Rotational invariance conditions in elasticity, gradient elasticity and its connection to isotropy
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Publication:4563215
DOI10.1177/1081286516666134zbMath1391.74032arXiv1603.06153OpenAlexW2963328860MaRDI QIDQ4563215
Publication date: 7 June 2018
Published in: Mathematics and Mechanics of Solids (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1603.06153
orthogonal groupisotropyrotational invariancecovariancestrain gradient elasticitycouple stressframe-indifferenceinvariance conditionssymmetric stresspolar continuaform-invariancehyperstressesmodified couple-stress modelRayleigh product
Nonlinear elasticity (74B20) Equations linearized about a deformed state (small deformations superposed on large) (74B15)
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Cites Work
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- Local symmetry group in the general theory of elastic shells
- On the frame invariance of linear elasticity theory
- Covariance in linearized elasticity
- Conservation and balance laws in linear elasticity of grade three
- Subgrid interaction and micro-randomness - novel invariance requirements in infinitesimal gradient elasticity
- Elastic materials with couple-stresses
- Compatibility equations for large deformations
- The symmetry group of second-grade materials
- Symmetry considerations for materials of second grade
- On the impossibility of linear Cauchy and Piola-Kirchhoff constitutive theories for stress in solids
- Geometrical theory of uniform Cosserat media
- Homogeneity conditions for generalized Cosserat media
- Microstructures as a refinement of Cauchy theory. Problems of physical concreteness
- A new view on boundary conditions in the grioli-Koiter-Mindlin-toupin indeterminate couple stress model
- Stable identification of linear isotropic Cosserat parameters: bounded stiffness in bending and torsion implies conformal invariance of curvature
- Integrability conditions between the first and second Cosserat deformation tensor in geometrically nonlinear micropolar models and existence of minimizers
- Material inhomogeneities and their evolution. A geometric approch.
- Theories of elasticity with couple-stress
- The energy function for isotropic materials with couple stresses
- The energy function for anisotropic materials with couple stresses - cubic and hexagonal systems
- Effects of couple-stresses in linear elasticity
- Elasticita asimmetrica
- Finite gradient elasticity and plasticity: a constitutive mechanical framework
- Lie point symmetries, conservation and balance laws in linear gradient elastodynamics
- Material symmetry group and constitutive equations of micropolar anisotropic elastic solids
- Elasticity and Plasticity of Large Deformations
- Existence, Uniqueness and Stability in Linear Cosserat Elasticity for Weakest Curvature Conditions
- On constitutive and configurational aspects of models for gradient continua with microstructure
- Generalized Hooke's law for isotropic second gradient materials
- NOTES ON STRAIN GRADIENT PLASTICITY: FINITE STRAIN COVARIANT MODELLING AND GLOBAL EXISTENCE IN THE INFINITESIMAL RATE-INDEPENDENT CASE
- Linear Cosserat Elasticity, Conformal Curvature and Bounded Stiffness
- A variant of the linear isotropic indeterminate couple-stress model with symmetric local force-stress, symmetric nonlocal force-stress, symmetric couple-stresses and orthogonal boundary conditions
- Curl bounds Grad on SO(3)
- Nonlinear problems of elasticity
