Search results
Results From The WOW.Com Content Network
The first Piola–Kirchhoff stress is the 3D generalization of the 1D concept of engineering stress. If the material rotates without a change in stress state (rigid rotation), the components of the first Piola–Kirchhoff stress tensor will vary with material orientation. The first Piola–Kirchhoff stress is energy conjugate to the deformation ...
The nominal stress = is the transpose of the first Piola–Kirchhoff stress (PK1 stress, also called engineering stress) and is defined via = = = or = = = This stress is unsymmetric and is a two-point tensor like the deformation gradient.
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 the above, is the first Piola-Kirchhoff stress tensor, and is the mass density in the reference configuration. The first Piola-Kirchhoff stress tensor is related to the Cauchy stress tensor by The first Piola-Kirchhoff stress tensor is related to the Cauchy stress tensor by
Objective stress rate. In continuum mechanics, objective stress rates are time derivatives of stress that do not depend on the frame of reference. [1] Many constitutive equations are designed in the form of a relation between a stress-rate and a strain-rate (or the rate of deformation tensor). The mechanical response of a material should not ...
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 ...
A neo-Hookean solid[1][2] is a hyperelastic material model, similar to Hooke's law, that can be used for predicting the nonlinear stress-strain behavior of materials undergoing large deformations. The model was proposed by Ronald Rivlin in 1948 using invariants, though Mooney had already described a version in stretch form in 1940, and Wall had ...
Continuum mechanics. 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 ...