Thermoelasticity without energy dissipation

This paper deals with thermoelastic material behavior without energy dissipation; it deals with both nonlinear and linear theories, although emphasis is placed on the latter. In particular, the linearized theory of thermoelasticity discussed possesses the following properties: (a) the heat flow, in contrast to that in classical thermoelasticity characterized by the Fourier law, does not involve energy dissipation; (b) a constitutive equation for an entropy flux vector is determined by the same potential function which also determines the stress; and (c) it permits the transmission of heat as thermal waves at finite speed. Also, a general uniqueness theorem is proved which is appropriate for linear thermoelasticity without energy dissipation.     

Frictional energy dissipation in materials containing cracks

Kachanov's simplified model of microcrack interaction is applied to an investigation of the behaviour of a cracked body under predominantly compressive periodic loading, so that the cracks experience periods of closure and slip, with frictional dissipation. The model is shown to be equivalent to a discrete elastic frictional system with each crack representing one node. Theorems and algorithms from such systems are applied to determine the conditions under which the system shakes down to a state with no slip and hence no energy dissipation in friction. For conditions not too far beyond the shakedown state, the dissipation is significantly affected by the initial conditions, but with larger oscillating loads, it becomes a unique and increasing function of load amplitude. The effect of crack interaction is assessed by comparison with an uncoupled model, for which the dissipation is obtained as a summation of closed form expressions over the crack population. For small numbers of cracks, the results are significantly dependent on the randomly chosen crack locations and sizes, but with larger populations, a statistically significant decrease in dissipation is observed with increasing interaction terms.     

Vibrations of mechanical systems with energy dissipation hysteresis

A phenomenological approach which we refer to as kinematic is proposed to describe hysteresis; according to this approach, the force and kinematic parameters of a mechanical system are related by a first-order ordinary differential equation. The right-hand side is chosen in the class of functions ensuring the asymptotic approach of the solution to the curves of the enveloping (limit) hysteresis cycle of steady-state vibrations. The coefficients of the equation are identified by experimental data for the enveloping cycle. The proposed approach permits describing the hysteresis trajectory under the conditions of unsteady vibrations with an arbitrary starting point inside the region of the enveloping cycle. As an example, we consider the problem on forced vibrations of a pendulum-type damper of low-frequency vibrations.     

Directional instability of crack propagation with energy dissipation

It was shown that the behavior of propagating curved and branched cracks isinherently governed by the dynamics of the crack system provided that dissipation in the potential energy is accountedfor. A model is proposed by introducing the concept of an “equivalent crack particle” such that the deterministic aspect of the propagating crack in an idealized continuum and the stochastic nature of the micro chemical characteristics the real material can be modelled. The Langevin equations of motion and the corresponding Fokker-Planck equations are thus derived.     

Generation and direct viscous dissipation of turbulent energy

Existing information about the generation and viscous dissipation of turbulent energy is based, as a rule, on the Laufer test data obtained for fluid flow in circular tubes at two Reynolds numbers (5 · 10⁵ and 5 · 10⁴). Computational dependences are presented herein for the generation and viscous dissipation of turbulent energy, common over the whole stream section and for the whole range of variation of the Reynolds number. The equation of the average energy balance during fluid flow in a circular tube and a flat channel is solved taking account of the equation of motion and the turbulent friction profile obtained by the author [1]. The computational dependences satisfy all the evident boundary conditions, agree with the Laufer test results [2] and yield a well-founded passage to the limit modes of average turbulent motion.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 30–36, November–December, 1973.     

