The isotropic Cosserat shell model including terms up to \(O(h^5)\). I: Derivation in matrix notation
From MaRDI portal
Publication:2224459
DOI10.1007/s10659-020-09796-3zbMath1456.74116arXiv2003.00549OpenAlexW3092131173MaRDI QIDQ2224459
Ionel-Dumitrel Ghiba, Patrizio Neff, Peter Lewintan, Mircea Bîrsan
Publication date: 3 February 2021
Published in: Journal of Elasticity (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2003.00549
dimensional reductionisotropydislocation density tensorwryness tensorin-plane drill rotation6-parameter resultant shellgeometrically nonlinear shell
Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics (74G10) Shells (74K25)
Related Items
A constrained Cosserat shell model up to order \(O(h^5)\): modelling, existence of minimizers, relations to classical shell models and scaling invariance of the bending tensor ⋮ On solvability of initial boundary-value problems of micropolar elastic shells with rigid inclusions ⋮ A linear isotropic Cosserat shell model including terms up to \(O(h^5)\). Existence and uniqueness ⋮ A geometrically nonlinear Cosserat shell model for orientable and non-orientable surfaces: discretization with geometric finite elements ⋮ Linear constrained Cosserat-shell models including terms up to \({O}(h^5)\): conditional and unconditional existence and uniqueness ⋮ Hilbert complexes: analysis, applications, and discretizations. Abstracts from the workshop held June 19--25, 2022 ⋮ A geometrically nonlinear Cosserat (micropolar) curvy shell model via gamma convergence ⋮ The isotropic Cosserat shell model including terms up to \(O(h^5)\). II: Existence of minimizers ⋮ Alternative derivation of the higher-order constitutive model for six-parameter elastic shells
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Numerical treatment of a geometrically nonlinear planar Cosserat shell model
- Thermomechanics of shells undergoing phase transition
- Orientation-preserving condition and polyconvexity on a surface: application to nonlinear shell theory
- Strong convergence results for the asymptotic behavior of the 3D-shell model
- A new linear shell model for shells with little regularity
- A finite-strain elastic-plastic Cosserat theory for polycrystals with grain rotations
- On natural strain measures of the non linear micropolar continuum
- On shear correction factors in the nonlinear theory of elastic shells
- Existence theorem for geometrically nonlinear Cosserat micropolar model under uniform convexity requirements
- On material conservation laws for a consistent plate theory
- Local symmetry group in the general theory of elastic shells
- Nonlinear Korn inequalities
- Formulations of finite elasticity with independent rotations
- Convexity conditions and existence theorems in nonlinear elasticity
- Nonlinearly elastic shell models: A formal asymptotic approach. I: The membrane model
- Nonlinearly elastic shell models: A formal asymptotic approach. II: The flexural model
- A justification of nonlinear properly invariant plate theories
- Nonlinear shell formulations for complete three-dimensional constitutive laws including composites and laminates
- Large elasto-plastic finite element analysis of solids and shells with the enhanced assumed strain concept
- On the physical significance of higher-order kinematic and static variables in a three-dimensional shell formulation
- Shells without drilling rotations: a representation theorem in the framework of the geometrically nonlinear 6-parameter resultant shell theory
- On Grioli's minimum property and its relation to Cauchy's polar decomposition
- Existence theorem for a nonlinear elliptic shell model
- A geometrically exact viscoplastic membrane-shell with viscoelastic transverse shear resistance avoiding degeneracy in the thin-shell limit. I: The viscoelastic membrane-plate
- The nonlinear theory of elastic shells with phase transitions
- On consistent plate theories
- Theories of plates and shells. Critical review and new applications. Papers from the EUROMECH colloquium 444, Bremen, Germany, September 22--25, 2002.
- Restrictions on nonlinear constitutive equations for elastic shells
- The limits of Hamiltonian structures in three-dimensional elasticity, shells, and rods
- Koiter's shell theory from the perspective of three-dimensional nonlinear elasticity
- Growth and non-metricity in Föppl-von Kármán shells
- The isotropic Cosserat shell model including terms up to \(O(h^5)\). II: Existence of minimizers
- A new linear Naghdi type shell model for shells with little regularity
- Finite elastic wrinkling deformations of incompressible fiber-reinforced plates
- A geometrically exact Cosserat shell model for defective elastic crystals. Justification via \(\Gamma\)-convergence
- Asymptotic analysis of linearly elastic shells. II: Justification of flexural shell equations
- Asymptotic analysis of linearly elastic shells. III: Justification of Koiter's shell equations
- A geometrically exact Cosserat shell-model including size effects, avoiding degeneracy in the thin shell limit. I: Formal dimensional reduction for elastic plates and existence of minimizers for positive Cosserat couple modulus
- On a model of a flexural prestressed shell
- Cosserat-Type Shells
- Existence of minimizers in the geometrically non-linear 6-parameter resultant shell theory with drilling rotations
- A Fully Nonlinear Thin Shell Model of Kirchhoff-Love Type
- Local existence and uniqueness for a geometrically exact membrane-plate with viscoelastic transverse shear resistance
- THE REISSNER–MINDLIN PLATE IS THE Γ-LIMIT OF COSSERAT ELASTICITY
- Rotation and strain
- Semicontinuity theorem in the micropolar elasticity
- A geometrically exact thin membrane model—investigation of large deformations and wrinkling
- On the linear theory of micropolar plates
- Shell theory versus degeneration—a comparison in large rotation finite element analysis
- The Nonlinear Theory of Elastic Shells
- An existence theorem for a two-dimensional nonlinear shell model of Koiter’s type
- Explicit Global Minimization of the Symmetrized Euclidean Distance by a Characterization of Real Matrices with Symmetric Square
- A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity
- New estimates of the distance between two surfaces in terms of the distance between their fundamental forms
- Iterative methods for solving a poroelastic shell model of Naghdi's type
- Refined dimensional reduction for isotropic elastic Cosserat shells with initial curvature
- Shell design from planar pre-stressed structures
- Derivation of a refined six-parameter shell model: descent from the three-dimensional Cosserat elasticity using a method of classical shell theory
- Existence theorem for nonlinear micropolar elasticity
- A GEOMETRICALLY EXACT PLANAR COSSERAT SHELL-MODEL WITH MICROSTRUCTURE: EXISTENCE OF MINIMIZERS FOR ZERO COSSERAT COUPLE MODULUS
- Curl bounds Grad on SO(3)