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

Lecture

Eshelby 3: Modulus Mismatch

In course

ME-437: Advanced solid mechanics

Description

This lecture discusses the concept of modulus mismatch in elastic inhomogeneities. It covers the problem of including materials with different elastic moduli, the solution proposed by Eshelby, and the implications of using Green's function. The lecture explains how to fit a homogeneous inclusion to the deformed shape of a real inclusion, ensuring the same stress inside. It also delves into the extra distortion required and the crucial limits that need to be satisfied. The analysis includes the stored elastic energy, the free energy, and the work done by tractions on the outer boundary.

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)

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.

Stress (mechanics)

In continuum mechanics, stress is a physical quantity that describes forces present during deformation. An object being pulled apart, such as a stretched elastic band, is subject to tensile stress and may undergo elongation. An object being pushed together, such as a crumpled sponge, is subject to compressive stress and may undergo shortening. The greater the force and the smaller the cross-sectional area of the body on which it acts, the greater the stress. Stress has units of force per area, such as newtons per square meter (N/m2) or pascal (Pa).

Elastic modulus

An elastic modulus (also known as modulus of elasticity) is the unit of measurement of an object's or substance's resistance to being deformed elastically (i.e., non-permanently) when a stress is applied to it. The elastic modulus of an object is defined as the slope of its stress–strain curve in the elastic deformation region: A stiffer material will have a higher elastic modulus. An elastic modulus has the form: where stress is the force causing the deformation divided by the area to which the force is applied and strain is the ratio of the change in some parameter caused by the deformation to the original value of the parameter.

Stress–strain analysis

Stress–strain analysis (or stress analysis) is an engineering discipline that uses many methods to determine the stresses and strains in materials and structures subjected to forces. In continuum mechanics, stress is a physical quantity that expresses the internal forces that neighboring particles of a continuous material exert on each other, while strain is the measure of the deformation of the material. In simple terms we can define stress as the force of resistance per unit area, offered by a body against deformation.

Related lectures (48)

Elasticity: Constitutive Modelling in Geomechanics

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

Linear Elasticity and Atomic Structure

Explores linear elasticity properties of materials and their atomic structure, covering stresses, strains, rigidity, and loading cases.

Elasticity and Deformation

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

Deformation of Materials: Stresses, Deformations, and Elasticity

Explores the deformation of materials through stresses, deformations, and elasticity, focusing on the behavior of metals, ceramics, and polymers.

Elasticity-Plasticity: Materials Science Fundamentals