Showing papers in "Acta Mechanica in 1983"
TL;DR: In this article, the derivation of certain new classes of variational principles for material laws and boundary conditions resulting from nonconvex, generally non-differentiable, potentials is discussed.
Abstract: The purpose of the present paper is the derivation of certain new classes of variational principles for material laws and boundary conditions resulting from nonconvex, generally nondifferentiable, potentials. To this end two recently defined notions are employed the “generalized gradient” of Clarke and the “derivate container” of Warge. Several general classes of problems are discussed and the respective variational forms called here hemivariational inequalities are derived. For the respective static problems the equivalence of these forms to the “substationarity” of the potential and complementary energy is discussed. Finally an integral inclusion formulation for certain classes of static problems is presented.
234 citations
94 citations
TL;DR: Etude du probleme d'un barreau infiniment long subissant des oscillations longitudinales and de torsion dans un fluide incompressible and homogene du second ordre as discussed by the authors.
Abstract: Etude du probleme d'un barreau infiniment long subissant des oscillations longitudinales et de torsion dans un fluide incompressible et homogene du second ordre
79 citations
TL;DR: In this article, a theory for a newtonian thermoviscous fluid is proposed, based on the ideas of the extended irreversible thermodynamics and the entropy principle in its general formulation of rational thermodynamics.
Abstract: Some critical considerations on the models of “extended irreversible thermodynamics” are given. By developing a methodology (“invariance of the generators”) based both on the ideas of the “extended irreversible thermodynamics” and the “entropy principle” in its general formulation of “rational thermodynamics”, a theory for a newtonian thermoviscous fluid is proposed. The theory has the following properties, new when compared with previous ones: a) the system of equations is hyperbolic for any value of the field variables, provided that the usual thermodynamic stability condition (maximum entropy at equilibrium) holds; all wave-propagation speeds are then real and finite; b) the system is conservative and it is possible to seek for weak solutions and, in particular, for shockwaves; moreover, the system is symmetric-hyperbolic in the sense of Friedrichs; special properties hold therefore for weak solutions and shocks; c) the only thermodynamic variables at non-equilibrium, modified with respect to the corresponding ones at equilibrium, are the entropy density and chemical potential; consequentely, there exists only a single absolute temperature, playing an important role in relaxations; d) the entropy principle is automatically satisfied.
69 citations
TL;DR: In this paper, a Mohr-Coulomb, single-hardening, rigid-plastic model with non-associated flow rule is proposed to model rigid-granular dilatant material.
Abstract: Diffuse and localized bifurcation modes in axisymmetric, rectilinear deformations on rigid-granular dilatant material are analyzed. Rigid-granular behavior is described by a Mohr-Coulomb, single-hardening, rigid-plastic model with non-associated flow rule. Diffuse bulging in the compression test and diffuse necking in the extension test are always possible in the vicinity of the plastic limiting state. Localizations in the compression test occur in the softening regime, and in the extension test they occur in the hardening regime of the considered stress ratio-strain curve.
50 citations
TL;DR: The asymptotic solution in the sence of Krylov-Bogoliubov-Mitropolskii of a 3-dimensional weakly nonlinear autonomous differential system is investigated and the system models oscillating processes characterized by strong damping.
Abstract: The asymptotic solution in the sence of Krylov-Bogoliubov-Mitropolskii of a 3-dimensional weakly nonlinear autonomous differential system is investigated. The system models oscillating processes characterized by strong damping.
37 citations
TL;DR: The kinetic theory of ideal gases as discussed by the authors provides a limit for the validity of the principle of material frame indifference, which can therefore be used to confirm or reject the axioms and principles of the phenomenological constitutive theory.
Abstract: The kinetic theory provides constitutive equations of ideal gases and it can therefore be used to confirm or reject the axioms and principles of the phenomenological constitutive theory. Thus the kinetic theory provides a limit for the validity of the principle of material frame indifference. It generalizes the laws of Fick, Fourier and Navier-Stokes and provides finite speeds of waves of concentration, temperature and shear. Moreover the theory permits the calculation of entropy and entropy flux in non-equilibrium and it confirms Onsager relations in a rotating mixture of ideal gases.
34 citations
TL;DR: In this article, the distribution of displacement and stresses in a tube with fixed ends of elastic-plastic material under the assumption of Tresca's yield condition, its associated flow rule and linear strain-hardening was investigated.
Abstract: Subject of the investigation is the distribution of displacement and stresses in a tube with fixed ends of elastic-plastic material under the assumption of Tresca's yield condition, its associated flow rule and linear strain-hardening.
