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Tonon, Maria Luisa

doi:10.1023/a:1027334213793

Cited by 5 publications

(6 citation statements)

References 22 publications

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“…This paper represents a natural carrying on of [1], [2], [6], [7], [8], [9], [10], [11], since the linearized finite theory of elasticity is here applied to constrained materials with orthotropic symmetry.…”

Section: Discussionmentioning

confidence: 99%

“…The results obtained in [1], [2], [3], [10] emphasize the need to use the LFTE in order to have the accuracy required by a linear model, since the classical linear theory of elasticity (CLTE in the following) provides constitutive equations that are not accurate to first order in the displacement gradient. The application of LFTE also to static problems (see [1], [3], [8], [9]) or dynamical problems (see [6], [7]) confirms the inadequacy of CLTE.…”

Section: Introductionmentioning

confidence: 90%

“…Expansion (17) takes into account the conditionĉ(O) = 0 provided by (6), while expansion (18) has been obtained under the hypothesis…”

Section: Linear Constitutive Equations According To the Linearized Fimentioning

confidence: 99%

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Constrained Linearly Elastic Materials Reinforced by Two Families of Fibres

Tonon

2016

Int. J. of Pure and Appl. Math.

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In this paper the linearized finite theory of elasticity is applied to obtain linear constitutive equations for constrained materials reinforced by two orhogonal families of fibres. Explicit expressions for the three stress tensors are derived for inextensible in both fibre directions materials, for incompressible materials and finally for materials that are both incompressible and inextensible in the two fibre directions. Comparison with the corresponding constitutive equations provided by the classical approach shows that the classical equations are not accurate to first order in the strain.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 90%

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Constrained Linearly Elastic Materials Reinforced by Two Families of Fibres

Tonon

2016

Int. J. of Pure and Appl. Math.

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“…In the previous formulas and in the following O is the zero tensor, while the symbol · denotes scalar product; note that the hypothesis of zero residual stress, that is ∂Ŵ ∂E G (O) = O, has been used to write expansion (10), while expansion (11) takes into account the conditionĉ (O) = 0 provided by (5). The final expression for the Cauchy stress T appropriate for LFTE is the following…”

Section: The First-order Stress Relations According To the Linearizedmentioning

confidence: 99%

“…Comparison shows that only LFTE provides stress relations which are accurate to first order of approximation with respect to the displacement gradient. Many other papers are devoted to LFTE (see [2], [4], [5], [6], [7], [8]). They concern both static problems (see [2], [4], [7], [8]) and dynamical problems (see [5], [6]); in both cases application of LFTE shows that for constrained materials CLTE is inadequate to guarantee the accuracy required by a linear model.…”

Section: Introductionmentioning

confidence: 99%

Second-Order Stress Relations for Hyperelastic Constrained Materials

Tonon¹

2014

Int. J. of Pure and Appl. Math.

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In this paper the second-order stress relations for hyperelastic internally constrained materials are derived, both for the Cauchy stress and the two Piola-Kirchhoff stresses. In our approach the constitutive equations are obtained by the corresponding finite constitutive equations by means of suitable expansions. In contrast to the classical approach, our method guarantees the accuracy required by a second-order theory. For incompressible isotropic materials explicit stress relations are derived and compared with those used in classical theory, in order to show that only our constitutive equations are accurate to second order of approximation.

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Weak shock waves and shear bands in compressible, inextensible thermoelastic solids

Alyavuz

Gültop

2009

Arch Appl Mech

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A study of weak shock waves propagating into a solid, which is compressible but temperaturedependent extensible in a specified direction is presented. The inextensible solid is also considered. The constitutive equations of constrained thermoelastic material are written as the summation of constrained and unconstrained counterparts of the relevant quantities. The equation of motion of weak shock waves, which is recovered by the theory of singular surfaces, reduces to an eigenvalue problem. The solution of this eigenvalue problem yields the speeds of propagation of weak shock waves. In the case of an undeformed solid, the speeds of these waves are explicitly expressed. Additionally, a discussion on the ductility limits of constrained thermoelastic material subjected to the uniaxial and biaxial extensions is presented.

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Untitled

Cited by 5 publications

References 22 publications

Constrained Linearly Elastic Materials Reinforced by Two Families of Fibres

Constrained Linearly Elastic Materials Reinforced by Two Families of Fibres

Second-Order Stress Relations for Hyperelastic Constrained Materials

Weak shock waves and shear bands in compressible, inextensible thermoelastic solids

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