholas Triantafyllidis, Stefan Müller
Publication date: 15 September 1993
Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf00380256
linearized problemperiodic compositescommutabilitylong wavelength instabilitiesmacroscopic instabilitiesmicroscopic instabilities
Nonlinear elasticity (74B20) Inhomogeneity in solid mechanics (74E05) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
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- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Homogenization of nonconvex integral functionals and cellular elastic materials
- Non-homogeneous media and vibration theory
- The emergence of shear bands in plane strain
- Convexity conditions and existence theorems in nonlinear elasticity
- Periodic solutions and homogenization of non linear variational problems
- Comportements local et macroscopique d'un type de milieux physiques heterogenes
- Elastic moduli of perfectly disordered composite materials
- Elastic properties of reinforced solids: Some theoretical principles
- Quasi-convexity and the lower semicontinuity of multiple integrals
- Homogenization and Linear Thermoelasticity
- On the Comparison Between Microscopic and Macroscopic Instability Mechanisms in a Class of Fiber-Reinforced Composites
- Optimal design and relaxation of variational problems, I
- Bounds and Self-Consistent Estimates for the Overall Properties of Nonlinear Composites
- A Variational Approach to the Theory of the Effective Magnetic Permeability of Multiphase Materials
- Variational and Related Methods for the Overall Properties of Composites
- Rank-one convexity does not imply quasiconvexity
- Semicontinuity problems in the calculus of variations