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Figure 1: View of Drucker–Prager yield surface in 3D space of principal stresses for =, = The Drucker–Prager yield criterion [1] is a pressure-dependent model for determining whether a material has failed or undergone plastic yielding. The criterion was introduced to deal with the plastic deformation of soils.
The Hill yield criterion developed by Rodney Hill, is one of several yield criteria for describing anisotropic plastic deformations.The earliest version was a straightforward extension of the von Mises yield criterion and had a quadratic form.
The Tsai-Wu criterion predicts failure when the failure index in a laminate reaches 1. This failure criterion is a specialization of the general quadratic failure criterion proposed by Gol'denblat and Kopnov [ 2 ] and can be expressed in the form
The mode I fracture toughness for plane strain is defined as K I c = Y σ c π a {\displaystyle K_{\rm {Ic}}=Y\sigma _{c}{\sqrt {\pi a}}} where σ c {\displaystyle \sigma _{c}} is a critical value of the far field stress and Y {\displaystyle Y} is a dimensionless factor that depends on the geometry, material properties, and loading condition.
The two plastic limit theorems apply to any elastic-perfectly plastic body or assemblage of bodies. Lower limit theorem: If an equilibrium distribution of stress can be found which balances the applied load and nowhere violates the yield criterion, the body (or bodies) will not fail, or will be just at the point of failure.
Mode III is a tearing (antiplane shear) mode where the crack surfaces move relative to one another and parallel to the leading edge of the crack. Mode I is the most common load type encountered in engineering design. Different subscripts are used to designate the stress intensity factor for the three different modes.
Mode III – Tearing mode (a shear stress acting parallel to the plane of the crack and parallel to the crack front). When the size of the plastic zone at the crack tip is too large, elastic-plastic fracture mechanics can be used with parameters such as the J-integral or the crack tip opening displacement .
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.