Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Elastic Inhomogeneity: Eshelby's Solution

In course

ME-437: Advanced solid mechanics

Description

This lecture discusses the concept of elastic inhomogeneity and presents Eshelby's solution to the problem of a homogeneous inclusion in a deformed shape. By choosing the right strain, the homogeneous inclusion can match the real inclusion's shape and stress. The lecture explains how to ensure the same tractions and displacements at the inclusion interface, leading to the same stresses and displacements outside the inclusion. It covers the extra distortion needed and the conditions for stress equivalence. The presentation concludes with the analysis of the free energy and the crucial limits that need to be satisfied in the context of elastic inhomogeneity.

This video is available exclusively on Mediaspace for a restricted audience. Please log in to MediaSpace to access it if you have the necessary permissions.

Watch on Mediaspace

Official source

Ontological neighbourhood

Chemical engineering

Materials science: Deformation of materials

Related concepts (32)

Stress–strain curve

In engineering and materials science, a stress–strain curve for a material gives the relationship between stress and strain. It is obtained by gradually applying load to a test coupon and measuring the deformation, from which the stress and strain can be determined (see tensile testing). These curves reveal many of the properties of a material, such as the Young's modulus, the yield strength and the ultimate tensile strength. Generally speaking, curves representing the relationship between stress and strain in any form of deformation can be regarded as stress–strain curves.

Price elasticity of demand

A good's price elasticity of demand (, PED) is a measure of how sensitive the quantity demanded is to its price. When the price rises, quantity demanded falls for almost any good, but it falls more for some than for others. The price elasticity gives the percentage change in quantity demanded when there is a one percent increase in price, holding everything else constant. If the elasticity is −2, that means a one percent price rise leads to a two percent decline in quantity demanded.

Deformation (physics)

In physics and continuum mechanics, deformation is the transformation of a body from a reference configuration to a current configuration. A configuration is a set containing the positions of all particles of the body. A deformation can occur because of external loads, intrinsic activity (e.g. muscle contraction), body forces (such as gravity or electromagnetic forces), or changes in temperature, moisture content, or chemical reactions, etc. Strain is related to deformation in terms of relative displacement of particles in the body that excludes rigid-body motions.

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.

Deformation (engineering)

In engineering, deformation refers to the change in size or shape of an object. Displacements are the absolute change in position of a point on the object. Deflection is the relative change in external displacements on an object. Strain is the relative internal change in shape of an infinitesimally small cube of material and can be expressed as a non-dimensional change in length or angle of distortion of the cube. Strains are related to the forces acting on the cube, which are known as stress, by a stress-strain curve.

Related lectures (45)

Elasticity: Constitutive Modelling in Geomechanics

Explores constitutive equations in geomechanics, stress-strain behavior, and practical applications in engineering.

Elasticity and Deformation

Covers stress, strain, modulus of elasticity, and material behavior under different loads.

Deformation and Strain Tensors

Explores deformation and strain tensors, Lagrange representation, elasticity theory, and the divergence theorem.

Linear Elasticity: Equations of Linear Elasticity Log in to Mediaspace to watch this video

Covers the equations of linear elasticity for static problems with small strain, emphasizing uniqueness of solutions and Navier's Equations.

3D Linear Elasticity & Beams Log in to Mediaspace to watch this video