Showing papers in "Archive of Applied Mechanics in 1995"
TL;DR: In this article, a nonlinear shell theory, including transverse strains perpendicular to the shell midsurface, as well as transverse shear strains, with exact description of the kinematical fields, is developed.
Abstract: A nonlinear shell theory, including transverse strains perpendicular to the shell midsurface, as well as transverse shear strains, with exact description of the kinematical fields, is developed. The strain measures are derived by considering theGreen strain tensor of the three-dimensional shell body. A quadratic displacement field over the shell thickness is considered. Altogether seven kinematical fields are incorporated in the formulation. The kinematics of the shell normal is described by means of a difference vector, avoiding the use of a rotation tensor and resulting in a configuration space, where the structure of a linear vector space is preserved. In the case of linear constitutive equations, a possible consistent reduction to six degrees of freedom is discussed. The finite element formulation is based on a hybrid variational principle. The accuracy of the theory and its wide range of applicability is demonstrated by several examples. Comparison with results based on shell theories formulated by means of a rotation tensor are included.
131 citations
TL;DR: In this article, a seven-parametric yield function for geomaterials such as soils and rocks is presented, which is able to describe the effects of primary yielding, as well as of isotropic and kinematic hardening.
Abstract: The article outlines a seven-parametric yield function for geomaterials such as soils and rocks. Proceeding from a geometric representation in the principal stress space, the yield surface exhibits a closed shape, thus reflecting the sensitivity of the plastic response of this type of media to hydrostatic stresses. The yield function is able to describe the effects of primary yielding, as well as of isotropic and kinematic hardening. In addition the failure envelope contains an open cone when the number of material parameters is reduced from seven to five.
115 citations
101 citations
TL;DR: In this article, the normal and tangential stress states of axi-symmetric bodies are modeled as a superposition of infinitesimal rigid flat-ended punches and the normal stress distribution can be calculated as a summation of differential flat punch solutions.
Abstract: Two axi-symmetric bodies are pressed together, so that their axes of symmetry coincide with the contact normal and the normal force is held constant. A small torque about the contact normal or a small tangential force is applied. For bodies of equal material, the normal and tangential stress states are uncoupled, and can solved separately. The surfaces of the bodies are thought as a superposition of infinitesimal rigid flat-ended punches. Consequently, the normal stress distribution can be calculated as a summation of differential flat punch solutions. A formula results, which is identical with the solution of Green and Collins. After application of a torque an annular sliding area forms at the border of the contact area. For reasons of symmetry, the common displacement of the inner stick area must be a rigid body rotation. Similarly to the normal problem, the solution can be thought as a superposition of rigid punch rotations. The tangential solution can be derived analogically, in form of a superposition of rigid punch displacements. The present method also solves the problem of simultanous normal and torsional or tangential loading with complete adhesion. As an example, Steuermann's problem for polynomial surfaces of the formA2nr2nis solved. The solutions for constant normal forces can be used as basic functions for loading histories with varying normal and tangential forces.
86 citations
Metz1
TL;DR: In this article, a general approach to the problem of determining elastoplastic behavior of metallic polycrystals at finite deformation is presented, where the relation between moving dislocation density and global slip rate for grains is developed.
Abstract: A general approach to the problem of determination of elastoplastic behavior of metallic polycrystals at finite deformation is presented. The relation between moving dislocation density and global slip rate for grains is developed. Transition to grain response is obtained by introducing the hardening matrix. Field equations for heterogeneous elastoplastic metals are transformed into an integral equation, using Green functions technique. This allows to find the spin of the lattice related to texture formation.
60 citations
TL;DR: In this article, a metric transformation tensor is introduced to map a locally defined six-dimensional plastic metric onto the metric of the current configuration, which provides a basis for the definition of a local isotropic hyperelastic stress response in the thermoplastic solid.
