Mechanics of Continuous Media

This lecture covers the fundamental concepts of the relationship between stress tensors and strain vectors, the equilibrium of forces, and the interpretation of equations of motion in the context of continuous media mechanics. The instructor explains the importance of stress-strain relationships, the geometric interpretation of these concepts, and the use of Cauchy's relation to determine unknown constants. The lecture also delves into the properties of isotropic and anisotropic materials, the homogeneity of materials, and the significance of symmetry in elasticity. The discussion concludes with a detailed exploration of the linear relationship between stress and strain, highlighting the essential coefficients and their symmetries in the context of elastic solids.

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Related concepts (39)

CIVIL-225: Continuum mechanics (for GC)

La mécanique des milieux continus, essentielle à la compréhension du travail de l'ingénieur civil, est abordée dans ce cours. Ce cours couvre les notions de contraintes et déformations, les grands pri

Elasticity (physics)

In physics and materials science, elasticity is the ability of a body to resist a distorting influence and to return to its original size and shape when that influence or force is removed. Solid objects will deform when adequate loads are applied to them; if the material is elastic, the object will return to its initial shape and size after removal. This is in contrast to plasticity, in which the object fails to do so and instead remains in its deformed state. The physical reasons for elastic behavior can be quite different for different materials.

Linear elasticity

Linear elasticity is a mathematical model of how solid objects deform and become internally stressed due to prescribed loading conditions. It is a simplification of the more general nonlinear theory of elasticity and a branch of continuum mechanics. The fundamental "linearizing" assumptions of linear elasticity are: infinitesimal strains or "small" deformations (or strains) and linear relationships between the components of stress and strain. In addition linear elasticity is valid only for stress states that do not produce yielding.

Solid mechanics

Solid mechanics (also known as mechanics of solids) is the branch of continuum mechanics that studies the behavior of solid materials, especially their motion and deformation under the action of forces, temperature changes, phase changes, and other external or internal agents. Solid mechanics is fundamental for civil, aerospace, nuclear, biomedical and mechanical engineering, for geology, and for many branches of physics and chemistry such as materials science.

Infinitesimal strain theory

In continuum mechanics, the infinitesimal strain theory is a mathematical approach to the description of the deformation of a solid body in which the displacements of the material particles are assumed to be much smaller (indeed, infinitesimally smaller) than any relevant dimension of the body; so that its geometry and the constitutive properties of the material (such as density and stiffness) at each point of space can be assumed to be unchanged by the deformation.

Orthotropic material

In material science and solid mechanics, orthotropic materials have material properties at a particular point which differ along three orthogonal axes, where each axis has twofold rotational symmetry. These directional differences in strength can be quantified with Hankinson's equation. They are a subset of anisotropic materials, because their properties change when measured from different directions. A familiar example of an orthotropic material is wood.