Linear elasticity

About: Linear elasticity is a research topic. Over the lifetime, 9080 publications have been published within this topic receiving 258684 citations.

Mathematical Modeling in Continuum Mechanics

Abstract: Part I. Fundamental Concepts in Continuum Mechanics: 1. Describing the motion of a system: geometry and kinematics 2. The fundamental law of dynamics 3. The Cauchy stress-tensor. Applications 4. Real and virtual powers 5. Deformation tensor. Deformation rate tensor. Constitutive laws 6. Energy equations. Shock equations Part II. Physics of Fluids: 7. General properties of Newtonian fluids 8. Flows of perfect fluids 9. Viscous fluids and thermohydraulics 10. Magnetohydrodynamics and inertial confinement of plasmas 11. Combustion 12. Equations of the atmosphere and of the ocean Part III. Solid Mechanics: 13. The general equations of linear elasticity 14. Classical problems of elastostatics 15. Energy theorems. Duality. Variational formulations 16. Introduction to nonlinear constitutive laws and to homogenization Part IV. Introduction to Wave Phenomena: 17. Linear wave equations in mechanics 18. The soliton equation: the Korteweg-de Vries equations 19. The nonlinear Schrodinger equation Appendix A.

Singular plastic flow fields near surfaces of maximum friction stress

Abstract: Assuming a rigid/perfectly plastic material model with arbitrary isotropic smooth yield criterion, it is shown that the velocity fields adjacent to surfaces of maximum friction, except for some special planar flows, must be describable by non-differentiable functions where the maximum shear strain rate and the effective strain rate approach infinity. This is consistent with experimental results that show very large gradients of velocity near such surfaces and with computational results that indicate difficulty in describing such behavior with finite elements using simple interpolation functions. Moreover, this result leads naturally to the definition of a strain rate intensity factor which has similar meaning to the stress intensity factor in linear elastic fracture mechanics. As an example of the application of the singular velocity field, simple compression of a plastic layer between parallel, rough plates is considered. An upper bound solution is found by assuming the singular field in the layer. As expected, it lies between the upper bound obtained by assuming simple compression in the layer and a slip line solution.

Micromechanics-based stress-strain behaviour of soils at small strains

Abstract: A model that describes the small-strain behaviour of soils is derived using micromechanics theory. The model allows examination of the effects of fabric anisotropy, stress conditions and contact characteristics on the small-strain modulus of soils. The closed-form solutions of the small-strain modulus are presented for the case of an isotropic fabric assembly under isotropic stress conditions. A fabric tensor is used to model the fabric anisotropy, and the small-strain modulus for the case of cross-anisotropic fabric assembly under general stress conditions is numerically calculated. The effect of the contact condition between soil particles is examined by incorporating three different contact laws (the linear elastic, Hertz–Mindlin and rough-surface contact models) into the model. It was found that the numerical results using the rough-surface contact model compare well with the published experimental data, and that the model provides microscopic insight into the small-strain behaviour of soils observed ...

Failure criteria for linear elastic materials with U-notches

Abstract: This paper provides a simple, albeit accurate, criterion for prediction of the rupture loads of brittle, or quasi-brittle, U-notched samples, where linear elastic fracture mechanics is not applicable because blunted notches do not exhibit stress singularities. Good agreement is found between numerical predictions and experimental results. The results of fracture tests from 18 different ceramic materials and a polymer (at − 60°C) are summarized and are used as a reference for checking the fracture criterion. Seven fracture criteria are reviewed and it is shown that all can be recast into the proposed criterion.