Introduction to the Mechanics of a Continuous Medium

Sedov, L. I.; Hodge, Philip G.

doi:10.1115/1.3625016

Cited by 73 publications

(92 citation statements)

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“…13 demonstrate a good agreement of the experimental data with our theoretical model at short distances from the crack tips. Some disagreement between experimental and theoretical results at distances away from the crack tips is due to an asymptotical character of the expressions used for stress tensor components [41] that are valid only for short distances. Fig.13(a) shows that external compressive stress partially compensates for tensile residual stress acting near the tip of crack 1.…”

Section: Theoretical Model Of Photoacoustic Thermoelastic E® Ect Nearmentioning

confidence: 99%

Theoretical and experimental investigation of the photoacoustic effect in solids with residual stresses

Muratikov

Глазов

2003

Open Physics

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Modern experiment and theory in the eld of residual stress detection by the photoacoustic method are summarized and analyzed. A multimode approach based on the simultaneous application of several photothermal and photoacoustic methods is proposed for the study of thermal and thermoelastic e¬ects in solids with residual stress. Some experimental results obtained within the framework of this approach for Vickers indentation zones in ceramics are presented. The e¬ect of annealing on the photoacoustic, piezoelectric signal for ceramics and the in®uence of the given external loading on the behavior of the photoacoustic signal near the radial crack tips is investigated. It is experimentally shown that both compressive and shear stresses contribute to the photoacoustic signal near the radial crack tips. The model of the photoacoustic, thermoelastic e¬ect in solids with residual stress is proposed. It is based on the modi ed Murnaghan model of non-linear elastic bodies, which takes into account a possible dependence of the thermoelastic constant on stress. This model is further developed to explain the photoacoustic signal behavior near the radial crack tips. It is demonstrated that this model of the photoacoustic e¬ect agrees qualitatively with the available experimental data.

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Section: Theoretical Model Of Photoacoustic Thermoelastic E® Ect Nearmentioning

confidence: 99%

Theoretical and experimental investigation of the photoacoustic effect in solids with residual stresses

Muratikov

Глазов

2003

Open Physics

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“…(8) Heat transfer, associated with diffusion of heat dQ from region of higher temperature T h to lower temperature T l , with entropy change:…”

Section: Entropy In Friction and Wear Processesmentioning

confidence: 99%

A Model of Mechanothermodynamic Entropy in Tribology

Sosnovskiy

Sherbakov

2017

Entropy

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A brief analysis of entropy concepts in continuum mechanics and thermodynamics is presented. The methods of accounting for friction, wear and fatigue processes in the calculation of the thermodynamic entropy are described. It is shown that these and other damage processes of solids are more adequately described by tribo-fatigue entropy. It was established that mechanothermodynamic entropy calculated as the sum of interacting thermodynamic and tribo-fatigue entropy components has the most general character. Examples of usage (application) of tribo-fatigue and mechanothermodynamic entropies for practical analysis of wear and fatigue processes are given.Keywords: entropy; mechanothermodynamics; tribo-fatigue; tribology; fatigue; damage Thermodynamic EntropyThe following functions are used to describe the state of thermodynamic systems [1]:where temperature T, volume V, and number of moles of chemical components N k are the macroscopic state variables. In the general case of an open system, the change dU of internal energy U is presented [1] as:where dQ is the amount of heat; dA is the amount of mechanical energy; dU sub is the amount of substance, which the system exchanged with the environment for a time interval dt; p is the pressure; the µ k 's are the chemical potentials. Planck especially emphasized that dU in Equation (2) is an infinitely small difference, whereas dQ, dA, and dU sub are the infinitely small amounts. It follows from (2) that entropy S change in a thermodynamic system (subscript T) is: Abstract: A brief analysis of entropy concepts in continuum mechanics and thermodynamics is presented. The methods of accounting for friction, wear and fatigue processes in the calculation of the thermodynamic entropy are described. It is shown that these and other damage processes of solids are more adequately described by tribo-fatigue entropy. It was established that mechanothermodynamic entropy calculated as the sum of interacting thermodynamic and tribofatigue entropy components has the most general character. Examples of usage (application) of tribo-fatigue and mechanothermodynamic entropies for practical analysis of wear and fatigue processes are given.

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“…The equation of motion and the geodesic line equation in nonmetrical manifold can be derived from the Sedov variational principle [13] which is the generalization of the least action principle: δS(q) + δW (q) = 0 (15) where S(q) is the holonomic functional called action andW (q) is the nonholonomic functional, i.e. δδ ′W ≡ δ ′ δW .…”

Section: Appendixmentioning

confidence: 99%

“…As the result the motion of the systems subjected to dissipative forces on the metric manifold is equivalent to the free motion of the test particle on the nonmetric (generalized path) manifold. Note that the equation of motion and the geodesic line equation in the nonmetrical manifold can be derived from Sedov variational principle [13] which is the generalization of the least action principle.…”

Section: Introductionmentioning

confidence: 99%

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Bosonic string in affine-metric curved space

Tarasov

1994

Physics Letters B

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The sigma model approach to the closed bosonic string on the affine-metric manifold is considered. The two-loop metric counterterms for the nonlinear twodimensional sigma model with affine-metric target manifold are calculated. The correlation of the metric and affine connection is considered as the result of the conformal invariance condition for the nonlinear sigma model. The examples of the nonflat nonRiemannian manifolds resulting in the trivial metric beta-function are suggested.

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Introduction to the Mechanics of a Continuous Medium

Cited by 73 publications

References 0 publications

Theoretical and experimental investigation of the photoacoustic effect in solids with residual stresses

Theoretical and experimental investigation of the photoacoustic effect in solids with residual stresses

A Model of Mechanothermodynamic Entropy in Tribology

Bosonic string in affine-metric curved space

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