A correction method for measuring turbulence kinetic energy dissipation rate by PIV

The accuracy of turbulent kinetic energy (TKE) dissipation rate measured by PIV is studied. The critical issue for PIV-based dissipation measurements is the strong dependency on the spatial resolution, Δx, as reported by Saarenrinne and Piirto (Exp Fluids Suppl:S300–S307, 2000). When the PIV spacing is larger than the Kolmogorov scale, η, the dissipation is underestimated because the small scale fluctuations are filtered. For the case of Δx smaller than the Kolmogorov scale, the error rapidly increases due to noise. We introduce a correction method to eliminate the dominant error for the small Δx case. The correction method is validated by using a novel PIV benchmark, random Oseen vortices synthetic image test (ROST), in which quasi-turbulence is generated by randomly superposing multiple Oseen vortices. The error of the measured dissipation can be more than 1,000% of the analytical dissipation for the small Δx case, while the dissipation rate is underestimated for the large Δx case. Though the correction method does not correct the underestimate due to the low resolution, the dissipation was accurately obtained within a few percent of the true value by using the correction method for the optimal resolution of η/10 < Δx < η/2.     

计入膜力塑性耗散效应的矩形板塑性动力响应

从能量的观点在小挠度理论中引入表征膜力塑性耗散效应的修正因子,基于刚性板块的总体平衡给出矩形板大挠度塑性动力响应的完全运动方程组,分析了理想刚塑性简支和固支矩形板在矩形脉冲和冲击载荷下包括移行塑性铰相的完全大挠度响应过程。解决了当矩形板的挠度达到厚度量级时弯矩、膜力的联合作用问题,理论预报的结果在板的挠度为10倍板厚的量级与实验结果符合良好,改进了只考虑弯矩作用的小挠度理论结果和模态近似估计。     

Effect of energy dissipation on the shaped-charge flow regime

Convergence of a viscous shaped-charge liner to the symmetry axis is described. It is shown that energy dissipation has a significant effect on the process considered. Convergence at small angles can lead to a strong phase explosion of the metastable liquid of the inner, strongly heated, layers of the liner, which is comparable toTNT explosion. An increase in the angle of convergence results in a weak phase “explosion,” which leads to different behavior of shaped-charge jets for different types of linear material. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 4, pp. 3–11, July–August, 2000.     

Human leg impact: energy dissipation of wobbling masses

In terrestrial locomotion, the soft-tissue masses of the body undergo damped oscillations following leg impacts with the ground. Appropriate biomechanical models, therefore, describe gross soft-tissue dynamics by “wobbling masses”. We calculated mechanical energy balances of shank and thigh wobbling masses of the stance leg for the first 90 ms after touch-down in human heel-toe running. Thereto, we re-visited a data set on wobbling mass kinematics which had formerly been gained non-invasively by acquiring the motion of grids of lines painted on the skin of the corresponding muscle masses with high-speed cameras. We found frequencies ranging from 3 Hz to 55 Hz and maximum wobbling mass excursions relative to the bone ranging from 3 mm to 4 cm for the centres of mass and from 2.2° to 11.4° for the rotations. The rotational energy balance is practically neutral (±1 J). Usually, there is clearly more energy that is dissipated by wobbling mass movement in horizontal (thigh: <50 J) than in vertical direction (thigh: <15 J). There is less energy dissipated in the shank (horizontal: <10 J, vertical: <5 J). We argue that the energetic costs of separating significant wobbling masses from the skeleton may be over-compensated by avoiding metabolic costs of active impact reduction and by decreasing loads on passive skeletal structures, in particular when distal leg masses are functional, as in humans. Within reasonable biological limits, impacts are known to be even necessary for structural strengthening of bones. Beyond that, impacts might also be useful for stabilising locomotion, both by increasing basins of attraction and by providing simple mechanical signals for control.     

Damage evolution and energy dissipation of polymers with crazes

Craze damage evolution and energy dissipation of amorphous polymers with crazes have been studied. A mathematical model of a single craze (SC) is proposed by adopting the fibril creep mechanism. The viscoelastic characteristics of craze fibrils are supposed to obey the Maxwell model and the craze fibrils are assumed to be compressible. The assumption of Kausch [H.H. Kausch, The role of network orientation and microstructure in fracture initiation, J. Polym. Sci. C 32 (1971) 1–44] is adopted to describe the rupture of stressed fibril bonds. The craze damage evolution and the energy dissipation equations of a SC are derived. The equations are solved numerically and the life of a SC is computed. In a significant range of far-field stress, the dissipated energy varies linearly with the stress. Using the proposed model, the uniaxial stress-strain relation of polymers with low-density craze arrays (PLDCA) is investigated. The damage evolution equation of PLDCA is derived, which shows the mathematical relation between the damage of a SC and that of PLDCA. Based on the computed results, the variation of life of PLDCA with respect to applied stress is determined. Discussions are then given to the results and some significant conclusions are drawn.     

