jovo jaric - Profile on Academia.edu (original) (raw)

Papers by jovo jaric

The aim of our contribution is to draw attention to the fact, which so far has rarely absorbed th... more 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 incorporating phenomena with singularities. These singularities will present as discontinuous functions or their derivatives, and in the form of the discontinuity in respect to the Lebesgue measure of physical quantities. A special focus exists on the fracture at interfaces. Current topics include the role of thermal residual or processing induced stresses, the detailed role of plasticity, and geometric effects on interface crack driving forces. We model a situation of this kind by the movement of a surface separating two well-behaved material media, while attributing to the surface the physical properties of a phase change. For a proper und...

Theoretical and Applied Mechanics

In this paper, the anisotropic linear damage mechanics is presented starting from the principle o... more 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 damage tensor also in closed form. The procedure we present here was applied for several crystal classes which are subjected to hexagonal, orthotropic, tetragonal, cubic and isotropic damage. As an example isotropic system is considered in order to present some possibility to evaluate its damage parameters.

Mathematics

Using the apparatus of traditional differential geometry, the transport theorem is derived for th... more 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 moving subdomain are material are discussed. Then, the transport at hypersurfaces of discontinuity is considered. Finally, the general local balance equations for continuum of arbitrary dimensions with discontinuities are derived.

On the mean rotation in finite deformation

Proceedings. Mathematical, physical, and engineering sciences / the Royal Society, Jan 8, 2015

In the light of recent progress in coarsening the discrete dislocation mechanics, we consider two... more 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 dislocation mechanics and under what conditions? (ii) how can physical or phenomenological expressions for size-dependent energy be computed from dislocation mechanics in the general case of elastically anisotropic crystal? The analysis based on material and slip system symmetries implies the negative answer to the first question. However, the coarsening method developed in response to the second question, and based on the physical interpretation of the size-dependent energy as the coarsening error in dislocation interaction energy, introduces additional symmetries. The result is that the equivalence between the phenomenological and the physica...

Reality and Compatibility of Physical and Mathematical Formalisms

Surfactant Science, 2005

Journal of Elasticity, 1998

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

On anisotropic elasticity damage mechanics

International Journal of Damage Mechanics, 2013

The energy release rate in quasi-static crack propagation and J-integral

International Journal of Solids and Structures, 1986

... Next, by (As) and (Ay), ab Sn(f-fr)dssSsupf-fr S-ndJ->0, J9D, aaaj D, aa Jao, B rfrds=fT-a... more ... Next, by (As) and (Ay), ab Sn(f-fr)dssSsupf-fr S-ndJ->0, J9D, aaaj D, aa Jao, B rfrds=fT-aa JSI Sn-f7-d5=fr-Snds-0, WOf aaa jsDs a (4.5) (4.6) (4.7) Sn-fd5-0. JaO, aa The energy release rate in quasi-static crack ... SH ^=0; wr ' ^=0' 77S Jovi) P. JAK 1C as can be seen from (7.1). ...

Six-dimensional orthogonal tensorrepresentation of the rotation about an axis in three dimensions

International Journal of Solids and Structures, 1995

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

On Noeter's Theorem in Nonlinear Continua

Journal of the Mechanical Behavior of Materials, 2000

Theoretical and Applied Mechanics, 2010

The algebraic proof of the fundamental theorem concerning pure shear, by making use only of the n... more 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.

Theoretical and Applied Mechanics, 2008

An objective of this paper is to reconcile the "symmetry" approach with the "symme... more 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 symmetry transformation. Particularly, we paid attention to the compliance tensor for cubic and hexagonal crystals.

On compatibility conditions for singular surfaces – a general approach part I

Philosophical Magazine, 2005

The study provides a natural generalization and unification of the classical treatments of compat... more The study provides a natural generalization and unification of the classical treatments of compatibility conditions for moving surfaces and curves as submanifolds of E3. 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 standard quantities from differential geometry and explicitly displaying

On the conditions for the existence of a plane of symmetry for anisotropic elastic material

Mechanics Research Communications, 1994

Lois de conservation du type integrale J en elastostatique des milieux micropolaires

Mechanics Research Communications, 1978

Thermodynamics of Non-Simple Heat-Conducting Interface

Journal of Thermal Stresses, 1984

Following Moeckel's approach, thermodynamics of non-simple, heat-conducting material inte... more 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 are stated. The constitutive equations of the bulk material (the three-dimensional non-simple,

Fourier's Law of Heat Conduction in a Nonlinear Fluid

Journal of Thermal Stresses, 1999

Journal of Elasticity, 1996

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

Journal of Elasticity, 2005

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

The aim of our contribution is to draw attention to the fact, which so far has rarely absorbed th... more 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 incorporating phenomena with singularities. These singularities will present as discontinuous functions or their derivatives, and in the form of the discontinuity in respect to the Lebesgue measure of physical quantities. A special focus exists on the fracture at interfaces. Current topics include the role of thermal residual or processing induced stresses, the detailed role of plasticity, and geometric effects on interface crack driving forces. We model a situation of this kind by the movement of a surface separating two well-behaved material media, while attributing to the surface the physical properties of a phase change. For a proper und...

