Lecture

Effective Elastic Moduli

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

In course

ME-437: Advanced solid mechanics

Description

This lecture covers the concept of effective elastic moduli in composite materials, focusing on the Eshelby inclusion theory. It explains how to determine the average stress and strain fields in a material with multiple inclusions, and how to calculate the effective stiffness tensor. The lecture also discusses the Hashin-Shtrikman lower bound and the application of the Composite Spheres model. Various equations and derivations are presented to illustrate the analysis of the stress and strain distribution in the composite material.

Official source

Ontological neighbourhood

Chemical engineering

Materials science: Deformation of materials

Related concepts (32)

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.

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).

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.

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.

Composite material

A composite material (also called a composition material or shortened to composite, which is the common name) is a material which is produced from two or more constituent materials. These constituent materials have notably dissimilar chemical or physical properties and are merged to create a material with properties unlike the individual elements. Within the finished structure, the individual elements remain separate and distinct, distinguishing composites from mixtures and solid solutions.

Related lectures (64)

Rigorous Bounds: Isotropic Phases

Explores rigorous upper and lower bounds for isotropic phase composites and their microstructure arrangement, focusing on laminated plates and stress-strain relationships.

Homogenization Theory: Isotropic Phases and Laminated Plates

Explores the rigorous bounds on effective properties of isotropic phases and laminated plates.

Laminate Analysis: Introduction

Introduces the theory behind laminates and their applications in different industries.

Solid Mechanics Principles: Greens Functions

Explores Greens functions in solid mechanics, emphasizing the solution of point forces and their impact on displacement fields.

Fracture Mechanics: Crack Growth and Weakest Link