Showing papers on "Continuum mechanics published in 1988"
874 citations
562 citations
TL;DR: In this article, a damage tensor is proposed to deal with some sets of discontinuities distributed in a rock mass, for example, joint systems, which are characterized by a second-order symmetric tensor.
Abstract: The mechanical behaviour of a rock mass is strongly affected by discontinuities such as faults and joints. In this paper, a damage mechanics theory is proposed which deals with some sets of discontinuities distributed in a rock mass, for example, joint systems. In this theory, the distributed discontinuities are characterized by a second-order symmetric tensor, called the damage tensor. By introducing the damage concept, the deformation and fracturing behaviour of the rock mass can be reated in a framework of continuum mechanics. A numerical procedure is developed in order to implement the damage mechanics model by using the finite element method. The theory and numerical analysis are applied to several laboratory tests and a practical underground opening problem. Numerical results are compared with measured data.
197 citations
TL;DR: In this paper, the problem of minimizing a possibly nonconvex and non-coercive functional is studied and necessary or sufficient conditions for the existence of solutions are given, involving a generalized recession functional, whose properties are discussed thoroughly.
Abstract: The problem of minimizing a possibly non-convex and non-coercive functional is studied. Either necessary or sufficient conditions for the existence of solutions are given, involving a generalized recession functional, whose properties are discussed thoroughly. The abstract results are applied to find existence of equilibrium configurations of a deformable body subject to a system of applied forces and partially constrained to lie inside a possibly unbounded region.
135 citations
TL;DR: In this article, a simplification of classical physics and continuum mechanics that decouples thermal and mechanical effects is presented, and the existence of the isoenergy density function provides an elegant means of resolving the multidimensionality of the problem; the translation of unidimensional data to multidimensional states.
112 citations
TL;DR: The K•BKZ constitutive model is now 25 years old as mentioned in this paper and the connections of the model and its variants with continuum mechanics, molecular theory, and experiment are reviewed.
Abstract: The K‐BKZ constitutive model is now 25 years old. The article reviews the connections of the model and its variants with continuum mechanics, molecular theory, and experiment. An application of this type of model to computation is mentioned.
81 citations
TL;DR: In this paper, a theory of second order diffusion processes and associated stochastic differential equations of second-order diffusion processes was developed. But the theory is not satisfied for a large class of reciprocal Gaussian processes.
Abstract: We develop a theory of second order diffusion processes and associated stochastic differential equations of second order. We show that equations of evolution of the density, mean velocity and momentum flux are a family of first order conservation laws similar to those of continuum mechanics. We verify that the theory is satisfied for a large class of reciprocal Gaussian processes
65 citations
TL;DR: In this paper, a model for diffusion in polymers is established from basic principles of irreversible thermodynamics, employing the methodology of continuum mechanics The polymeric materials are considered to respond viscoelastically, with ageing, and effects of stress on diffusion and certain anomalies in the moisture sorption process can be explained by the present model.
Abstract: : A model for diffusion in polymers is established from basic principles of irreversible thermodynamics, employing the methodology of continuum mechanics The polymeric materials are considered to respond viscoelastically, with ageing It is shown that effects of stress on diffusion and certain anomalies in the moisture sorption process can be explained by the present model Diffusion, Viscoelasticity, Moisture
61 citations
TL;DR: In this article, a cumulative damage model for the prediction of stiffness loss in graphite/epoxy laminates applies a thermomechanical constitutive theory for elastic composites with distributed damage.
Abstract: The present cumulative damage model for the prediction of stiffness loss in graphite/epoxy laminates applies a thermomechanical constitutive theory for elastic composites with distributed damage. The model proceeds from a continuum mechanics and thermodynamics approach in which the distributed damage is characterized by a set of second-order tensor-valued internal state variables. A set of damage-dependent laminated plate equations is obtained; this is developed by modifying classical Kirchhoff plate theory.
47 citations
TL;DR: In this article, the authors present a continuum damage model for viscoelastic materials, where damage is expressed by two symmetric, second-rank tensors which are related to the total areas of active and passive micro-cracks within a representative volume element of the multi-fractured material.
