Study On The Concrete Models With Random Irregular Aggregates Based On P-AFEM And The Two-level Hierarchical PCG Methods

At the meso-level,concrete is often considered as a three-phase composite composed of aggregate,cement matrix and interfacial layer,in which the shape,distribution and content of aggregate will have a great influence on the mechanical properties of concrete materials.In order to analyze the related mechanical properties of concrete materials better,it is necessary to simulate the shape and content of actual aggregate as much as possible,and to generate irregular aggregate geometric model that conforms to the actual shape of aggregate.In the finite element simulation of irregular aggregate model,due to the thinner interfacial layer and the irregularity of aggregate,especially the concavity and convexity of aggregate,the adaptive finite element method is often used to ensure that the calculation results near the interface of aggregate are kept high accuracy.In the adaptive finite element algorithm,the solving module,namely the algebraic solution of the corresponding discrete system,also has a great influence on the whole efficiency of the finite element analysis of aggregate model.In practical application,the material constants of each component of aggregate model may vary greatly,which will lead to a highly ill-conditioned coefficient matrix of the corresponding discrete system.The efficiency of the usual solution method will be greatly reduced,so it is necessary to design a solution method with higher computational efficiency.This paper focuses on the geometric model establishment of two-dimensional irregular aggregate model of concrete,the efficient adaptive finite element method and the algebraic solution of the corresponding discretization system.The main work and conclusions are as follows:1.Based on ANSYS Parametric Language(APDL),an algorithm for generating two-dimensional random irregular aggregate geometric model is designed and compiled.The algorithm can rapidly realize the geometric model of arbitrary irregular aggregates(such as concave-convex and curved)with two-grade,three-grade and four-graded aggregates and more than 60% content,which can satisfy the requirement of aggregate content in concrete micro-mechanics analysis,and also provide real-time geometric model data for subsequent mesh division,finite element numerical simulation and post-processing analysis.2.In this paper,a p-type adaptive finite element method(p-AFEM)based on "zoning and grading" local error control is proposed.The influence of error control standard on the calculation results near the aggregate interface is discussed in detail.And the corresponding adaptive calculation program and post-processing program are compiled.By applying this method to several typical irregular concrete aggregate models of elastic and elastic-plastic finite element analysis,the numerical results show that the method is effective and adaptable,and can well solve the stress concentration phenomenon caused by irregular aggregate,especially concave-convex aggregate.It provides an efficient calculation method for the numerical analysis of aggregate model based on real aggregate shape database.3.According to the hierarchical quadratic element discrete system of aggregate model,two simple and effective preconditioners are designed by using the hierarchical structure of coefficient matrix and the properties of block diagonal matrix.The calculation of these preconditioners is mainly reduced to the solution of linear element discrete system.The existing GAMG method can provide an efficient method for solving these preconditioners.Several typical aggregate models are tested numerically to verify the validity and robustness of the corresponding PCG method,which provides a fast solution method for the finite element analysis of the actual concrete aggregate model.