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In continuum mechanics, the Cauchy stress tensor (symbol , named after Augustin-Louis Cauchy), also called true stress tensor[1] or simply stress tensor, completely defines the state of stress at a point inside a material in the deformed state, placement, or configuration. The second order tensor consists of nine components and relates a unit ...
In continuum mechanics, stress is a physical quantity that describes forces present during deformation. For example, 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 ...
Alternative stress measures. In continuum mechanics, the most commonly used measure of stress is the Cauchy stress tensor, often called simply the stress tensor or "true stress". However, several alternative measures of stress can be defined: [1][2][3] The Kirchhoff stress (. τ {\displaystyle {\boldsymbol {\tau }}} ).
It defines a family of tensors, which describe the configuration of the body in either the current or the reference state. The first Piola–Kirchhoff stress tensor, , relates forces in the present ("spatial") configuration with areas in the reference ("material") configuration. where is the deformation gradient and is the Jacobian determinant.
The stress–energy tensor involves the use of superscripted variables (not exponents; see tensor index notation and Einstein summation notation).If Cartesian coordinates in SI units are used, then the components of the position four-vector x are given by: (x 0, x 1, x 2, x 3) = (t, x, y, z), where t is time in seconds, and x, y, and z are distances in meters.
As an example, the stress state of a steel beam in compression differs from the stress state of a steel axle under torsion, even if both specimens are of the same material. In view of the stress tensor, which fully describes the stress state, this difference manifests in six degrees of freedom , because the stress tensor has six independent ...
Stress tensor may refer to: Cauchy stress tensor, in classical physics. Stress deviator tensor, in classical physics. Piola–Kirchhoff stress tensor, in continuum mechanics. Viscous stress tensor, in continuum mechanics. Stress–energy tensor, in relativistic theories. Maxwell stress tensor, in electromagnetism.
Biaxial tensile testing. In materials science and solid mechanics, biaxial tensile testing is a versatile technique to address the mechanical characterization of planar materials. It is a generalized form of tensile testing in which the material sample is simultaneously stressed along two perpendicular axes.