Mohr-Coulomb failure criterion
Introduction
The Mohr-Coulomb theory is a mathematical model (see Yield surface) that describes the response of brittle materials, such as concrete, or particulate aggregates such as soil,[1] to shear stress, as well as normal stress. Most materials in classical engineering behave following this theory at least in part of the cut. In general, the theory is applied to materials for which the compressive strength is much higher than the tensile strength, such as ceramic materials. The theory explains that the cutting of a material occurs for a combination of normal stress and tangential stress, and that the greater the normal stress, the greater the tangential stress necessary to cut the material.[2].
Applications
In geotechnical engineering it is used to define shear resistance of soils and rocks in different cases of effective stress.
In structural engineering it is used to determine the breaking load as well as the angle of failure of a displacement fracture in ceramics and similar materials (such as concrete). The Coulomb hypothesis is used to determine the combination of shear and normal stress that causes a material to fracture. Mohr's circle is used to determine the angles where these stresses are maximum. Generally, failure will occur in the case of maximum principal stress.
Model
Mohr-Coulomb failure criterion
The Mohr-Coulomb failure criterion[3] is represented by the linear envelope of the Mohr circles that occur at failure. The relationship of that envelope is expressed as.
where:.
Compression is assumed positive for the compressive stress, although the case with negative stress can also be studied by changing the sign of.
Yes, the Mohr-Coulomb criterion reduces to the Tresca criterion. If the Mohr-Coulomb model is equivalent to the Rankine model. Higher values of are not allowed.
From Mohr's circles we have:
where.
y is the maximum principal stress and is the minimum principal stress.
In this way the Mohr-Coulomb criterion can also be expressed as:.