31 citations
TL;DR: In this paper, nonlinear equations governing the motion of a wobblestone are derived assuming no slippage at the point of contact to the supporting rigid plane, which corresponds to a conservative model.
Abstract: The wobblestone is a generalized form of a top with distinct inertias and a nonspherical surface at the point of contact to the horizontal plane on which it moves. Some wobble-stones exhibit a curious property of allowing steady rotation about the vertical principal inertia axis only when rotated in one direction, while other wobblestones exhibit repeated reversals of the direction of rotation after being spun. Here, nonlinear equations governing the motion of a wobblestone are derived assuming no slippage at the point of contact to the supporting rigid plane, which corresponds to a conservative model. The equations are formulated in a manner suitable for numerical integration. The major observed properties of the motion of these asymmetrical tops are demonstrated in numerical simulations. The results lead to a better understanding of their complex and fundamentally nonlinear motion.
31 citations
TL;DR: In this article, the problem of a thin sheet containing a slant crack and subjected to a biaxial load is examined by giving the expressions for stresses in a series form, which are equally valid near and far (r < 2a) from the crack tip.
Abstract: The problem of a thin sheet containing a slant crack and subjected to a biaxial load is examined by giving the expressions for stresses in a series form, which are equally valid near and far (r<2a) from the crack tip. The progressive importance of the higher-order terms in the series representation for stresses, which were added to the singular and constant ones was demonstrated by giving the isochromatic fringe patterns near and far the crack-tip area. Based on these expressions, a photoelastic determination of the exact values of the complex stress intensity factor was given without necessitating appropriate correction factors and diagrams. The values of SIFs thus determined are valid independently of the polar angle and distance of measurements from the crack tip.
30 citations
TL;DR: An infinite at both ends closed cylindrical free surface liquid column is subjected to various instationary axial temperature timewise periodic fields, such as linear, parabolic, sinusoidal and exponential temperature changes, which are imposed at the free liquid surface as mentioned in this paper.
Abstract: An infinite at both ends closed cylindrical free surface liquid column is subjected to various instationary axial temperature timewise periodic fields, such as linear, parabolic, sinusoidal and exponential temperature changes, which are imposed at the free liquid surface.
TL;DR: In this paper, the authors presented a new approximative method for predicting the changes in pressure drop in laminar entrance region flow of purely viscous power law fluids in circular tubes.
Abstract: The main purpose of this paper is to present a new approximative method for predicting the changes in pressure drop in laminar entrance region flow of purely viscous power law fluids in circular tubes. The “transformation method for describing the tube flow of non-Newtonian purely viscous fluids”, first introduced by the present authors [1, 2, see also Appendix] has been extended and adopted to construct a pseudo-Newtonian model of the flow under consideration. To derive the dimensionless equations for calculating the changes in pressure drop in the entrance region flow and the velocity distribution in both the developing boundary layer and inside the inviscid core the momentum integral method has been applied. The analysis leads to only one single curve correlation — independent of any value of flow behaviour index — between the pressure drop and the axial distance from the tube entrance which is presented in a form suitable for engineering designs. A comparison of the dimensionless pressure drop curve as predicted in this paper with the experimental data obtained by other authors points out an excellent agreement. The results of the present work hold for high Reynolds number (Re>500) flow only.
TL;DR: In this article, a ray series approach is employed to reduce the governing integro-differential equation to a set of differential-difference equations which may be solved, and various general properties of the propagation process are derived in a simple and direct fashion.
Abstract: The linear Gurtin-Pipkin theory of heat conduction is invoked to study the problem of an inhomogeneous half space whose boundary is subjected to step inputs of temperature. A ray series approach is employed to reduce the governing integro-differential equation to a set of differential-difference equations which may be solved. Various general properties of the propagation process are derived in a simple and direct fashion and the solution constructed for particular choices of the heat-flux and energy relaxation functions.
TL;DR: In this paper, the definition of a thermodynamic approach of discrete memory type for strictly irreversible processes is given, where a discrete memory form of Gibbs' equation is presented and a physical meaning is given to a loading-unloading criterion which defines a set of memorized states.
Abstract: This paper gives the definition of a thermodynamic approach of discrete memory type for strictly irreversible processes. The class of the associated constitutive equations is briefly recalled: it describes hysteresis and hardening by expressing the effective stress as the sum of two hereditary contributions, of discrete and continuous memory types respectively. A discrete memory form of Gibbs' equation is presented and a physical meaning is given to a loading-unloading criterion which defines a set of memorized states. For example, a precise formulation is given for the constitutive equations of an elastoviscoplastic material and an elastoplastic material with strain hardening. The results are obtained numerically and are related to simple geometries, including an axisymmetrical thin shell.
