Abstract
This paper proposes a modified return mapping algorithm for a series of nonlinear yield criteria. The algorithm is established in the principal stress space and ignores the effect of the intermediate principal stress. Three stress return schemes are derived in this paper: return to the yield surface, return to the curve, and return to the apex point. The conditions used for determining the correct stress return type are also constructed. After the proposed algorithm is programmed in the finite element software, we merely need the equivalent Mohr–Coulomb (M-C) strength parameters, the derivatives of their functions, and the tensile strength of these nonlinear yield criteria. In addition, the Hoek–Brown (H-B) yield criterion is taken as an example to validate the proposed method. The results show that the updated stresses and the final principal stresses obtained by the proposed method are in good agreement with those obtained by other methods. Furthermore, the proposed method is more suitable for the associated plastic-flow rule.
Highlights
State Key Laboratory of Hydraulic and Mountain River Engineering, School of Water Resource and Hydropower, Sichuan University, Chengdu 610065, China
Academic Editor: Rizal Rashid is paper proposes a modified return mapping algorithm for a series of nonlinear yield criteria. e algorithm is established in the principal stress space and ignores the effect of the intermediate principal stress. ree stress return schemes are derived in this paper: return to the yield surface, return to the curve, and return to the apex point. e conditions used for determining the correct stress return type are constructed
A return mapping algorithm suitable for a series of nonlinear yield criteria ignoring the effect of the intermediate principal stress is proposed
Summary
The approach for obtaining the equivalent M-C strength parameters and the equivalent parameters of the plastic potentials has been presented. E crucial procedure to bring σB back to the yield surface is to evaluate the plastic corrector, Δσp.Δσp was derived by Crisfield [35] and is written in the principal stress space as follows: Δσp fσB. Erefore, if the predictor stress is returned to the curve (satisfying σ1 σ2), defined by the intersection of the primary yield plane and the adjacent yield surface satisfying σ2 ≥ σ1 ≥ σ3 in the principal stress space, the following equation can be obtained:. Note that the gradient and the plastic potential of the adjacent yield surface can be obtained by interchanging the components of a and b in equation (6). E approach for obtaining an initial value in equation (14) is the same as that of the return to the yield surface case. With the stress return schemes and the conditions for choosing the proper return schemes at hand, it is necessary to determine a consistent matrix. e general method for calculating the consistent matrix in the principal stress space has been derived by Clausen et al [9, 10]. e details, need not be given here
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