Abstract: : This paper presents a continuum damage model for viscoelastic materials. Viscoelastic response in the presence of distributed micro-flaws occurs in solid propellants and is likely to be encountered in thermoplastic composites. In contrast to rock and metals, polymeric materials absorb various kinds of solvents, which may damage the polymeric composites in a variety of ways. In the case of water absorption by epoxy-based composites, such damage was noted by several investigators. Damage is expressed by two symmetric, second- rank tensors which are related to the total areas of active and passive micro- cracks within a representative volume element of the multi-fractured material. Viscoelasticity is introduced through scalar-valued internal state variables that represent the internal degrees of freedom associated with the motions of long-chain polymeric molecules. The constitutive relations are established from basic considerations of continuum mechanics and irreversible thermodynamics, with detailed expressions derived for the case of initially isotropic materials. It is shown that damage causes softening of the material moduli as well as changes in material symmetry. The special cases of uni-axial damage under uni-axial stress and the interaction of damage with moisture diffusion are also considered.
37 citations
TL;DR: In this article, a thermomechanical model of continuous media based on second gradient theory has been used to study the motions in liquid-vapor interfaces, which is shown to be fundamentally equivalent to molecular theories.
Abstract: A thermomechanical model of continuous media based on second gradient theory has been used to study the motions in liquid-vapor interfaces. In the equilibrium state this model is shown to be fundamentally equivalent to molecular theories. Conservative motions in such fluids verify the first integrals that provide Kelvin’s circulation theorems and potential equations. The dynamic surface tension of a liquid-vapor interface has been deduced from equations written with a viscosity factor. The result provides and explains the Marangoni effect.
TL;DR: A formalism is developed in which the random nature of a real porous medium can be incorporated quantitatively into a numerical simulation scheme based on a discretization of the continuum fluid-mechanical equations.
Abstract: The problem of two-phase fluid flow in statistically homogeneous but random porous media is addressed. Particular emphasis is placed on the role of the stochastic nature of the porous medium in the development of unstable interfaces at large mobility ratios. A formalism is developed in which the random nature of a real porous medium can be incorporated quantitatively into a numerical simulation scheme based on a discretization of the continuum fluid-mechanical equations. In particular, it is not necessary to set the discretization length close to the pore scale and to perform a detailed structural analysis of the microgeometry in order to characterize the random nature of the porous matrix. The formalism is based on the concepts of tubes and chambers which give rise, on the discretization length scale, to random hydrodynamic conductivity and fluid capacity, respectively, and on larger scales to the macroscopically determined permeability and porosity, respectively. In the absence of detailed information about the statistical properties of the random medium at the discretization length scale, a maximum entropy criterion is used to deduce the most random distribution of properties of tubes and chambers consistent with macroscopically observable quantities. This criterion reveals the fundamental significance of an exponentially distributed fluid capacity. A number of numerical experiments are reported. The relation of the present simulation algorithm to diffusion-limited aggregation (DLA) and related algorithms for the simulation of two-phase flows is revealed, and exponentially distributed fluid capacity is again found to be of fundamental significance. In particular, it is found that a number of further assumptions which are physically plausible but difficult to justify rigorously are required to relate the DLA and similar ``random-walk'' models to a fluid-mechanical model based on the equations of continuum mechanics applied to a stochastic medium.
01 Apr 1988
TL;DR: In this paper, a viscoplastic constitutive theory is presented for representing the high temperature deformation behavior of metal matrix composites, where the composite is considered a material in its own right, with its own properties that can be determined for the composite as a whole.
Abstract: A viscoplastic constitutive theory is presented for representing the high temperature deformation behavior of metal matrix composites. The point of view taken is a continuum one where the composite is considered a material in its own right, with its own properties that can be determined for the composite as a whole. It is assumed that a single preferential (fiber) direction is identifiable at each material point (continuum element) admitting the idealization of local transverse isotropy. A key ingredient is the specification of an experimental program for the complete determination of the material functions and parameters for characterizing a particular metal matrix composite. The parameters relating to the strength of anisotropy can be determined through tension/torsion tests on longitudinally and circumferentially reinforced thin walled tubes. Fundamental aspects of the theory are explored through a geometric interpretation of some basic features analogous to those of the classical theory of plasticity.
01 Apr 1988
TL;DR: In this paper, a continuum mechanics frame-vork for analyzing necking and shear band instabilities is discussed, and the predicted onset of instability depends sensitively on the material's constitutive characterization, not only through properties, such as strain hardening and strain rate sensitivity, that can be measured in proportional loading tests, but also through the material response to a change in loading path.
Abstract: The continuum mechanics framevork for analyzing necking and shear band instabilities is discussed. The predicted onset of instability depends sensitively on the material’s constitutive characterization, not only through properties, such as strain hardening and strain rate sensitivity, that can be measured in proportional loading tests, but also through the material’s response to a change in loading path. A specific problem is discussed that illustrates the influence of the curvature of flow potential surfaces even when a softening mechanism plays a major role in precipitating localization.
