CoulombMohrmodellen

CoulombMohrmodellen, often written as Coulomb-Mohr-modellen, is a constitutive model used in geotechnical engineering to describe the strength and failure behavior of soils and rocks under combined stress. It combines the Mohr-Coulomb failure criterion with an elastic-plastic framework to represent yielding, strength, and, in some variants, post-yield behavior. The model attributes shear strength to cohesion and internal friction, providing a simple yet widely applicable description of when a material will fail.

The Mohr-Coulomb failure criterion states that shear strength on a plane is governed by tau = c + sigma_n tan(phi), where c is cohesion, phi is the internal friction angle, tau is the shear stress on the plane, and sigma_n is the normal stress on that plane. In terms of principal stresses (σ1 ≥ σ2 ≥ σ3), failure can be represented by a linear boundary in the σ1–σ3 plane: σ1 = σ3 (1 + sin φ)/(1 − sin φ) + 2 c cos φ/(1 − sin φ). This linear envelope, often referred to as the Mohr-Coulomb envelope, defines the yield surface of the material.

In practice, the model is implemented as an elastic-plastic material with a yield surface defined by c and φ, and, optionally, a dilatancy angle ψ for non-associated flow. Hardening or softening rules may adjust c and φ with accumulated plastic strain to capture strength changes. The Coulomb-Mohr model is rate-independent and commonly used for soils, clays, sands, and some rocks, particularly in slope stability, foundation design, and geotechnical finite element analyses.

Limitations include the simplified linear envelope, potential numerical challenges due to non-smooth yield surfaces, and the assumption of constant c and φ unless explicit hardening rules are applied.