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

Lecture

Homogenization Theory: Isotropic Phases and Laminated Plates

In course

ME-437: Advanced solid mechanics

Description

This lecture covers the rigorous upper and lower bounds on the effective properties of 2-phase composites, focusing on isotropic phases and laminated plates. The discussion includes the relationship between stress and strain, the microstructure arrangement determining the bounds, and the implications when there are no cracks in the material.

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.

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.

Hooke's law

In physics, Hooke's law is an empirical law which states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distance—that is, F_s = kx, where k is a constant factor characteristic of the spring (i.e., its stiffness), and x is small compared to the total possible deformation of the spring. The law is named after 17th-century British physicist Robert Hooke. He first stated the law in 1676 as a Latin anagram.

Type system

In computer programming, a type system is a logical system comprising a set of rules that assigns a property called a type (for example, integer, floating point, string) to every "term" (a word, phrase, or other set of symbols). Usually the terms are various constructs of a computer program, such as variables, expressions, functions, or modules. A type system dictates the operations that can be performed on a term. For variables, the type system determines the allowed values of that term.

Type theory

In mathematics, logic, and computer science, a type theory is the formal presentation of a specific type system, and in general, type theory is the academic study of type systems. Some type theories serve as alternatives to set theory as a foundation of mathematics. Two influential type theories that were proposed as foundations are Alonzo Church's typed λ-calculus and Per Martin-Löf's intuitionistic type theory. Most computerized proof-writing systems use a type theory for their foundation, a common one is Thierry Coquand's Calculus of Inductive Constructions.

Related lectures (51)

Designing Learning Experiences: CS411 Class Project

Introduces the CS411 Class Project, where students design and test a lesson using learning theories.

Collision Kinetics: Theory and Applications

Covers the theory and applications of collision kinetics in understanding molecular interactions.

Matrix to Density Operator

Explains the transformation from a matrix to the density operator in quantum physics.

Fracture Mechanics: Crack Growth and Weakest Link Log in to Mediaspace to watch this video

Explores fracture mechanics, crack growth, and the weakest link theory, emphasizing the statistical distribution of crack sizes and the significance of the largest crack in material failure.

Rigorous Bounds: Isotropic Phases Log in to Mediaspace to watch this video