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The purpose of this paper is to present a two-dimensional (2D) model of the base force element method (BFEM) based on the complementary energy principle. The study proposes a model of the BFEM for arbitrary mesh problems.

The BFEM uses the base forces given by Gao (2003) as fundamental variables to describe the stress state of an elastic system. An explicit expression of element compliance matrix is derived using the concept of base forces. The detailed formulations of governing equations for the BFEM are given using the Lagrange multiplier method. The explicit displacement expression of nodes is given. To verify the 2D model, a program on the BFEM using MATLAB language is made and a number of examples on arbitrary polygonal meshes and aberrant meshes are provided to illustrate the BFEM.

A good agreement is obtained between the numerical and theoretical results. Based on the studies, it is found that the 2D formulation of BFEM with complementary energy principle provides reliable predictions for arbitrary mesh problems.

Due to the use of Lagrange multiplier method, there are more basic unknowns in the control equation. The proposed method will be improved in the future.

This paper presents a new idea and a new numerical method, and to explore new ways to solve the problem of arbitrary meshes.

The paper presents a 2D model of the BFEM using the complementary energy principle for arbitrary mesh problems.

Based on the base force element method, a two-dimensional random circle aggregate model with Monte Carlo principle is proposed to carry out research on softening curve in meso-level.

The meso-level structure of recycled concrete is considered as the five-phase materials composed of aggregate, old interfacial transition zone, old mortar, new interfacial transition zone and new mortar. A multi-polyline damage model is adopted to describe the nonlinear mechanical behavior of recycled concrete material. The destruction state of the element is determined by the first strength theory. The research studies on damage process of recycled concrete under the loading conditions of uniaxial tension were established using the base force element method.

The softening curves of recycled concrete are obtained, which are in good agreement with experiment results. Simulation results show that the macroscopic mechanical properties and failure mechanism can analyze more reasonably from mesoscopic structure. Besides that, it can be investigated from the numerical results of the size effect in recycled concrete through the mesoscopic heterogeneity. Furthermore, the form of aggregate distribution has influence on the crack path but little effect on the tensile strength of recycled concrete.

The results show that the base force element method has been successfully applied to the study of softening curve of recycled concrete under uniaxial tension.

This paper aims to propose the five-phase sphere equivalent model of recycled concrete, which can be used to deduce the theoretical formulas for the Poisson’s ratio and effective elastic modulus.

At a mesoscopic level, the equivalent model converts the interfacial layer, which consists of the new interfacial transition zone (ITZ), the old mortar and the old (ITZ), into a uniform equivalent medium. This paper deduces a strength expression for the interfacial transition zone at the microscopic level using the equivalent model and elastic theory. In addition, a new finite element method called the base force element method was used in this research.

Through numerical simulation, it was found that the mechanical property results from the five-phase sphere equivalent model were in good agreement with those of the random aggregate model. Furthermore, the proposed model agree on quite well with the available experimental data.

The equivalent model can eliminate the influence of the interfacial layer on the macroscopic mechanical properties, thereby improving the calculation accuracy and computational efficiency. The proposed model can also provide a suitable model for multi-scale calculations.

Based on the random aggregate model of recycled aggregate concrete (RAC), this paper aims to focus on the effect of loading rate on the failure pattern and the macroscopic mechanical properties.

RAC is regarded as a five-phase inhomogeneous composite material at the mesoscopic level. The number and position of the aggregates are modeled by the Walraven formula and Monte–Carlo stochastic method, respectively. The RAC specimen is divided by the finite-element mesh to establish the dynamic base force element model. In this model, the element mechanical parameters of each material phase satisfy Weibull distribution. To simulate and analyze the dynamic mechanical behavior of RAC under axial tension, flexural tension and shear tension, the dynamic tensile modes of the double-notched specimens, the simply supported beam and the L specimens are modeled, respectively. In addition, the different concrete samples are numerically investigated under different loading rates.

The failure strength and failure pattern of RAC have strong rate-dependent characteristics because of the inhomogeneity and the inertial effect of the material.

The dynamic base force element method has been successfully applied to the study of recycled concrete.