TL;DR: In this paper, the one-dimensional flow of a vapor through a porous membrane is considered, and it is shown that heat conduction in flow direction is important if the Joule-Kelvin coefficient of the vapor is positive and the permeability of the membrane is sufficiently small.
Abstract: The one-dimensional flow of a vapor through a porous membrane is considered. Upstream the membrane the vapor is assumed to be in a state of saturation, downstream the membrane there may be superheated vapor, saturated vapor or a two-phase mixture. It is shown that heat conduction in flow direction is important if the Joule-Kelvin coefficient of the vapor is positive and the permeability of the membrane is sufficiently small. This results in condensation at the front surface of the membrane, liquid flow in the membrane or part of it, and re-evaporation at the rear surface or in an evaporation front in the interior of the membrane. If the permeability of the membrane is below a critical value that depends on thermodynamic quantities only, the energy balance requires the formation of a condensate film in front of the membrane. Four possible types of throttling processes are analyzed for small pressure variations and an equation for the mass flow rate in terms of the pressure difference across the membrane is given. The predicted mass flow rate of isobutane through a microporous polypropylene membrane compares favourably with measurements.
TL;DR: In this paper, a solution for the interacting vibrations of a linear elastic arch dam with a linear compressible, three-dimensional, irregularly shaped fluidbody is presented for a time harmonic excitation of the arch dam and, with regard to an earthquake analysis, for nonstationary stochastic excitation processes.
Abstract: Solutions for the interacting vibrations of a linear elastic arch dam with a linear compressible, three-dimensional, irregularly shaped fluidbody are presented. The vibration response is derived for a time harmonic excitation of the arch dam and, with regard to an earthquake analysis, for nonstationary stochastic excitation processes. The expansions of the stochastic responses are based on time-dependent power spectral density functions, demanding the evaluation of the frequency response spectras in advance. These time-harmonic solutions are obtained by means of substructure synthesis method, thereby applying a boundary integral equation formulation for the vibrating fluidbody.
TL;DR: In this paper, the authors found that turbulence intensities in turbulent wall jets along a concave surface increase remarkably, when the radius of curvature becomes smaller beyond a certain condition.
Abstract: The present experiment found that turbulence intensities in turbulent wall jets along a concave surface increase remarkably, when the radius of curvature becomes smaller beyond a certain condition. The critical condition is discussed in comparison with the Taylor-Gortler instability for turbulent wall jets. The measurements are also made for the mean velocity field, the Reynolds stress, the turbulence energy balance and the velocity correlations.
TL;DR: In this paper, an oscillatory flow of a viscous incompressible fluid in an elastic tube of variable cross section has been investigated at low Reynolds number under the assumption that the variation of the cross-section is slow in the axial direction for a tethered tube.
Abstract: An oscillatory flow of a viscous incompressible fluid in an elastic tube of variable cross section has been investigated at low Reynolds number. The equations governing, the flow are derived under the assumption that the variation of the cross-section is slow in the axial direction for a tethered tube. The problem is then reduced to that of solving for the excess pressure from a second order ordinary differential equation with complex valued Bessel functions as the coefficients. This equation has been solved numerically for geometries of physiological interest and a comparison is made with some of the known theoretical and experimental results.
TL;DR: In this article, the buckling of magnetically saturated elastic bodies in an external magnetic field is discussed, from which a linearized version of the general nonlinear equations for the magnetoelastic interactions in magnetically saturation bodies is derived.
Abstract: The buckling of magnetically saturated elastic bodies in an external magnetic field is discussed. A linearized version of the general nonlinear equations for the magnetoelastic interactions in magnetically saturated bodies is presented, from which a buckling criterion is derived. This criterion is applied in two examples, viz. a thin plate and a circular rod. Results obtained are compared with those for soft ferromagnetic bodies, as known in the literature. It turns out that, although the descriptions are essentially different, the final results for the saturation model and for the soft magnetic model are in good correspondence with one another.
TL;DR: In this paper, the authors examined the possibility of existence of an evolution criterion for thermodynamical waves and found that a monotonic transition of the thermodynamic waves from non-equilibrium states to stationary states is insured only when dissipative processes are dominant over relaxation phenomena.
