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The quadratic Hill yield criterion [1] has the form : + + + + + = . Here F, G, H, L, M, N are constants that have to be determined experimentally and are the stresses. The quadratic Hill yield criterion depends only on the deviatoric stresses and is pressure independent.
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.
Prior to yield, material response can be assumed to be of a linear elastic, nonlinear elastic, or viscoelastic behavior. In materials science and engineering , the von Mises yield criterion is also formulated in terms of the von Mises stress or equivalent tensile stress , σ v {\displaystyle \sigma _{\text{v}}} .
Greenwood and Williamson [31] defined a dimensionless parameter called the plasticity index that could be used to determine whether contact would be elastic or plastic. The Greenwood-Williamson model requires knowledge of two statistically dependent quantities; the standard deviation of the surface roughness and the curvature of the asperity peaks.
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 .
Which can be expressed as: [2] = where m is known as the Schmid factor = Both factors τ and σ are measured in stress units, which is calculated the same way as pressure (force divided by area). φ and λ are angles.
If can be expressed as a product then is called a separable state. Otherwise, is said to be an entangled state. From the Schmidt decomposition, we can see that is entangled if and only if has Schmidt rank strictly greater than 1. Therefore, two subsystems that partition a pure state are entangled if and only if their reduced states are mixed ...
The plasticity index is the size of the range of water contents where the soil exhibits plastic properties. The PI is the difference between the liquid and plastic limits (PI = LL-PL). Soils with a high PI tend to be clay, those with a lower PI tend to be silt, and those with a PI of 0 (non-plastic) tend to have little or no silt or clay.