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In continuum mechanics, the maximum distortion energy criterion (also von Mises yield criterion [1]) states that yielding of a ductile material begins when the second invariant of deviatoric stress reaches a critical value. [2] It is a part of plasticity theory that mostly applies to ductile materials, such as some metals.
Maximum distortion energy theory (von Mises yield criterion) also referred to as octahedral shear stress theory. [4] – This theory proposes that the total strain energy can be separated into two components: the volumetric ( hydrostatic ) strain energy and the shape (distortion or shear ) strain energy.
Maximum distortion energy theory, also known as maximum distortion energy theory of failure or von Mises–Hencky theory. This theory postulates that failure will occur when the distortion energy per unit volume due to the applied stresses in a part equals the distortion energy per unit volume at the yield point in uniaxial testing.
He developed the distortion energy theory of stress, an important factor in material strength calculations. His ideas were not universally well received, although Alexander Ostrowski had said of him: "Only with the appointment of Richard von Mises to the University of Berlin did the first serious German school of applied mathematics with a ...
Yielding does not occur until the stress increases from zero (the origin) to some point on this surface. For isotropic elastic materials with a ductile failure mode, the most used criteria are the Tresca criterion of maximum tangential stress and von Mises yield criterion [48] based on maximum distortion energy.
Then they describe the maximum distortion strain-energy theory and the octahedral stress theory and then shows those two to be the same as the Mises theory. It gives a footnote: "The physical interpretation of the Mises yield criterion via the maximum distortion energy theory was suggested by H. Hencky in 1924.
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Within the branch of materials science known as material failure theory, the Goodman relation (also called a Goodman diagram, a Goodman-Haigh diagram, a Haigh diagram or a Haigh-Soderberg diagram) is an equation used to quantify the interaction of mean and alternating stresses on the fatigue life of a material. [1]