Finite element formulation of the Ogden material model with application to rubber-like shells

DOI<1279::AID-NME437>3.0.CO;2-I 10.1002/(SICI)1097-0207(19980815)42:7<1279::AID-NME437>3.0.CO;2-IzbMath0912.73052OpenAlexW2115574609MaRDI QIDQ4209704

Mikhail Itskov, Yavuz Başar

Publication date: 25 May 1999

Full work available at URL: https://doi.org/10.1002/(sici)1097-0207(19980815)42:7<1279::aid-nme437>3.0.co;2-i

zbMATH Keywords

strain energy densitylarge strainstransverse shear strainsright Cauchy-Green tensorfinite rotationsvariational proceduremultiple eigenvaluesincompressibility conditionstretching parameterfour node isoparametric finite elementsix-parametric shell kinematics

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Finite element methods applied to problems in solid mechanics (74S05) Optimization of other properties in solid mechanics (74P10) Membranes (74K15)

Related Items

Analysis of thin shells using anisotropic polyconvex energy densities, Stabilized formulation for phase‐field fracture in nearly incompressible hyperelasticity, A generalized orthotropic hyperelastic material model with application to incompressible shells, A reduced integration solid-shell finite element based on the EAS and the ANS concept-Large deformation problems, A robust nonlinear solid shell element based on a mixed variational formulation, Robust numerical analysis of homogeneous and non-homogeneous deformations, On the theory of fourth-order tensors and their applications in computational mechanics, Finite element linear and nonlinear, static and dynamic analysis of structural elements – an addendum – A bibliography (1996‐1999)

Cites Work

• The analysis of incompressible hyperelastic bodies by the finite element method
• Determination of \(C^{1/2}\), \(C^{-1/2}\) and more general isotropic tensor functions of C
• A three-dimensional finite-strain rod model. II. Computational aspects
• On a stress resultant geometrically exact shell model. IV: Variable thickness shells with through-the-thickness stretching
• A nonlinear theory for sandwich shells including the wrinkling phenomenon
• Theory and numerical analysis of shells undergoing large elastic strains
• Quasi-incompressible finite elasticity in principal stretches. Continuum basis and numerical algorithms
• Shear deformation models for large-strain shell analysis
• Refined shear-deformation models for composite laminates with finite rotations
• On the behaviour of rubberlike materials in compression and shear
• A theory and finite element formulation of shells at finite deformations involving thickness change: Circumventing the use of a rotation tensor
• A finite element formulation for nonlinear incompressible elastic and inelastic analysis
• On the development of explicit robust schemes for implementation of a class of hyperelastic models in large‐strain analysis of rubbers
• Theory and finite element formulation of rubberlike membrane shells using principal stretches
• A fully non‐linear axisymmetrical quasi‐kirchhoff‐type shell element for rubber‐like materials
• Three‐dimensional extension of non‐linear shell formulation based on the enhanced assumed strain concept
• Finite element analysis of hyperelastic thin shells with large strains