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The (infinitesimal) strain tensor (symbol ) is defined in the International System of Quantities (ISQ), more specifically in ISO 80000-4 (Mechanics), as a "tensor quantity representing the deformation of matter caused by stress. Strain tensor is symmetric and has three linear strain and three shear strain (Cartesian) components."
Similarly, the sliding rate, also called the deviatoric strain rate or shear strain rate is the derivative with respect to time of the shear strain. Engineering sliding strain can be defined as the angular displacement created by an applied shear stress, τ {\displaystyle \tau } .
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 ...
The stress and strain can be normal, shear, or mixture, and can also can be uniaxial, biaxial, or multiaxial, even change with time. The form of deformation can be compression, stretching, torsion, rotation, and so on. If not mentioned otherwise, stress–strain curve refers to the relationship between axial normal stress and axial normal ...
In this expression, ε 1 and ε 2 are normal strains in the 1- and 2-direction and Υ 12 is the shear strain. σ 1 and σ 2 are the normal stresses and τ 12 is the shear stress. The orientation of the axes 1 and 2 in the above figure is arbitrary. This means that the values for E, G and v are the same in any material direction.
Torsion of a square section bar Example of torsion mechanics. In the field of solid mechanics, torsion is the twisting of an object due to an applied torque [1] [2].Torsion could be defined as strain [3] [4] or angular deformation [5], and is measured by the angle a chosen section is rotated from its equilibrium position [6].
The formula to calculate average shear stress τ or force per unit area is: [1] =, where F is the force applied and A is the cross-sectional area.. The area involved corresponds to the material face parallel to the applied force vector, i.e., with surface normal vector perpendicular to the force.
The shear modulus is one of several quantities for measuring the stiffness of materials. All of them arise in the generalized Hooke's law: . Young's modulus E describes the material's strain response to uniaxial stress in the direction of this stress (like pulling on the ends of a wire or putting a weight on top of a column, with the wire getting longer and the column losing height),