In this paper we obtain the constitutive equation for the second Piola-Kirchhoff stress tensor according to the linearized finite theory of elasticity for hyperelastic constrained materials. We show that in such a theory the three stress tensors (Cauchy stress tensor, first and second Piola-Kirchhoff stress tensor) differ by terms that are first order in the strain, while in classical linear theory of elasticity they are indistinguishable to first order of approximation both for unconstrained and constrained materials. Moreover we show that the constitutive equations for the three stress tensors usually adopted in classical linear elasticity are not correct to first order in the strain. Finally we provide an example for a particular material symmetry and for a particular constraint in which the three stress tensors coincide, while in general they are different.

On the three stress tensors for linearly elastic constrained materials

TONON, Maria Luisa
2014-01-01

Abstract

In this paper we obtain the constitutive equation for the second Piola-Kirchhoff stress tensor according to the linearized finite theory of elasticity for hyperelastic constrained materials. We show that in such a theory the three stress tensors (Cauchy stress tensor, first and second Piola-Kirchhoff stress tensor) differ by terms that are first order in the strain, while in classical linear theory of elasticity they are indistinguishable to first order of approximation both for unconstrained and constrained materials. Moreover we show that the constitutive equations for the three stress tensors usually adopted in classical linear elasticity are not correct to first order in the strain. Finally we provide an example for a particular material symmetry and for a particular constraint in which the three stress tensors coincide, while in general they are different.
2014
91
4
459
475
http://www.ijpam.eu
Hyperelastic constrained materials. Linearized finite elasticity. Stress tensors.
M.L. TONON
File in questo prodotto:
File Dimensione Formato  
On the three stress tensors.pdf

Accesso aperto

Tipo di file: PDF EDITORIALE
Dimensione 111.52 kB
Formato Adobe PDF
111.52 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/143099
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? ND
social impact