Boundary layers in finite thermoelasticity

Rajagopal, K. R.

doi:10.1007/bf00040851

Cited by 25 publications

(3 citation statements)

References 40 publications

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“…More recently, Rajagopal and coauthors (see for example [19,25,[37][38][39]) have considered the possibility that the deformation of non-linear elastic solids within a thermodynamic framework could exhibit boundary layers or shear concentration zones in that the strains could be concentrated adjacent (that is that the gradients of strain could be large) to solid boundaries or to special regions. While they assume that the shear modulus of the material can depend on the temperature and also possibly on the shear, they consider the following special constitutive relation for the heat flux vector:…”

Section: Introductionmentioning

confidence: 99%

Response of an Elastic Body whose Heat Conduction Is Pressure Dependent

Rajagopal

Saccomandi

2011

J Elast

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The properties of many real materials such as the viscosity, thermal and electrical conductivity, specific heat, relaxation time, as well as optical properties, depend upon the pressure to which the body is subject. For instance, the viscosity of fluids can vary by several orders of magnitude due to the variation in the pressure. In this paper we investigate the change in the response of an elastic solid due to the thermal conductivity being pressure dependent. It is well known that higher pressure leads to reduced molecular mobility, in rubber-like materials, leading in turn to higher cross-linking reaction rates. We find that the response of the solid is quite different from the classical response that is obtained by using Fourier's law of heat conduction. The theoretical predictions according to the assumption that the thermal conductivity is pressure dependent, are in keeping with experimental results concerning the vulcanization of rubbers wherein one observes the conduction to be dependent on the pressure. To our knowledge, this is the first theoretical study that evaluates the response of non-linear elastic solids due the thermal conductivity depending on the pressure.

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Section: Introductionmentioning

confidence: 99%

Response of an Elastic Body whose Heat Conduction Is Pressure Dependent

Rajagopal

Saccomandi

2011

J Elast

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“…For this class of solutions, Petroski [15, 16] studied the deformation/heating of spherical sectors and the torsion/radial heating of a cylinder. Rajagopal et al [17, 18] investigated inhomogeneous deformations in nonlinear thermoelasticity and found, for a generalized neo-Hookean material with elastic properties that depend on stretch and temperature, exact solutions that exhibit a boundary-layer structure (i.e. the deformation in the core is homogeneous (or inhomogeneous) while in a layer adjacent to the boundary it is inhomogeneous (or homogeneous)).…”

Section: Introductionmentioning

confidence: 99%

Geometric nonlinear thermoelasticity and the time evolution of thermal stresses

Sadik

Yavari

2015

Mathematics and Mechanics of Solids

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In this paper we formulate a geometric theory of nonlinear thermoelasticity that can be used to calculate the time evolution of temperature and thermal stress fields in a nonlinear elastic body. In particular, this formulation can be used to calculate residual thermal stresses. In this theory the material manifold (natural stress-free configuration of the body) is a Riemannian manifold with a temperature-dependent metric. Evolution of the geometry of the material manifold is governed by a generalized heat equation. As examples, we consider an infinitely long circular cylindrical bar with a cylindrically symmetric temperature distribution and a spherical ball with a spherically-symmetric temperature distribution. In both cases we assume that the body is made of an arbitrary incompressible isotropic solid. We numerically solve for the evolution of thermal stress fields induced by thermal inclusions in both a cylindrical bar and a spherical ball, and compare the linear and nonlinear solutions for a generalized neo-Hookean material.

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“…The study nonlinear thermomechanical behavior problems remains subject of many researches in different fields, such as Rajagopal (1995), Rajagopal et al (1996), Brnic (2009), Canadija andBrnic (2010), Ozakin and Yavari (2010) and Yavari and Goriely (2013).…”

Section: Introductionmentioning

confidence: 99%

A Simple FEM Formulation Applied to Nonlinear Problems of Impact with Thermomechanical Coupling

Cavalcante

Maciel

Greco

et al. 2017

Lat. Am. j. solids struct.

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The thermal effects of problems involving deformable structures are essential to describe the behavior of materials in feasible terms. Verifying the transformation of mechanical energy into heat it is possible to predict the modifications of mechanical properties of materials due to its temperature changes. The current paper presents the numerical development of a finite element method suitable for nonlinear structures coupled with thermomechanical behavior; including impact problems. A simple and effective alternative formulation is presented, called FEM positional, to deal with the dynamic nonlinear systems. The developed numerical is based on the minimum potential energy written in terms of nodal positions instead of displacements. The effects of geometrical, material and thermal nonlinearities are considered. The thermodynamically consistent formulation is based on the laws of thermodynamics and the Helmholtz free-energy, used to describe the thermoelastic and the thermoplastic behaviors. The coupled thermomechanical model can result in secondary effects that cause redistributions of internal efforts, depending on the history of deformation and material properties. The numerical results of the proposed formulation are compared with examples found in the literature.

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Boundary layers in finite thermoelasticity

Cited by 25 publications

References 40 publications

Response of an Elastic Body whose Heat Conduction Is Pressure Dependent

Response of an Elastic Body whose Heat Conduction Is Pressure Dependent

Geometric nonlinear thermoelasticity and the time evolution of thermal stresses

A Simple FEM Formulation Applied to Nonlinear Problems of Impact with Thermomechanical Coupling

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