Book•
01 Jan 1988
TL;DR: Chapter I. Elements of Linear Algebra and Mathematical Programming and Elements of Continuum Mechanics.
Abstract: Chapter I. Elements of Linear Algebra and Mathematical Programming. II. Elements of Continuum Mechanics. III. Differential Description of an Element. IV. Discrete Description of an Element. V. Discrete Description of a Structure. VI. Elastic Analysis. VII. Elastic-Plastic Analysis. VIII. Ultimate Load Analysis. References. Appendices. Index.
01 Jan 1988
TL;DR: In this article, the main goal is to describe operator splitting methods for the solution of time dependent differential equations, and to discuss their application to the numerical solution of nonlinear problems such as the Navier-Stokes equations for incompressible viscous fluids, the linear eigenvalue problem, the Hartree equation for the Helium atom, and finally to the non-convex problem from the calculus of variations associated to the physics of liquid crystals.
Abstract: The main goal of this paper is to describe operator splitting methods for the solution of time dependent differential equations, andto discuss their application to the numerical solution of nonlinear problems such as the Navier-Stokes equations for incompressible viscous fluids, the linear eigenvalue problem, the Hartree equation for the Helium atom, and finally to the solution of a non convex problemfrom the calculus of variations associated to the physics of liquid crystals. Numerical results will be presented showing the potential of such methods.
TL;DR: In this article, the structure of amorphous Fe1-xBx is described within the framework of a recent structural model that takes into account experimental and theoretical results on density, atomic short-range order and microphase separation applying methods of stochastic geometry.
Abstract: The structure of amorphous Fe1-xBx is described within the framework of a recent structural model that takes into account experimental and theoretical results on density, atomic short-range order and microphase separation applying methods of stochastic geometry. The determination of internal stresses is based on a statistical continuum mechanics approach using the 'maximum entropy formalism'. The sources of the internal stresses are given by differential thermal strains which the microphase clusters undergo during quenching. Analytical expressions for the stress distributions, Young's modulus and bulk modulus are derived for the isotropic case. Numerical results are discussed in terms of dependence on boron concentration. The present method is applicable to all types of rapidly quenched materials whose structures, can be considered to consist of an arrangement of microphase clusters.
TL;DR: In this paper, it is shown that any frame-dependent terms in constitutive equations must arise from the intrinsic spin tensor and are negligible provided that the ratio of microscopic to macroscopic time scales is extremely small.
TL;DR: In this article, a set of constitutive equations consisting of the mechanical constitutive equation and of the transformation kinetics were presented to describe the transformation pseudoelasticity, the partial pseudoelsasticity and the shape memory effect.
Abstract: The stress-strain-temperature relation in TiNi alloys was investigated from the phenomenological point of view. A set of constitutive equations consisting of the mechanical constitutive equation and of the transformation kinetics were presented to describe the transformation pseudoelasticity, the partial pseudoelasticity and the shape memory effect. The material constants in the theory were determined from the tension tests on TiNi wire specimens at various temperatures. The theory was successfully applied to the calculation of the recovery force induced in the heating process under the condition of constraint strain.
TL;DR: In this article, a model which incorporated the recovery effect by diffusion of atoms is presented to explain the initiation of grain-boundary wedge-type crack in high-temperature fatigue.
Abstract: A continuum mechanics model which incorporated the recovery effect by diffusion of atoms is presented to explain the initiation of grain-boundary wedge-type crack in high-temperature fatigue. The direction of deformation is periodically changed in fatigue, and the crack initiation depends on the deformation history of the grain boundary. A theoretical calculation based on the present model was made on the grain-boundary crack initiation in high-temperature fatigue where the deformation is path-dependent. The calculation results satisfactorily explained the experimental observations in polycrystalline metallic materials.
TL;DR: In this article, the analysis of stochastic mathematical models in continuum mechanics is discussed and a mathematical method to compute the time evolution of the probability density in conjunction with the dependent variable is presented.
15 Mar 1988
Abstract: The stress-strain-temperature relation in TiNi alloys was investigated from the phenomenological point of view. A set of constitutive equations consisting of the mechanical constitutive equation and of the transformation kinetics were presented to describe the transformation pseudoelasticity, the partial pseudoelasticity and the shape memory effect. The material constants in the theory were determined from the tension tests on TiNi wire specimens at various temperatures. The theory was successfully applied to the calculation of the recovery force induced in the heating process under the condition of constraint strain.