Abstract: A formulation of isotropic thermoplasticity for arbitrary large elastic and plastic strains is presented. The underlying concept is the introduction of a metric transformation tensor which maps a locally defined six-dimensional plastic metric onto the metric of the current configuration. This mixed-variant tensor field provides a basis for the definition of a local isotropic hyperelastic stress response in the thermoplastic solid. Following this fundamental assumption, we derive a consistent internal variable formulation of thermoplasticity in a Lagrangian as well as a Eulerian geometric setting. On the numerical side, we discuss in detail an objective integration algorithm for the mixed-variant plastic flow rule. The special feature here is a new representation of the stress return and the algorithmic elastoplastic moduli in the eigenvalue space of the Eulerian plastic metric for plane problems. Furthermore, an algorithm for the solution of the coupled problem is formulated based on an operator split of the global field equations of thermoplasticity. The paper concludes with two representative numerical simulations of thermoplastic deformation processes.
57 citations
TL;DR: A description is given of attempts to develop continuum damage mechanics so that the relationship with the physical mechanism approach is less abrupt.
Abstract: Continuum Damage Mechanics has been applied successfully to technical problems since the idea was introduced by Kachanov almost 40 years ago. In keeping with the traditions of mechanics, the formulation was based on the results of mechanical tests on specimens whose size is measured in centimeters. To model the observations which describe the deterioration of material properties it was found necessary to introduce internal variables referred to as ‘damage’. The approach is phenomenological, with only a minimal attempt to provide a physical interpretation of damage. For this reason the approach has had little appeal to those whose interest is in the physical mechanisms which cause material deterioration. In this presentation a description is given of attempts to develop continuum damage mechanics so that the relationship with the physical mechanism approach is less abrupt. The procedure is illustrated with reference to ceramic matrix composites.
46 citations
TL;DR: It is shown that, besides the consideration of simplification resulting from a careful representation of geometric relationships between contiguous links, only two factors determine the overall efficiency ofrecursive methods.
Abstract: Recursive methods represent a well-established and wide-spread technique for generation of dynamical equations of mechanical systems. Their main objective is to obtain computational schemes involving as few operations as possible. In this paper, we show that, besides the consideration of simplification resulting from a careful representation of geometric relationships between contiguous links, only two factors determine the overall efficiency of these methods. These factors are: the choice of an appropriate reference point for the kinematic and kinetic equations, and the frame of decomposition used to represent the involved vectors and tensors. Further, we derive a computational scheme which compares advantageously with existing methods. As only elementary laws of mechanics are applied, the exposition is also suitable for practising engineers seeking to understand the main differences between existing methods. A comparison with one of the reportedly most effective non-recursive method elucidates the advantages and bounds of the present approach.
29 citations
TL;DR: In this paper, a systematischer Weg zu ihrer Losung dargestellt is presented, in which the homogene Losung uber die Losung eines Eigenwertproblems gewonnen.
Abstract: Lineare, periodisch zeitvariante Bewegungsgleichungen treten im Hubschrauber- und Windturbinenbau auf. Der Getriebebau und die Rotordynamik liefern weitere Beispiele. In diesem Bericht wird ein systematischer Weg zu ihrer Losung dargestellt. Mit dem Ansatz von Hill wird die homogene Losung uber die Losung eines Eigenwertproblems gewonnen. Nach Anpassung an die Anfangsbedingungen liefert sie die Fundamentalmatrix des Systems. Ahnlich wie bei zeitinvarianten Systemen, existieren auch bei zeitvarianten Systemen Orthogonalitatsbedingungen, die die Eigenvektoren erfullen. Die Eigenvektoren selbst sind allerdings zeitabhangig. Benutzt man die Eigenvektoren als Ansatzvektor zur Berechnung der erzwungenen Schwingungen (Transformation mit der zeitvarianten Modalmatrix des Systems), so gelingt es, die Bewegungsgleichungen des Systems in entkoppelte, zeitinvariante zu uberfuhren. Sie lassen sich in bekannter Weise losen. Dieses Vorgehen wird auf eine moderne Windkraftanlage angewandt. Sie wurde zunachst mit 372 Freiheitsgraden modelliert, die aber auf 18 vor der numerischen Weiterbehandlung kondensiert wurden. Das Stabilitatsverhalten und die Antwortspektren auf stochastische Anregung durch den Wind wurden auf dem oben beschriebenen Weg ermittelt.
