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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 ...
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.
The tensors are classified according to their type (n, m), where n is the number of contravariant indices, m is the number of covariant indices, and n + m gives the total order of the tensor. For example, a bilinear form is the same thing as a (0, 2)-tensor; an inner product is an example of a (0, 2)-tensor, but not all (0, 2)-tensors are inner ...
The Maxwell stress tensor (named after James Clerk Maxwell) is a symmetric second-order tensor in three dimensions that is used in classical electromagnetism to represent the interaction between electromagnetic forces and mechanical momentum. In simple situations, such as a point charge moving freely in a homogeneous magnetic field, it is easy ...
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.
Orthotropic materials are a subset of anisotropic materials; their properties depend on the direction in which they are measured. Orthotropic materials have three planes/axes of symmetry. An isotropic material, in contrast, has the same properties in every direction. It can be proved that a material having two planes of symmetry must have a ...
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 }}} ).