On the Development of Volumetric Strain Energy Functions

Doll, Stefan; Schweizerhof, Karl

doi:10.1115/1.321146

Cited by 147 publications

(110 citation statements)

References 20 publications

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“…This is a special case of the more general strain-energy function W =Ŵ (Ī 1 ,Ī 2 ) + U(J) that has been examined by Doll and Schweizerhof [43]. It can easily be shown that with W given by (5.4) and the pre-stress as assumed above, the strong ellipticity condition (2.17) is satisfied if and only ifp > −1, wherep has the same meaning as in Section 2 and in the present case is half of the actual tension in the fibre direction.…”

Section: Surface Waves In a Pre-stressed Inextensible Materialsmentioning

confidence: 99%

Stroh formulation for a generally constrained and pre-stressed elastic material

Edmondson

2009

International Journal of Non-Linear Mechanics

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The Stroh formalism is essentially a spatial Hamiltonian formulation and has been recognized to be a powerful tool for solving elasticity problems involving generally anisotropic elastic materials for which conventional methods developed for isotropic materials become intractable. In this paper we develop the Stroh/Hamiltonian formulation for a generally constrained and prestressed elastic material. We derive the corresponding integral representation for the surface-impedance tensor and explain how it can be used, together with a matrix Riccati equation, to calculate the surface-wave speed. The proposed algorithm can deal with any form of constraint, pre-stress, and direction of wave propagation. As an illustration, previously known results are reproduced for surface waves in a pre-stressed incompressible elastic material and an unstressed inextensible fibre-reinforced composite, and an additional example is included analyzing the effects of pre-stress upon surface waves in an inextensible material.

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Section: Surface Waves In a Pre-stressed Inextensible Materialsmentioning

confidence: 99%

Stroh formulation for a generally constrained and pre-stressed elastic material

Edmondson

2009

International Journal of Non-Linear Mechanics

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“…(3.15) 2 which reflects a linear relationship between the pressure and the relative volume change. A more detailed description of the volumetric material response can be achieved by the adjustment of a more sophisticated volumetric energy U (cf Doll and Schweizerhof, 2000). However, such an approach would require a more thorough experimental study.…”

Section: Application To Metallic Materialsmentioning

confidence: 99%

Numerical implementation of finite strain elasto-plasticity without yield surface

Suchocki

2017

jtam

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In the present study, the finite element (FE) implementation of elasto-plasticity without a yield surface is discussed. For that purpose, the method of perturbing the deformation gradient tensor is employed to calculate approximate tangent moduli. The development of a user subroutine that enables one to use the proposed model within the FE program ABAQUS is covered. A number of exemplary numerical simulations is conducted in order to check the performance of this subroutine. Material parameter values determined for different materials are utilized. Finally, the presented constitutive equation is examined upon its ability to capture the shear-softening process.

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“…In [3,20] the isochoric-volumetric different forms of decoupling of the elastic strain energy function (cf. (5) in the paper) are analyzed.…”

Section: Final Remarksmentioning

confidence: 99%

Incompressible limit for a magnetostrictive energy functional

Gambin¹,

Bielski²

2013

Bulletin of the Polish Academy of Sciences: Technical Sciences

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Abstract. The modern materials undergoing large elastic deformations and exhibiting strong magnetostrictive effect are modelled here by free energy functionals for nonlinear and non-local magnetoelastic behaviour. The aim of this work is to prove a new theorem which claims that a sequence of free energy functionals of slightly compressible magnetostrictive materials with a non-local elastic behaviour, converges to an energy functional of a nearly incompressible magnetostrictive material. This convergence is referred to as a Γ-convergence. The non-locality is limited to non-local elastic behaviour which is modelled by a term containing the second gradient of deformation in the energy functional.

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On the Development of Volumetric Strain Energy Functions

Cited by 147 publications

References 20 publications

Stroh formulation for a generally constrained and pre-stressed elastic material

Stroh formulation for a generally constrained and pre-stressed elastic material

Numerical implementation of finite strain elasto-plasticity without yield surface

Incompressible limit for a magnetostrictive energy functional

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