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Lecture

Strain and Stress Analysis

In course

ME-231(b): Structural mechanics for SV

This course aims to provide a concise understanding of how materials and structures react to loads. It covers the basics of stress and strain in multi dimensions, deformation and failure criteria. The course is tailored to problems students from life scien ...

Description

This lecture covers the application of physics principles to analyze the extension and compression of springs, focusing on the energy stored in a compressed bar and the strain energy density. The instructor explains the relationship between stress, strain, and energy, emphasizing the importance of understanding strain energy per volume. Additionally, the lecture delves into the concept of strain tensor and its components in two and three dimensions, highlighting the interdependence of different directions in three-dimensional systems. The instructor also discusses shear strain and its calculation, providing insights into the strain tensor representation and its significance in material analysis.

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Instructor

Georg Fantner

Official source

Ontological neighbourhood

Chemical engineering

Materials science: Deformation of materials

Related concepts (32)

Finite strain theory

In continuum mechanics, the finite strain theory—also called large strain theory, or large deformation theory—deals with deformations in which strains and/or rotations are large enough to invalidate assumptions inherent in infinitesimal strain theory. In this case, the undeformed and deformed configurations of the continuum are significantly different, requiring a clear distinction between them. This is commonly the case with elastomers, plastically-deforming materials and other fluids and biological soft tissue.

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.

Strain rate

In materials science, strain rate is the change in strain (deformation) of a material with respect to time. The strain rate at some point within the material measures the rate at which the distances of adjacent parcels of the material change with time in the neighborhood of that point. It comprises both the rate at which the material is expanding or shrinking (expansion rate), and also the rate at which it is being deformed by progressive shearing without changing its volume (shear rate).

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 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.

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Normal Stresses: Internal Stress and Strain

Introduces internal stress and strain, material properties, and design considerations for axial loads and direct shear.

Solid mechanics in biomechanics: Large strain and stress definitions

Explores large strain in soft tissues and various stress definitions in solid mechanics.

Elasticity and Deformation

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

Solid Mechanics: Stress, Strain, Invariants

Explores stress, strain invariants, constitutive laws, failure criteria, and material properties in solid mechanics.

Shear and Bearing Stresses