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In this paper, an algorithm is proposed to solve the frictional contact problems while considering elasto-plastic material properties. The static and dynamic solution procedures are derived in incremental form, respectively. The proposed method employs a two-layer iteration strategy. In the outer iteration layer, the equilibrium equations are solved, with the stress and stiffness matrix updated at each iteration. Within the inner iteration layer, the contact force is calculated, where the contact equations, expressed as B-differentiable equations, incorporate only contact conditions in normal and tangential directions, and the contact flexibility matrix, obtained by applying unit force pair to all contact node pairs in turn, is introduced. Consequently, the solution for nonlinear equilibrium equations and contact equations is decoupled, requiring only one decomposition of the stiffness matrix for each calculation of the contact flexibility matrix, as it remains constant within the contact iteration layer. In addition, the constitutive model of concrete developed by Lee and Fenves is utilized. This model adopts two independent variables to describe tensile and compressive damage, together considering the strength recovery of the concrete. Numerical examples demonstrate the accuracy of the proposed method by comparing the results from Abaqus. Furthermore, the present algorithm is applied to static and dynamic analyses of a concrete arch dam with several transverse joints, where the effects of gravity, water level, the number of contact surfaces, and seismic load are considered, and some conclusions are obtained. • An algorithm is developed to solve the elasto-plastic contact problems. • Two-layer iteration strategy is adopted in the proposed method. • Contact equations are expressed in the form of B-differentiable equations. • This method can be applied to static and dynamic analysis of concrete arch dams. [ABSTRACT FROM AUTHOR]

Highlights • A method for simulation of spatial variability of gravity dams was established. • Mean value of the tensile strength has a great influence on the plastic damage. • Research results can be used as a reference for gravity dams with similar profiles. Abstract A method to simulate the random field of the strength parameters of gravity dams considering their spatial variability based on the theory of random fields and the autocorrelation function is proposed. Taking a gravity dam project as an example, the elastic modulus and tensile strength are selected as random variables and the corresponding random fields are generated. Based on the concrete damage plasticity (CDP) model, the effects of the spatial variability of parameters on the dynamic response characteristics of gravity dams are expressed from the standpoints of damage development, residual displacement, and energy dissipation. The impacts of the mean value, coefficients of variation, autocorrelation distance, realizations of the tensile strength random field, and seismic inputs on the structural damage are also investigated. It is found that the spatial variability of parameters, especially the tensile strength, has a great influence on the dynamic damage of gravity dams, and that increasing the mean value of the tensile strength can improve their seismic performance. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a method for the integration of a class of plastic-damage material models. The integration of the evolution equations results in a nonlinear problem, which is linearized and solved with the Newton–Raphson method using a sub-stepping strategy. The consistent tangent matrix can be formulated either in terms of the stress components in a general reference system or in terms of the principal stress and strain components with the former then transformed to the general reference system. In order to account for plane stress conditions, the stress–strain relations of the 3d material model are then condensed out. Plane stress conditions are imposed by the linearization of the stresses that need to be set equal to zero; thus the strain fields are updated in the corresponding directions. This solution method is extended to include transverse pressure and the effect of transverse reinforcing steel for a 3d concrete material model. The equilibrium of the stresses in the reinforcing steel and concrete is linearized and the strain fields are updated until the residual satisfies a specified tolerance. The consistent tangent matrix due to the condensation process is derived. The proposed algorithms are tested at the material and element level by comparison of numerical solutions with available experimental data. [Copyright &y& Elsevier]