Theoretical and Applied Mechanics

In this paper, the anisotropic linear damage mechanics is presented starting from the principle o... more 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 damage tensor also in closed form. The procedure we present here was applied for several crystal classes which are subjected to hexagonal, orthotropic, tetragonal, cubic and isotropic damage. As an example isotropic system is considered in order to present some possibility to evaluate its damage parameters.

Mathematics

Using the apparatus of traditional differential geometry, the transport theorem is derived for th... more 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 moving subdomain are material are discussed. Then, the transport at hypersurfaces of discontinuity is considered. Finally, the general local balance equations for continuum of arbitrary dimensions with discontinuities are derived.

On the mean rotation in finite deformation

Proceedings. Mathematical, physical, and engineering sciences / the Royal Society, Jan 8, 2015

In the light of recent progress in coarsening the discrete dislocation mechanics, we consider two... more 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 dislocation mechanics and under what conditions? (ii) how can physical or phenomenological expressions for size-dependent energy be computed from dislocation mechanics in the general case of elastically anisotropic crystal? The analysis based on material and slip system symmetries implies the negative answer to the first question. However, the coarsening method developed in response to the second question, and based on the physical interpretation of the size-dependent energy as the coarsening error in dislocation interaction energy, introduces additional symmetries. The result is that the equivalence between the phenomenological and the physica...

Reality and Compatibility of Physical and Mathematical Formalisms

Surfactant Science, 2005

Journal of Elasticity, 1998

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

On anisotropic elasticity damage mechanics

International Journal of Damage Mechanics, 2013

The energy release rate in quasi-static crack propagation and J-integral

International Journal of Solids and Structures, 1986

... Next, by (As) and (Ay), ab Sn(f-fr)dssSsupf-fr S-ndJ->0, J9D, aaaj D, aa Jao, B rfrds=fT-a... more ... Next, by (As) and (Ay), ab Sn(f-fr)dssSsupf-fr S-ndJ->0, J9D, aaaj D, aa Jao, B rfrds=fT-aa JSI Sn-f7-d5=fr-Snds-0, WOf aaa jsDs a (4.5) (4.6) (4.7) Sn-fd5-0. JaO, aa The energy release rate in quasi-static crack ... SH ^=0; wr ' ^=0' 77S Jovi) P. JAK 1C as can be seen from (7.1). ...

Six-dimensional orthogonal tensorrepresentation of the rotation about an axis in three dimensions

International Journal of Solids and Structures, 1995

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

On Noeter's Theorem in Nonlinear Continua

Journal of the Mechanical Behavior of Materials, 2000

Theoretical and Applied Mechanics, 2010

The algebraic proof of the fundamental theorem concerning pure shear, by making use only of the n... more 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.

Theoretical and Applied Mechanics, 2008

An objective of this paper is to reconcile the "symmetry" approach with the "symme... more 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 symmetry transformation. Particularly, we paid attention to the compliance tensor for cubic and hexagonal crystals.

On compatibility conditions for singular surfaces – a general approach part I

Philosophical Magazine, 2005

The study provides a natural generalization and unification of the classical treatments of compat... more The study provides a natural generalization and unification of the classical treatments of compatibility conditions for moving surfaces and curves as submanifolds of E3. 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 standard quantities from differential geometry and explicitly displaying

On the conditions for the existence of a plane of symmetry for anisotropic elastic material

Mechanics Research Communications, 1994

Lois de conservation du type integrale J en elastostatique des milieux micropolaires

Mechanics Research Communications, 1978

Thermodynamics of Non-Simple Heat-Conducting Interface

Journal of Thermal Stresses, 1984

Following Moeckel's approach, thermodynamics of non-simple, heat-conducting material inte... more 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 are stated. The constitutive equations of the bulk material (the three-dimensional non-simple,

Fourier's Law of Heat Conduction in a Nonlinear Fluid

Journal of Thermal Stresses, 1999

Journal of Elasticity, 1996

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

Journal of Elasticity, 2005

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