An approach for providing quasi‐convexity to yield functions and a generalized implicit integration scheme for isotropic constitutive models based on 2 unknowns |
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| Authors: | Andrea Panteghini Rocco Lagioia |
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| Institution: | DICATAM, University of Brescia, Brescia, Italy |
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| 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. |
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| Keywords: | convexity yield function implicit integration |
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