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Quadratic-stretch elasticity (Q5867023)

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scientific article; zbMATH DE number 7590434

Language	Label	Description	Also known as
English	Quadratic-stretch elasticity	scientific article; zbMATH DE number 7590434

Statements

scholarly article

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Quadratic-stretch elasticity (English)

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10.1177/10812865211022417

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Mathematics and Mechanics of Solids

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publication date

22 September 2022

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full work available at URL

https://arxiv.org/abs/2104.11714

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Mathematics Subject Classification ID

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zbMATH DE Number

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zbMATH Keywords

nonlinear elasticity

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stretch

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rotation

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Biot strain

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invariants

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explicit formulation

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MaRDI profile type

MaRDI publication profile

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Elastic theory of unconstrained non-Euclidean plates

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A continuum mechanics based derivation of Reissner's large-displacement finite-strain beam theory: the case of plane deformations of originally straight Bernoulli-Euler beams

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Some observations on variational elasticity and its application to plates and membranes

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On the Kirchhoff-Love hypothesis (Revised and Vindicated)

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General solutions for plane extensible elasticae having nonlinear stress-strain laws

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On one-dimensional finite-strain beam theory: the plane problem

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An exact solution in a nonlinear theory of rods

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Behaviour of the extensible elastical solution

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Nonlinear problems of elasticity

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Plane strain problems for a perfectly elastic material of harmonic type

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A shell theory with independent rotations for relaxed Biot stress and right stretch strain

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A variational formulation for finite elasticity with independent rotation and Biot-axial fields

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Gaussian curvature from flat elastica sheets

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Tension-field theory

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On the origins of the idea of the multiplicative decomposition of the deformation gradient

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Exact theory of stress and strain in rods and shells

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On the uniqueness of the square-root of a symmetric, positive-definite tensor

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Determination of the stretch and rotation in the polar decomposition of the deformation gradient

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Determination of \(C^{1/2}\), \(C^{-1/2}\) and more general isotropic tensor functions of C

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The square root of a three-dimensional positive tensor

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On the Direct Determination of the Rotation Tensor from the Deformation Gradient

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Determination of the rotation tensor in the polar decomposition

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On the explicit determination of the polar decomposition in \(n\)-dimensional vector spaces

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Direct determination of the rotation in the polar decomposition of the deformation gradient by maximizing a Rayleigh quotient

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\(\mathbf{U} = \mathbf{C}^{1/2}\) and its invariants in terms of \(\mathbf{C}\) and its invariants

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Explicit representation for the \(\mathrm{SO}(3)\) rotation tensor of deformable bodies

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Alternate stress and conjugate strain measures, and mixed variational formulations involving rigid rotations, for computational analyses of finitely deformed solids, with application to plates and shells—I

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Symmetric Cauchy stresses do not imply symmetric Biot strains in weak formulations of isotropic hyperelasticity with rotational degrees of freedom

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Finite strain solutions in compressible isotropic elasticity

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A new variational principle for finite elastic displacements

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On the work theorems for finite and incremental elastic deformations with discontinuous fields: A unified treatment of different versions

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The Biot stresses in nonlinear elasticity and the associated generalized variational principles

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Buckling equations for elastic shells with rotational degrees of freedom undergoing finite strain deformation

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Formulations of finite elasticity with independent rotations

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An exact finite rotation shell theory, its mixed variational formulation and its finite element implementation

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On drilling degrees of freedom in nonlinear elasticity and a hyperelastic material description in terms of the stretch tensor. I: Theory

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On drilling degrees of freedom in nonlinear elasticity and a hyperelastic material description in terms of the stretch tensor. II: Application to membranes

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On the derivatives of the stretch and rotation with respect to the deformation gradient

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Invariants of the Stretch Tensors and their Application to Finite Elasticity Theory

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Transversely isotropic biological, soft tissue must be modelled using both anisotropic invariants

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A unifying treatise of variational principles for two types of micropolar continua

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On natural strain measures of the non linear micropolar continuum

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On the representation of finite rotation in nonlinear field theory of continuum mechanics

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Continuum plasticity at finite strain for stress paths of arbitrary composition and direction

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Deformations of an elastic, internally constrained material. I: Homogeneous deformations

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Sitelinks

Mathematics(1 entry)

mardi Publication:5867023

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