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

Lecture

Anisotropic Elastic Materials

In course

ME-437: Advanced solid mechanics

Description

This lecture covers anisotropic elastic materials, focusing on examples such as crystalline materials with specific atomic symmetries, layered structures like in geology, and composites with aligned fibers. The instructor explains the concept of transversely isotropic materials, where properties are independent of rotations around certain axes. The lecture delves into the Voigt contracted notation to represent stress and strain components, highlighting the 6 independent components of stress and strain and 21 independent components of the stiffness tensor. The stiffness tensor's particular blocks are defined, emphasizing the coupling between different types of loading. The compliance matrix is introduced as an alternative representation to the stiffness tensor, simplifying the analysis of isotropic materials.

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)

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.

Material

Material is a substance or mixture of substances that constitutes an object. Materials can be pure or impure, living or non-living matter. Materials can be classified on the basis of their physical and chemical properties, or on their geological origin or biological function. Materials science is the study of materials, their properties and their applications. Raw materials can be processed in different ways to influence their properties, by purification, shaping or the introduction of other 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.

Materials science

Materials science is an interdisciplinary field of researching and discovering materials. Materials engineering is an engineering field of finding uses for materials in other fields and industries. The intellectual origins of materials science stem from the Age of Enlightenment, when researchers began to use analytical thinking from chemistry, physics, and engineering to understand ancient, phenomenological observations in metallurgy and mineralogy. Materials science still incorporates elements of physics, chemistry, and engineering.

Elasticity tensor

The elasticity tensor is a fourth-rank tensor describing the stress-strain relation in a linear elastic material. Other names are elastic modulus tensor and stiffness tensor. Common symbols include and . The defining equation can be written as where and are the components of the Cauchy stress tensor and infinitesimal strain tensor, and are the components of the elasticity tensor. Summation over repeated indices is implied. This relationship can be interpreted as a generalization of Hooke's law to a 3D continuum.

Related lectures (51)

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.

Linear Elasticity and Atomic Structure

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

Elasticity: Stiffness and Compliance Tensors Log in to Mediaspace to watch this video

Covers stiffness and compliance tensors, Hooke's law, stress-strain relations, and material symmetries.

Anisotropic Elasticity: Examples Log in to Mediaspace to watch this video