23 citations
TL;DR: An analysis for the self-propulsion of spermatozoa through mucus filling a channel with flexible boundaries finds that the propulsive velocity increases as the departure from the Newtonian theory grows.
Abstract: This paper presents an analysis for the self-propulsion of spermatozoa through mucus filling a channel with flexible boundaries. The mucus is characterized as a micropolar fluid, and the spermatozoa are modelled as a two-dimensional sheet, sending down lateral waves along its length. The model also considers the motion of flexible walls due to muscular activities. This motion is represented by transverse waves along the channel walls. The analysis has been carried out for inertia-free flow under the assumption that the waves travelling along the channel and the sheet are in synchronization under the steady state. It is observed that the propulsive velocity increases as the departure from the Newtonian theory grows.
22 citations
TL;DR: In this paper, a generalized and unified treatment for the antiplane problem of an elastic elliptical inclusion undergoing uniform eigenstrains and subjected to arbitrary loading in the surrounding matrix is presented.
Abstract: A generalized and unified treatment is presented for the antiplane problem of an elastic elliptical inclusion undergoing uniform eigenstrains and subjected to arbitrary loading in the surrounding matrix. The general solution to the problem is obtained through the use of conformal mapping technique and Laurent series expansion of the associated complex potentials. The resulting elastic fields are derived explicitly in both transformed and physical planes for the inclusion and the surrounding matrix. These relations are universal in the sense of being independent of any particular loading as well as the geometry of the matrix. The complete field solutions are provided for an elliptical inclusion under uniform loading at inifinity, and for a screw dislocation interacting with the elastic elliptical inclusion.
TL;DR: In this article, the principle of virtual work is applied to electromechanical systems as the foundation of a unifying concept for modelling mechatronical systems, which yields an analogous form to the central equation of mechanics which is valid for holonomic and nonholonomic systems.
Abstract: The principle of virtual work is applied to electromechanical systems as the foundation of a unifying concept for modelling mechatronical systems. After the presentation of an important result in the field of mechanics, the expansion of the principle on electrical networks and electromechanical systems is shown. The use of the principle of virtual work in the domain of electromechanics yields an analogous form to the central equation of mechanics which is valid for holonomic and nonholonomic systems. The electrotechnical part of the system is confined to networks. The derivation of the mathematical model is demonstrated on the example of a simple electromechanical oscillation circuit. In addition, the physical systems are separately treated, taking into account the explicit constraints on the basis of the Lagrangian multiplier method.
TL;DR: In this article, the authors investigated elastic composite plates with a microperiodic structure along the plate's midsurface and formulated and investigated a refined theory of the composite plates under consideration, which would describe the microdynamic plate behaviour caused by the microstructure.
Abstract: The subject of the contribution is an investigation of elastic composite plates with a microperiodic structure along the plate's midsurface. The computational models of the plates are largely based on the homogenization procedures leading to equations with constant coefficients. However, the homogenization theories neglect the microstructure length-scale effect on the plate's dynamic behaviour. The objective of this research is to formulate and investigate a refined theory of the composite plates under consideration, which would describe the microdynamic plate behaviour caused by the microstructure. The possible applications of the proposed theory are shown by an example.
TL;DR: In this paper, the dynamic behavior of an Euler beam traversed by a moving concentrated mass is analyzed for the general case of a mass moving with a varying speed, and the possibility of the mass separating from the beam is analyzed by examining the contact forces between the mass and the beam during the motion.
Abstract: The dynamic behaviour of an Euler beam traversed by a moving concentrated mass, is analyzed for the general case of a mass moving with a varying speed. The equation of motion in a matrix form is formulated using the Lagrangian approach and the assumed mode method. The dimensionless form of the equation enables the numerical results to be applicable for a wide range of system parameters. The possibility of the mass separating from the beam is analyzed by examining the contact forces between the mass and the beam during the motion.
TL;DR: In this paper, exact relationships between the deflection of isotropic sandwich plates and their corresponding Kirchhoff plates are presented, and the governing equilibrium equations for the sandwich plates are derived on the basis of the Reissner-Mindlin shear deformation plate theory.
