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In this paper, a modulus-based Shamanskii-Like Levenberg-Marquardt method is proposed for solving nonlinear complementarity problems (NCPs). First, the NCP is reformulated in the form of an equivalent non-smooth system of equations. Then, a non-smooth Shamanskii-Like Levenberg-Marquardt method using a non-monotone r-order Armijo line search is developed by generalizing a smooth Levenberg-Marquardt method to solve the resulting system. Global convergence of the proposed method is achieved under some suitable assumptions. Numerical experiments verify the feasibility and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

• A general algorithm for multisurface plasticity is presented. • A general frame to define sequential linear complementarity problem for plasticity. • The set of active constraints is naturally identified by Lemke's algorithm. • Stress is updated using the method of sequential linear complementarity problem. • The robustness of the algorithm is demonstrated via the 3D isoerror map. In this paper, a general algorithm is presented for the integration of multisurface plasticity models. The algorithm combines the return mapping with the technique of the sequential linear complementarity problem (SLCP) to update stress. The set of active constraints is naturally identified by the classical Lemke's algorithm. With the assumptions of isotropic linear elasticity, perfect plasticity, and the associated flow rule, all details are provided in matrix notations to facilitate computer implementation. The extension to hardening/softening multisurface plasticity models is also presented. The application of the algorithm is demonstrated via simulation of three types of geotechnical problems in 2D and 3D. Both linear and nonlinear multisurface plasticity models, e.g. Mohr-Coulomb and generalized Hoek-Brown yield criteria, are examined within the framework of the proposed algorithm. The numerical results are in good agreement with the analytic solutions. Moreover, the accuracy of the proposed stress integration procedure is investigated through 3D isoerror map. The convergence using the consistent tangent matrix at the global level is examined by a one-increment example consisting of one element. [ABSTRACT FROM AUTHOR]

The estimation of the wave-induced instantaneous liquefaction is particularly important for the design of foundations of offshore structures. Regarding the occurrence of liquefaction in a non-cohesive seabed, most existing studies using constant permeability were found to cause fallacious tensile stresses in the liquefied zone and further pollute the overall pore pressure distribution. A dynamic permeability model was previously presented to mitigate the shortcoming but posed difficulties in the nonlinear convergence. To overcome the shortcoming of the previous studies, this study proposes the concept of modelling the liquefaction-involved wave-seabed interactions as a nonlinear complementarity problem, wherein a Karush–Kuhn–Tucker condition is constructed, based on revisiting the liquefaction criterion most widely applied in ocean engineering. The Lagrange multiplier method and the primal–dual active set strategy are employed to numerically deal with the nonlinear complementarity problem. The performance of the chosen multiplier space is investigated by theoretical analyzing and numerical modelling. Compared with the previous dynamic permeability model, the present model is totally free of extra parameters and precisely fulfills the no-tension requirement. Moreover, the difficulties of dynamic permeability in the nonlinear convergence are overcome and no divergence is observed in the numerical tests. [ABSTRACT FROM AUTHOR]