A method for smoothing multiple yield functions

Abstract

Many models of plasticity are built using multiple, simple yield surfaces. Examples include geomechanical models and crystal plasticity. This leads to numerical difficulties, most particularly during the stress update procedure, since the combined yield surface is nondifferentiable; and when employing implicit time stepping to solve numerical models, since the Jacobian is often poorly conditioned. A method is presented that produces a single C 2 differentiable and convex yield function from a plastic model that contains multiple yield surfaces that are individually C 2 differentiable and convex.

The MOOSE geochemistry module

“…• pressure and temperature are tightly coupled with fluid flows • densities, viscosities, etc., may depend on solute concentrations, temperature and pressure • porosity and permeability can change with precipitation and dissolution • multiphase flows can be used • coupling with sophisticated geomechanics (including plasticity (Adhikary et al, 2016;Wilkins, Spencer, et al, 2020), fracture and large strains) is straightforward • sophisticated numerical stabilization is available.…”

Comment to “A method for smoothing multiple yield functions” by Wilkins, Spencer, Jain and Gencturk. Int J Numer Methods Eng. 2020; 121:434–449

“…This commenter has read the discussed article 1 with great interest. The presented idea of a general method of smoothing multiple yield functions can prove very useful in the development of material models for practical use.…”

Location of Tension Cracks at Slope Crests in Stability Analysis of Slopes

“…Tensile strength cut-off creates additional edges and vertices near the head of the yielding surface, as shown in Figure 1b, which further exacerbates the burden of constitutive integration. Since Zienkiewicz and Pande [19], followed by Menetrey and Willam [20], as a result, attempts to smooth the Mohr-Coulomb yielding surfaces have never ceased, see Abbo et al [21] and Andy et al [22]. Nevertheless, smoothing compromises precision in order to conserve the convexity of the yielding surface.…”