Topic
Continuum mechanics
About: Continuum mechanics is a research topic. Over the lifetime, 5042 publications have been published within this topic receiving 181027 citations.
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01 Jan 1996
TL;DR: In this article, the authors present an introductory survey of some selected topics in finite elasticity, including constitutive equations for compressible and incompressible, isotropic hyperelastic materials.
Abstract: This is an introductory survey of some selected topics in finite elasticity. Virtually no previous experience with the subject is assumed. The kinematics of finite deformation is characterized by the polar decomposition theorem; and Euler’s laws of balance and the local field equations of continuum mechanics are described. The general constitutive equation of hyperelasticity theory is deduced from a mechanical energy principle; and the implications of frame invariance and of material symmetry are presented. This leads to constitutive equations for compressible and incompressible, isotropic hyperelastic materials. Constitutive equations studied in experiments by Rivlin and Saunders (Ref. 1) for incompressible rubber materials and by Blatz and Ko (Ref. 2) for certain compressible elastomers are derived; and an equation characteristic of a class of biological tissues studied in primary experiments by Fung (Ref. 3) is discussed. Sample applications are presented for these materials. A balloon inflation experiment is described, and the physical nature of the inflation phenomenon is examined analytically in detail. Results for the different materials are compared. Two major problems of finite elasticity theory are discussed. Some results concerning Ericksen’s problem on controllable deformations possible in every isotropic hyperelastic material are outlined; and examples are presented in illustration of Truesdell’s problem concerning analytical restrictions imposed on constitutive equations. Universal relations valid for all compressible and incompressible, isotropic materials are discussed. The nonuniversal, antiplane shear problem and related theorems are presented. Some examples of nonuniqueness, including that of a neo-Hookean cube subject to uniform loads over its faces, are described. Elastic stability criteria and their connection with uniqueness in the theory of small deformations superimposed on large deformations are introduced, and a few applications are mentioned.
72 citations
TL;DR: In this article, the authors give a brief review of the various relations proposed for the interaction force in multiphase (or multicomponent) mixtures and provide an alternative approach for finding the drag force on a particle in a particulate mixture.
Abstract: In the mechanics of multiphase (or multicomponent) mixtures, one of the outstanding issues is the formulation of constitutive relations for the interaction force. In this paper, we give a brief review of the various relations proposed for this interaction force. The review is tilted toward presenting the works of those who have used the mixture theory (or the theory of interacting continua) to derive or to propose a relationship for the interaction (or diffusive) force. We propose a constitutive relation which is general and frame-indifferent and thus suitable for use in many flow conditions. At the end, we provide an alternative approach for finding the drag force on a particle in a particulate mixture. This approach has been used in the non-Newtonian fluid mechanics to find the drag force on surfaces.
72 citations
Book•
01 Jan 2003TL;DR: The theory of simple beams and the theory of Simple Beams I and II were discussed in this paper, where the theory was extended to include two-dimensional problems and stability of equilibrium.
Abstract: 1 Basic Concepts of Continuum Mechanics- 2 Elastic Material- 3 The Theory of Simple Beams I- 4 Torsion of Prismatic Bars- 5 Curved Beams- 6 Simple Beams II: Energy Principles- 7 Two-dimensional Problems- 8 Plates and Shells- 9 Stability of Equilibrium- 10 Some Basic Concepts of Dynamics- 11 Oscillators with One Degree of Freedom- 12 Systems of Several Degrees of Freedom- 13 Answers to the Exercises
72 citations
15 Dec 1971
TL;DR: In this article, the theory of dislocations in a continuum is developed and methods are presented for solving boundary value problems for stresses and displacements due to distributions of dislocations.
Abstract: : The theory of dislocations in a continuum is developed Methods are presented for solving boundary value problems for stresses and displacements due to distributions of dislocations Examples are presented of the application of the theory to crystalline materials
72 citations
TL;DR: In this paper, the fracture behavior of a graphene sheet, containing a center crack (length of 2a), was characterized based on the atomistic simulation and the concept of continuum mechanics, where two failure modes were considered by applying remote tensile and shear loading, respectively, on the graphene sheet.
72 citations