Base force element method based on the complementary energy principle for the damage analysis of recycled aggregate concrete

Abstract

Summary The finite element method (FEM) is an effective approach for exploring the failure mechanism of heterogeneous materials. According to the complementary energy principle, the use of FEM might suffer from several difficulties in terms of keeping the elements and their boundaries balanced, as well as finding interpolation functions. In this study, we introduced an efficient approach to researching the failure mechanism of the material, named base force element method (BFEM), according to complementary energy principle. Specifically, the element compliance matrix of an arbitrary quadrilateral element with four mid‐edge nodes was expressed based on the complementary energy principle. Then, the node displacement was obtained by the governing equation using the Lagrange multiplier method. In addition, both the compliance matrix and the node displacement were represented as explicit expressions without the use of Gaussian integration. A numerical model of the recycled aggregate concrete (RAC) was established according to the Monte Carlo method. A comparative sample of the digital image model was also established using digital image technology. The influences of substituting recycled aggregate and the relative mechanical properties of adhered mortar to those of new mortar on the failure mechanism of RAC were studied. The simulation results indicated that the BFEM is an effective approach to researching the damage mechanism of heterogeneous materials.

Mesoscopic Analysis of Rounded and Hybrid Aggregates in Recycled Rubber Concrete

“…They subsequently validated the method's accuracy for different deformation scales against traditional analytical solutions, showing its broad applicability even in mesh divisions of varied shapes with minimal sensitivity to distortions. Post 2013, Peng et al employed this method in concrete sectors, revealing insights into its meso-structure, mechanics, and fracture behavior [37]. The findings were further supported by subsequent studies, especially those exploring prismatic recycled concrete's damage mechanisms and the role of aggregates.…”

“…The main program algorithm for the two-dimensional BFEM of the complementary energy principle is shown in Figure 2. The formula of the flow chart is detailed in references [35,37].…”

“…The Monte Carlo method [37] is used to compile the FORTRAN program first, and then the pseudorandom number is generated by computer. Then, the position of the coarse aggregate in the center of the circle is determined according to the pseudorandom number and the size of the specimen.…”

“…In RRC, coarse aggregate adopts a bilinear constitutive model [37], as shown in Figure 9. The bilinear damage model uses the constitutive relationship of isotropic elastic damage mechanics to describe the mechanical properties of concrete materials.…”

Analysis of Tensile Strength and Failure Mechanism Based on Parallel Homogenization Model for Recycled Concrete

“…In reference [ 7 ], a statistical analysis on its composition has been performed considering the randomness in properties of old adhered mortar around recycled aggregate. Peng et al [ 8 , 9 , 10 , 11 ] proposed the base force element method and used this new type of finite element method to carry out a numerical simulation analysis on the recycled concrete, and conducted uniaxial tensile and compression tests under static and dynamic loads to study its mechanics and performance. In 2016, Rajendra [ 12 ] established a virtual crack model and a double-K fracture model, and determined the fracture parameters of recycled concrete with different coarse aggregate contents.…”