Lecture

Mechanical Properties: Elasticity and Shear Stress

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Description

This lecture covers the concepts of shear stress, pressure, and constitutive responses in materials, focusing on the elastic and plastic behavior of solids under different loading conditions. It also discusses the linear relationship between applied loading and deformation, the isotropic nature of solids, and the Lame coefficients. The lecture further explores the Poisson's ratio, Young's modulus, and the constitutive equations governing the mechanical behavior of materials.

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Ontological neighbourhood

Chemical engineering

Materials science: Deformation of materials

Related concepts (26)

Poisson's ratio

In materials science and solid mechanics, Poisson's ratio (nu) is a measure of the Poisson effect, the deformation (expansion or contraction) of a material in directions perpendicular to the specific direction of loading. The value of Poisson's ratio is the negative of the ratio of transverse strain to axial strain. For small values of these changes, is the amount of transversal elongation divided by the amount of axial compression. Most materials have Poisson's ratio values ranging between 0.0 and 0.5.

Shear modulus

In materials science, shear modulus or modulus of rigidity, denoted by G, or sometimes S or μ, is a measure of the elastic shear stiffness of a material and is defined as the ratio of shear stress to the shear strain: where = shear stress is the force which acts is the area on which the force acts = shear strain. In engineering , elsewhere is the transverse displacement is the initial length of the area. The derived SI unit of shear modulus is the pascal (Pa), although it is usually expressed in gigapascals (GPa) or in thousand pounds per square inch (ksi).

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.

Young's modulus

Young's modulus , the Young modulus, or the modulus of elasticity in tension or axial compression (i.e., negative tension), is a mechanical property that measures the tensile or compressive stiffness of a solid material when the force is applied lengthwise. It quantifies the relationship between tensile/compressive stress (force per unit area) and axial strain (proportional deformation) in the linear elastic region of a material and is determined using the formula: Young's moduli are typically so large that they are expressed not in pascals but in gigapascals (GPa).

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.

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