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To derive the equation of the Mohr circle for the two-dimensional cases of plane stress and plane strain, first consider a two-dimensional infinitesimal material element around a material point (Figure 4), with a unit area in the direction parallel to the -plane, i.e., perpendicular to the page or screen.
Mohr–Coulomb theory is a mathematical model (see yield surface) describing the response of brittle materials such as concrete, or rubble piles, to shear stress as well as normal stress. Most of the classical engineering materials follow this rule in at least a portion of their shear failure envelope.
A graphical representation of this transformation law is the Mohr's circle for stress. The Cauchy stress tensor is used for stress analysis of material bodies experiencing small deformations: it is a central concept in the linear theory of elasticity.
which is the equation of a circle of radius centered at a point with coordinates [,], called Mohr's circle. But knowing that for the principal stresses the shear stress τ n = 0 {\displaystyle \tau _{\mathrm {n} }=0\,\!} , then we obtain from this equation:
A graphical representation of this transformation law is the Mohr's circle of stress ... In this case the differential equations that define the stress tensor are ...
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This equation defines the yield surface as a circular cylinder (See Figure) whose yield curve, or intersection with the deviatoric plane, is a circle with radius , or . This implies that the yield condition is independent of hydrostatic stresses.