Abstract: This study presents exact relationships between the deflections of isotropic sandwich plates and their corresponding Kirchhoff plates. The governing equilibrium equations for the sandwich plates are derived on the basis of the Reissner-Mindlin shear deformation plate theory. The considered plates are either (i) simply supported, of general polygonal shape and under any transverse loading condition or (ii) simply supported and clamped circular plates under axisymmetric loading. As the relationships are exact under the assumptions used in the plate theories, one may obtain exact deflection solutions of sandwich plates if the Kirchhoff plate solutions are exact. The relationships should also be useful for the development of approximate formulas for plates with other shapes, boundary and loading conditions, and may serve to check numerical deflection values computed from sandwich plate analysis software.
TL;DR: In this article, the restriction to the admissible deformation of a fiber-reinforced composites (FRC) imposed by the failure strains of the fibres is investigated, and the complete and irreducible two-dimensional tensor function representations regarding tetratropy, hexatropy and octotropy derived in Part I are applied to formulate constitutive equations for FRCs.
Abstract: From the continuum mechanics points of view, most of commercial fibre-reinforced composites (FRCs) can be considered to be anisotropic materials with one of the five material symmetries: transverse isotropy, orthotropy, tetratropy, hexatropy and octotropy, as illustrated in the preceding paper (Part I) [1]. No properly general formulation of constitutive equations for tetratropic, hexatropic and octoctropic types of FRC has been found in the literature. In this paper, the restriction to the admissible deformation of a FRC imposed by the failure strains of the fibres is investigated. The complete and irreducible two-dimensional tensor function representations regarding tetratropy, hexatropy and octotropy derived in Part I are applied to formulate constitutive equations for FRCs in plane problems of elasticity, yielding and failure in the present work, and of heat conduction, continuum damage and asymmetric elasticity in a continued work (Part III, forthcoming).
TL;DR: The stationary problem of a rigid thermally insulated punch sliding over the boundary surface of a periodic two-layered thermoelastic half-space is considered in this paper, where the heat generated in the contact area is assumed to be caused by frictional forces.
Abstract: The stationary problem of a rigid thermally insulated punch sliding over the boundary surface of a periodic two-layered thermoelastic half-space is considered The heat generated in the contact area is assumed to be caused by frictional forces The problem is formulated within the framework of thermoelasticity with microlocal parameters, and it is reduced to a system of two integral equations, which is solved numerically The effects connected with the composite structure are analyzed
TL;DR: In this article, an axisymmetric shell element for large plastic strains is developed based on the multiplicative decomposition of the material deformation gradient into an elastic and a plastic part.
Abstract: An axisymmetrical shell element for large plastic strains is developed. The theory is based on the multiplicative decomposition of the material deformation gradient into an elastic and a plastic part. For quasi-Kirchhoff-type axisymmetric shells this leads to a product of the elastic and plastic stretches. By introduction of logarithmic strains the decomposition becomes additive. Plastic incompressibility is fulfilled in an exact manner.
TL;DR: In this paper, the problem of optimal prestress stabilization of elastic structures with frictional contact interfaces subject to static loads is studied, and the optimal control problem is nonsmooth and nonconvex, as it concerns the control of structures governed by variational inequalities.
Abstract: The problem of optimal prestress stabilization of elastic structures with frictional contact interfaces subject to static loads is studied in this paper. A linear elastic structure with given unilateral contact at frictional interfaces is considered. The prestressing control is modelled by the pin-load method. The static problem is formulated as a nonsymmetric variational inequality. The goal of the optimal control design is closing of the unilateral contact joints as well as minimization of the friction induced slips with a minimum effort. The resulting optimal control problem is nonsmooth and nonconvex, as it concerns the control of structures governed by variational inequalities. Appropriate techniques of nonsmooth analysis are used for its numerical solution. Effective computer realization and integration into existing finite element software is facilitated by appropriate static condensation techniques, which are outlined in the paper. Numerical examples illustrate the theory.
