Jovo Jaric

University of Belgrade · Department of Mechanics

Using the apparatus of traditional differential geometry, the transport theorem is derived for the general case of a M-dimensional domain moving in a N-dimensional space, M>= N. The interesting concepts of curvatures and normals are illustrated with well-known examples of lines, surfaces and volumes. The special cases where either the space or the...

The framework of irreversible thermodynamics is fundamental in development of constitutive models. One of the important aspects of the extended irreversible thermodynamics is the relationship between the entropy flux and the heat flux, especially for phenomena far from equilibrium. In this paper, we demonstrate that the assumption that Lagrange mul...

In this paper, the anisotropic linear damage mechanics is presented starting from the principle of strain equivalence. The authors have previously derived damage tensor components in terms of elastic parameters of undamaged (virgin) material in closed form solution. Here, making use of this paper, we derived elasticity tensor as a function of damag...

In the light of recent progress in coarsening the discrete dislocation mechanics, we consider two questions relevant for the development of a mesoscale, size-dependent plasticity: (i) can the phenomenological expression for size-dependent energy, as quadratic form of Nye's dislocation density tensor, be justified from the point of view of dislocati...

The anisotropic elasticity damage mechanics is considered within the framework of the classical theory of elasticity. Starting from the principle of strain equivalence and notion of isotropic group, damage tensor components are derived in terms of elastic parameters of undamaged (virgin) material in closed-form solution. The procedure was applied f...

In this article, the modified Noether's theorem is established in general form. Then, the inverse theorem is used in nonlinear micropolar continua in order to derive one-parameter family of transformations under which the corresponding functional is invariant. Next, the conservation laws are written. They include, as a special case, the conservatio...

A very simple proof of the Gauss-Bonnet Theorem is given in invariant form, i.e., independent of the coordinate system of a surface.

The algebraic proof of the fundamental theorem concerning pure shear, by making use only of the notion of orthogonal projector, is presented. It has been shown that the state of pure shear is the same for all singular symmetric traceless tensors in E3, up to the rotation.

An objective of this paper is to reconcile the "symmetry" approach with the "symmetry groups" approach as these two different points of view presently coexist in the literature. Here we will be concerned exclusively with linearly elastic materials. The starting point for an analysis of the inherent symmetry of elastic materials is the notion of a s...

In this study, we considered the extended polar decomposition using a more general approach than the one provided by Boulanger and Hayes [Int. J. Non-Linear Mech. 36 (2001) 399–420]. We showed that the procedure of the decomposition could be simplified by considering its rotation tensor. Our method is illustrated by examples.

The study provides a natural generalization and unification of the classical treatments of compatibility conditions for moving surfaces and curves as submanifolds of E 3. The motivation for such a generalization is twofold. First, it is desirable to exhibit the compatibility conditions in a single unified set of formulas expressed in terms of stand...

Assuming the existence of genuine unsheared triads, we examine the possibility of having unsheared tetrads, particularly unsheared genuine tetrads.

The objective of this chapter is to present perspective of physics of interfaces from standpoint of continuum physics. This approach develops the foundations more carefully than the traditional approach where there is a tendency to hurry on to the applications, and moreover, provides a back- ground for advanced study in modern nonlinear continuum p...

Following the approach of M. E. Gurtin and P. Podio-Guidugli [J. Mech. Phys. Solids 46, No. 8, 1343–1378 (1998; Zbl 0955.74004)], we consider the problem of crack propagation based on the notion of configurational forces and couples in micropolar continua. The derivation of Eshelby relation is accomplished without recourse to constitutive equations...

The procedure of the decomposition of symmetric tensors into traceless symmetric tensors is given. Then this procedure is applied to symmetric tensors of 2-7 order.

Mechanical moduli of cultured airway smooth muscle cells (Fabry, B., et al. Phys. Rev. Lett. 87:148102, 2001) reveal that the frequency dependence of cell rheological behavior conforms to a weak power-law relationship over a wide range of frequency (10-2 -103 Hz).Such a behavior cannot be accounted for by standard viscoelastic models characterized...

Following the approach of Gurtin and Podio-Guidugli (1998), the problem of crack propagation based on the notion of configurational forces and couples in micropolar continua is considered. .

The problem of deriving Fourier's law of heat conduction in a nonlinear fluid is considered. As a basis for its derivation, Muller's entropy principle and the assumption introduced by I-Shih Liu are used. It is shown that the absolute temperature, derived in this way, is the same for both linear and nonlinear fluids. Contrary to the absolute temper...

This note provides short proof of the representation of a symmetric isotropic 4-tensor in an n-dimensional real Euclidean space.

In this paper the gradients of the principal invariants of an arbitrary second-order tensor are derived in a very concise way.

The representation of the classical formula that contains Euler’s theorem on three-dimensional rigid body rotations, as an orthogonal tensor in three dimensions, is extended to a six-dimensional representation as a tool for accomplishing coordinate transformations of the anisotropic elasticity tensor.

We consider the problem of determining necessary and sufficient conditions for the existence of symmetry planes of an anisotropic elastic material. These conditions are given in several equivalent forms, and are used to determine special coordinate systems where the number of non-zero components in the elasticity tensor is minimized. By the method...

A transport theorem for a moving interface within a non-fixed region Ω, ⊂ R3 is derived.

The recent theory of nonlocal micropolar continuum is used to derive explicit expressions for both the energy release rate and J-integral. It was shown that this J-integral has a physical meaning of the energy release rate and, for the homogeneous body with a straight crack, is path independent. It was also shown that the influence of nonlocality i...

The finite element method has been applied on thin shell J integral evaluation. Thin shell J integral has been recently derived using Gurtin's approach, which has been shown to be path dependent, unless the crack is placed along a generatrix of a cylindrical shell. In any other case two line and one surface integral should be added to the Rice's J...

It is shown that Griffith criterion for fracture, considered within the framework of nonlinear micropolar thermoelasticity, is a necessary condition for crack initiation provided the initial temperature is continuous at the tip of the crack and the strain energy is properly interpreted. The Griffith criterion so derived is of the same form as that...

The energy release rate and its relation with J-integral is considered from some general point of view.

Following Moeckel's approach, thermodynamics of non-simple, heat-conducting material interface is investigated. In order to obtain field equations for the fields of mass density, motion, and temperature in the interface, specific balance equations are used for mass, momentum, moment of momentum, and energy in the surface, and constitutive equations...

Making use of Mueller's entropy principle and the concept of a distributed body, developed by Cowin and Goodman, a theory of thermoelasticity of granular materials is proposed.

Noether's theorem is used in an appropriate generalized form to deduce cnnservation laws of the type in the linear elastostatics of micropolar continua. The 1-parameter family of transformations associated with these conservation laws is determined on the basis of physically reasonable assumptions.

The model of a continuum with microstructure is introduced, giving its physical meaning and its mathematical formulation. In order to include the microstructure in the deformation, the deformation of a macro-element of a body is considered (as a limit volume element in which, from the viewpoint of molecular theory, it is not possible to consider ma...

The aim of our contribution is to draw attention to the fact, which so far has rarely absorbed theoreticians studying continuous media, that a moving surface may carry not only disturbances, but also physical properties different from those of the surrounding media. Here, we present a unified view of the theory of non-relativistic thermodynamics in...