Abstract: Irreversible systems in which both dissipative and relaxation phenomena are taking place can be appropriately described by the wave approach of Onsagerian thermodynamics proposed by Gyarmati. An important consequence of this theory is that it leads to hyperbolic transfer equations and these are referred to as thermodynamical waves. In the present note we examine the possibility of existence of an evolution criterion for such thermodynamical waves. It is found that a monotonic transition of the thermodynamical waves from non-equilibrium states to stationary states is insured only when dissipative processes are dominant over relaxation phenomena.
TL;DR: In this article, a general elastic laminate consisting of different transversely isotropic plane layers is discussed and closed formulas for the displacements, critical loads and eigenfrequencies are derived on the basis of the discrete and continuum model respectively.
Abstract: For a general elastic laminate consisting of different transversely isotropic plane layers an exact (but expensive) method for the calculation of the deformations, stability and eigenvibrations is discussed. The specialization to a laminate composed of alternating stiff reinforcing sheets and soft matrix layers (special discrete model), however, allows a considerable simplification. It is shown how this regular laminate (=inhomogeneous classical continuum) may be approximated by a homogeneous continuum with couple stresses using a suitable limiting process (continuum model). This model corresponds to a restricted Cosserat continuum and enables the derivation of closed formulas for the displacements, critical loads and eigenfrequencies. Numerical results are worked out on the basis of the discrete and continuum model respectively and compared with each other.
TL;DR: In this article, the authors suggest that two solids of different material properties are pressed together and sheared, and then, slip propagates asymmetrically from a region of low friction.
Abstract: Recent models of earthquake faults involve heterogeneous slip regions along the faults. Some of this work suggests the following problem: two solids of different material properties are pressed together and sheared. Then, slip propagates asymmetrically from a region of low friction.
TL;DR: In this paper, the authors characterized the isothermal properties of a poled ferroelectric ceramic PZT 65/35 in the absence of losses and showed that the resulting constitutive relations are the standard ones which appear in the literature.
Abstract: In this paper we characterize the isothermal three dimensional properties of a poled ferroelectric ceramic PZT 65/35 in the absence of losses. The resulting constitutive relations, in the absence of mechanical dissipation, domain switching, dipole dynamics and phase transformation, are the standard ones which appear in the literature. The characterization of the constitutive relations requires the determination of five elastic constants, three piezoelectric constants and two dielectric constants. We dientify the experimental measurements which are sufficient to determine these constants and describe the data reduction procedures. Our results differ relatively and absolutely from those given in the literature.
TL;DR: In this paper, the closed from expression for the Muskhelishvili complex stress function Φ(z) was used to define the exact form of the caustic.
Abstract: The form of caustics created by stress singularities in elastic problems was up-to-now derived from the Sneddon expressions for the components of stresses at the point of singularity, which are based on the first and singular term of the series expansion of the Muskhelishvili complex stress function. In this paper the closed from expression for the Muskhelishvili complex stress function Φ(z) was used to define the exact form of the caustic. Moreover, the forms of the caustics were constructed for several terms, besides the first one, in the Taylor expansion of Φ(z).
TL;DR: The avolume fraction theory as mentioned in this paper models the local dilatational motions of granular materials in terms of the partial density and the density of the material, which is a generalization of the volume fraction theory.
Abstract: Materials which are in discretized form, such as granular materials or a distribution of bubbles, can exhibit microstructural effects associated with the local deformations of the microelements. In this paper, a theory in which new kinematical variables are introduced to model the dilatational motions of the microelements is called avolume fraction theory. It is argued that two types of local motion should be considered — dilatation of the microelements and their dilatational motion relative to one another—and that two of the three variables volume fraction, partial density and density are necessary to model them. As an example, the theory of granular materials due to Goodman and Cowin is generalized by modeling the local dilatational motions in terms of the partial density and the density of the material.
TL;DR: In this article, the plane fundamental solution in steady linear aerodynamics is determined and it is shown how to use this solution in order to derive the motion in the presence of bodies.
Abstract: In this note the plane fundamental solution in steady linear aerodynamics is determined and it is shown how to use this solution in order to derive the motion in the presence of bodies. An application to the fluid flows in the presence of thin airfoils is done.
TL;DR: In this paper, a detailed interpretation of the mass coupling coefficient occurring in the equation of motion for a fluid-saturated porous medium is presented, which allows transformation of Derski's equations into those of Biot's equations and vice versa.
Abstract: Main aim of the paper is a detailed interpretation of the mass coupling coefficient occurring in the equation of motion for a fluid-saturated porous medium. Biot's (1956) and Darski's (1978) equations are discussed. A new kinematical model is presented which allows transformation of Derski's equations into those of Biot (and vice versa). The interpretation of their coefficients is given in detail and boundary conditions for these equations are discussed.