TL;DR: In this article, the problem of the elasto-viscoplastic dynamic behavior of geometrically nonlinear plates and shells is studied under the assumption of small strains and moderate rotations.
Abstract: In this paper, the problem of the elasto-viscoplastic dynamic behaviour of geometrically non-linear plates and shells is studied under the assumption of small strains and moderate rotations. The Chaboche and Bodner-Partom models were chosen among several types of constitutive laws. To avoid the calculation of the stiffness matrix, an effective procedure using the central difference method of solving the equations of motion was applied. The trapezoidal method was used to integrate the constitutive viscoplastic laws. A nine-node isoparametric shell element was utilised for the finite element algorithm.
TL;DR: In this paper, a numerical procedure to study one-dimensional waves in solids is considered in application to longitudinal loading of elastic-plastic rods of a variable cross section, assuming direct mathematical modelling of mechanical perturbations.
Abstract: A numerical procedure to study one-dimensional waves in solids is considered in application to longitudinal loading of elastic-plastic rods of a variable cross section. The procedure assumes direct mathematical modelling of mechanical perturbations. Multiple reflections of waves from the rod ends, alternating signs of stress, influence of isotropic and anisotropic hardening, and the Bauschinger effect are taken into account. A detailed description of stress waves in elastic-plastic rods of a variable cross section at the impact of a rigid body is presented.
TL;DR: In this paper, den Einflus von Kriechschadigung und Belastungsvorgeschichte auf das weitere kriechverhalten nach einer Anderung der BER zu bestimmen is discussed.
Abstract: Ziel der Untersuchung ist es, den Einflus von Kriechschadigung und Belastungsvorgeschichte auf das weitere Kriechverhalten nach einer Anderung der Belastungsrichtung zu bestimmen. Die ermittelten Kriechbruchzeiten werden stark von der Anderung der Belastungsrichtung beeinflust. Dieses Verhalten wird mit einer tensoriell nichtlinearen Theorie erklart, indem man den Einflus der Vorschadigung mit einem zweistufigen Tensor darstellt.
TL;DR: In this paper, the nonlinear dynamics of axisymmetric, inviscid, incompressible, thin, annular liquid jets subjected to fluctuating body forces is studied numerically by means of an adaptive finite difference method which maps the time-dependent, curvilinear geometry of the jet into a unit square.
Abstract: The nonlinear dynamics of axisymmetric, inviscid, incompressible, thin, annular liquid jets subjected to fluctuating body forces is studied numerically by means of an adaptive finite difference method which maps the time-dependent, curvilinear geometry of the jet into a unit square. The fluctuating body forces may arise from fluctuations in the gravitational acceleration in inertial frames or from the acceleration of a non-inertial frame of reference which translates parallelly to an inertial one. It is shown that both the pressure coefficient and the axial location at which the annular jet becomes a solid one are periodic functions of time with a period equal to that of the imposed body force fluctuations, and that their magnitude increases as the amplitude of the body force fluctuations is increased. It has also been shown that, for both intermittent, sinusoidal or rectangular excitations, increases in the frequency of the excitation result in the creation of superharmonics, broad, albeit peaked, spectra, and closed phase planes with many loops.
TL;DR: In this paper, a tensoriell nichtlineare Theorie fur tertiares Kriechen isotroper Werkstoffe is gegeben, and die anisotropicen Kriechschadigungen werden with einem zweistufigen Schadenstensor beschrieben.
Abstract: Eine tensoriell nichtlineare Theorie fur tertiares Kriechen isotroper Werkstoffe ist gegeben. Die anisotropen Kriechschadigungen werden mit einem zweistufigen “Schadenstensor” beschrieben. Zur Ermittlung der Materialkonstanten der Materialgleichung und Evolutionsgleichung werden einachsige Kriechversuche an Flachproben aus dem austenitischen Stahl X8 CrNiMoNb 16 16 durchgefuhrt.
TL;DR: In this article, the mechanical properties of a substructure based on the properties of individual phases and their interactions is presented on the example of the unidirectional SiC fiber-reinforced SiC composite.