Minimax principle on energy dissipation of incompressible shear flow

The energy dissipation rate is an important concept in the theory of turbulence. Doering-Constantin＇s variational principle characterizes the upper bounds （maxi- mum） of the time-averaged rate of viscous energy dissipation. In the present study, an optimization theoretical point of view was adopted to recast Doering-Constantin＇s formu- lation into a minimax principle for the energy dissipation of an incompressible shear flow. Then, the Kakutani minimax theorem in the game theory is applied to obtain a set of conditions, under which the maximization and the minimization in the minimax principle are commutative. The results explain the spectral constraint of Doering-Constantin, and confirm the equivalence between Doering-Constantin＇s variational principle and Howard- Busse＇s statistical turbulence theory.     

Principle of minimum energy dissipation rate in steady Hele-Shaw flows

A new local form of the principle, in which dissipation is estimated only in a small vicinity of a free interface in steady Hele-Shaw flows, is proposed. It is established that for the problem of bubble propulsion the principle proposed is mathematically equivalent to the variational principle formulated by Saffman and Taylor without physical validation. It is shown that the new local form of the minimum dissipation principle effectively solves the problem of selection of a unique selection in the problems of both bubble and finger propulsion.     

Rheology of concentrated disperse systems and minimum energy dissipation principle

Summary For concentrated disperse systems, exhibiting newtonian behaviour, a new viscosity-concentration relationship is deduced from the optimization of viscous energy dissipation. Comparison with several theoretical and experimental investigations gives satisfactory agreement up to packing concentrations.

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Zusammenfassung Eine neue Viskositäts-Konzentrations-Beziehung für konzentrierte disperse Systeme mit newtonschem Verhalten wird durch Optimierung der viskosen Energie-Dissipation abgeleitet. Der Vergleich mit verschiedenen theoretischen und experimentellen Untersuchungen ergibt eine befriedigende Übereinstimmung bis zu den höchsten Packungsdichten.

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Résumé Une nouvelle relation viscosité-concentration pour les systèmes dispersés concentrés, à comportement newtonien, a été déduite de l'optimisation de l'énergie dissipée par viscosité. Cette relation est comparée à différents résultats théoriques et expérimentaux, et donne un accord satisfaisant jusqu'à la concentration d'entassement maximum.

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With 5 figures and 2 tables     

A novel internal dissipation inequality by isotropy and its implication for inelastic constitutive characterization

In the present work a novel inelastic deformation caused internal dissipation inequality by isotropy is revealed. This inequality has the most concise form among a variety of internal dissipation inequalities, including the one widely used in constitutive characterization of isotropic finite strain elastoplasticity and viscoelasticiy. Further, the evolution term describing the difference between the rate of deformation tensor and the “principal rate” of the elastic logarithmic strain tensor is set, according to the standard practice by isotropy, to equal a rank-two isotropic tensor function of the corresponding branch stress, with the tensor function having an eigenspace identical to the eigenspace of the branch stress tensor. Through that a general form of evolution equation for the elastic logarithmic strain is formulated and some interesting and important results are derived. Namely, by isotropy the evolution of the elastic logarithmic strain tensor is embodied separately by the evolutions of its eigenvalues and eigenprojections, with the evolution of the eigenprojections driven by the rate of deformation tensor and the evolution of the eigenvalues connected to specific material behavior. It can be proved that by isotropy the evolution term in the present dissipation inequality stands for the essential form of the evolution term in the extensively applied dissipation inequality.