TL;DR: In this paper, a nonlinear theory of plates and shells for thick and thin models accounting for consistent and inconsistent kinematical approximations is presented in general curvilinear tensorial form.
01 Jan 1988
TL;DR: The theory of pseudo-rigid bodies as mentioned in this paper focuses on the large-scale motions of deformable bodies and provides a convenient framework, like classical rigid-body mechanics, for the analysis of gross changes in the position and orientation of a body.
Abstract: The theory of pseudo-rigid bodies focuses on the large-scale motions of deformable bodies. It provides a convenient framework, like classical rigid-body mechanics, for the analysis of gross changes in the position and orientation of a body. As such it represents a generalization of that classical theory. At the same time, the theory of pseudo-rigid bodies concerns deformation, treating changes in the shape of a body by use of certain gross measures of strain. As such it represents a restriction, or coarse version, of many theories now commonplace in continuum mechanics. Between these two extremes, the modern and the classical, the theory of pseudo-rigid bodies takes a middle road, focusing on problems that exhibit a high degree of interplay between deformation and rigid-body motion.
Book•
01 Jan 1988
TL;DR: Acerbi and Fusco as discussed by the authors proposed an approximation lemma for W 1,p functions and showed that W 1 p functions can be approximated with a constant number of holes.
Abstract: Contributors Preface E. Acerbi and N. Fusco: An approximation lemma for W 1,p functions E. Acerbi: Homogenization and periodic structures with holes G. Buttazzo: Thin insulating layers: the optimization point of view E. Cabib: Lower semicontinuity and relaxation for some problems in optimal design G. Caginalp: Mathematical models of phase boundaries G. Capriz: Continua with constrained or latent microstructure D. Cioranescu and J. Saint Jean Paulin: Elastic behaviour of very thin cellular structures B. Dacorogna and P. Marcellini: A counterexample in the vectorial calculus of variations C. Davini: Elastic invariants in crystal theory R.J. DiPerna: Concentrations in solutions to conservative systems J.L. Ericksen: Some constrained elastic crystals L.E. Fraenkel: Some results for a linear, partly hyperbolic model of viscoelastic flow past a plate R. Illner: Derivation and validity of the Boltzmann equations: some remarks on reversibility concepts, the H-functional and coarse-graining R.D. James: Microstructure and weak convergence C.K.R.T. Jones: Standing waves of nonlinear Schr dinger equations: existence and stability D. Kinderlehrer: Remarks about equilibrium configurations of crystals J.L. Lions: Some remarks on uniqueness properties K.A. Lurie and A.V. Cherkaev: On a certain variational problem of phase equilibrium E. Mascolo: Some remarks on non-convex problems D.G. McCartney and J.D. Hunt: Experimental and theoretical aspects of cellular and dendritic solidification A. Novick-Cohen: On the viscous Cahn-Hilliard equation O.A. Oleinik: Some asymptotic problems of linear elasticity R.L. Pego: Phase mixtures in nonlinear viscoelasticity in one dimension O. Penrose: Statistical mechanics and the kinetics of phase separation M. Pitteri: On 1- and 3-dimensional models in "non-convex" elasticity V. Roytburd and M. Slemrod: An application of the method of compensated compactness to a problem in phase transitions R. Schianchi: A review of some non-convex problems M.E. Schonbek: Nonlinear geometric optics and conservation laws M. Silhav 'y: On the admissibility of shocks and propagating phase boundaries in a van der Waals fluid F. Tomarelli: Unilateral problems in continuum mechanics A. Visintin: Surface tension effects in phase transitions Index.
TL;DR: In this paper, the authors analyzed the time dependent damage of a halfplane subjected to a normal surface displacement over a segment at 0.5 mm/s and found that the material is made of 4340 steel and dissipates energy in an irreversible manner such that the stress and strain response in each local element can change with time.
01 Jan 1988
TL;DR: In this paper, a reexamination of the definition of frame indifference, as it is expressed mathematically, is presented, and a number of frame indifferent constitutive equations are given to illustrate the concepts presented here.
Abstract: In the recent years a controversy has appeared in the literature in reference to the frame indifference of certain tensorial expressions. In this paper a reexamination of the definition of frame indifference, as it is expressed mathematically, is presented. It is emphasized that frame indifference cannot be examined before a choice of reference frame is made. Finally, a number of frame indifferent constitutive equations are given to illustrate the concepts presented here.