Abstract: The modelling of the mechanical properties of a substructure, based on the properties of the individual phases and their interactions, is presented on the example of the unidirectional SiC fibre-reinforced SiC composite. The substructure is selected in such a way that the total structure can be modelled from a wide number of substructures. The numerical evaluation of the model is accomplished by means of the finite element method (FEM). Finally, in numerical simulations of a particular example, the statistically verified events of damage in the substructure are described.
TL;DR: The investigation shows structural differences between the dynamic behaviour of models with distributions of mass over the “finite” elements as compared to continuous models.
Abstract: The harmonic and transient behaviours of one-dimensional discrete semi-infinite cascades of masses and springs have been derived from analytical pulse response solutions [1]. The investigation shows structural differences between the dynamic behaviour of models with distributions of mass over the “finite” elements as compared to continuous models. Two generally accepted ideas are scrutinized. Firstly, that the dynamic behaviour of a discrete model after a refinement of the mesh converges to the response of the underlying continuous model. Secondly, that a symmetric mass distribution over the element results in a better convergence. Both ideas need some adjustment.
TL;DR: In this article, a solution for the linear thermoelastic problem of determining axisymmetric stress and displacement fields in an isotropic elastic solid of infinite extent weakened by an external circular crack under general mechanical loadings and general thermal conditions is presented.
Abstract: The paper presents a solution for the linear thermoelastic problem of determining axisymmetric stress and displacement fields in an isotropic elastic solid of infinite extent weakened by an external circular crack under general mechanical loadings and general thermal conditions. The mechanical loadings and thermal conditions applied on the crack faces are axisymmetric, being non-symmetric about the crack plane. In similar lines of [7], equations of equilibrium of an elastic solid conducting heat have been solved using Hankel transforms and Abel operators of the first kind. Expressions for stress, displacement, temperature and heat flux functions are obtained in terms of Abel transforms of the first kind of the jumps of stress, displacement, temperature and heat flux at the crack plane. Two types of thermal conditions, that is, general surface temperatures and general heat flux on faces of the crack are considered. In both the cases, closed form solutions have been obtained for the unknown functions solving Abel type of integral equations. Explicit expressions for stresses, displacements, temperature fields, stress intensity factors have been obtained. Two special cases of thermal conditions in which: (i) crack faces are subjected to constant non-symmetric temperatures over a circular ring area, (ii) crack faces are subjected to constant non-symmetric heat flux over a circular ring area, have been considered. In some special cases, results have been compared with those from the literature.
TL;DR: In this paper, a survey on the orthotropic composite materials is given and the model of the interphase, assuming a third phase between fibre and matrix with some different properties, is used for the calculation of the elastic constants of a unidirectional fibre-reinforced epoxy resin composite.
Abstract: In this paper, a survey on the orthotropic composite materials is given. The model of the interphase, assuming a third phase between fibre and matrix with some different properties, is used for the calculation of the elastic constants of a unidirectional fibre-reinforced epoxy resin composite. Their values are used to determine the stress field at the crack tip and the stress intensity factor of a cracked orthotropic plate. The recently developed Det-criterion of fracture is taken into account to study the crack initiation.
TL;DR: In this article, a new technique is proposed to obtain an approximate probability density for the response of a general nonlinear system under Gaussian white noise excitations, which can yield exact stationary solutions for the nonlinear oscillators.
Abstract: A new technique is proposed to obtain an approximate probability density for the response of a general nonlinear system under Gaussian white noise excitations. In this new technique, the original nonlinear system is replaced by another equivalent nonlinear system, structured by the polynomial formula, for which the exact solution of stationary probability density function is obtainable. Since the equivalent nonlinear system structured in this paper originates directly from certain classes of real nonlinear mechanical systems, the technique is applied to some very challenging nonlinear systems in order to show its power and efficiency. The calculated results show that applying the technique presented here can yield exact stationary solutions for the nonlinear oscillators. This is obtained by using an energy-dependent system, and for a nonlinearity of a more complex type. A more accurate approximate solution is then available, and is compared with the approximation. Application of the technique is illustrated by examples.