An approach for providing quasi‐convexity to yield functions and a generalized implicit integration scheme for isotropic constitutive models based on 2 unknowns

Abstract

Yield and plastic potential surfaces are often affected by problems related to convexity. One such problem is encountered when the yield surface that bounds the elastic domain is itself convex; however, convexity is lost when the surface expands to pass through stress points outside the current elastic domain. In this paper, a technique is proposed, which effectively corrects this problem by providing linear homothetic expansion with respect to the centre of the yield surface.A very compact implicit integration scheme is also presented, which is of general applicability for isotropic constitutive models, provided that their yield and plastic potential functions are based on a separate mathematical definition of the meridional and deviatoric sections and that stress invariants are adopted as mechanical quantities. The elastic predictor-plastic corrector algorithm is based on the solution of a system of 2 equations in 2 unknowns only. This further reduces to a single equation and unknown in the case of yield and plastic potential surfaces with a linear meridional section. The effectiveness of the proposed convexification technique and the efficiency and stability of the integration scheme are investigated by running numerical analyses of a notoriously demanding boundary value problem.

Predictive potential of Perzyna viscoplastic modelling for granular geomaterials

“…Expected consequences might concern the predicted stability of the constitutive response, a subject so far never explored from this standpoint. When documented, convexity‐related issues might be remedied by resorting to recent convexification techniques …”

“…When documented, convexity-related issues might be remedied by resorting to recent convexification techniques. 74,75 The discussion offered in this work also aimed to discourage simplistic use of viscoplasticity as a mere numerical expedient against mesh dependence in strain-localisation problems. Conversely, the viscoplastic framework was reappraised as a physically sound approach to sand modelling, easy to extend to nonlocality whenever also characteristic length effects are relevant.…”

Large deformation coupled analysis of embedded pipeline – Soil lateral interaction

“…with the initial yield surface size controlled by p c0 [67]. B p represents the slope of the ε p ν − lnp ′ curve [65] and can be related to the conventional MCC parameters by (detailed in the Appendix):…”

“…The MCC model developed by Panteghini and Lagioia [67,68], which was adopted in the study, has advantages in convergence and integration efficiency by using fewer unknowns and improved yield functions with full convexity and homothety. For the elliptical yield surface used in the present study, the new expression is given by:…”

The difficult challenge of modelling the non‐linear elastic behaviour of soils within a theoretically sound framework

“…An extensive literature review performed by Franchi et al on yield functions revealed the extent of the ambiguity and confusion regarding the requirements of convexity. However, the discussion on convexity has been more recently reopened (Gluege and Bucci), and remedies have been proposed to provide convexity to non‐convex functions (Panteghini and Lagioia,) Lagioia et al, and Lagioia and Panteghini.…”