Modeling the Failure Pattern of Prenotched Recycled Aggregate Concrete Using FEM on Complementary Energy Principle

The reuse of recycled aggregate concrete (RAC) is being researched all over the world and lots of works are focused on the notched specimen to study the crack path of RAC. A mathematical algorithm of RAC meshing was presented to explore the failure pattern in RAC. According to this algorithm, the interfacial transition zone can be defined to be an actual thickness at the micron level. Further, a new finite element method (FEM) on the complementary energy principle was introduced to simulate the mechanical behavior of RAC’s mesostructure. The compliance matrix of the element with any shape can be calculated and expressed to be a uniform and explicit expression. Several numerical models of RAC were established, in which the effecting factors of the prenotch size, thickness of ITZ, and the distance from the prenotch to the aggregate were taken into account. Hereafter, these RAC models were subjected to uniaxial tension. The effect of the aforementioned factors on the crack path was simulated. The simulated data manifest that both the mesh mode of RAC and the FEM on complementary energy principle are effective approaches to explore the failure pattern of RAC. The size of the prenotch, thickness of ITZ, and distance from the prenotch to the recycled aggregate have a powerful influence on the path and distribution of the isolated crack, width and length of the crack path, and the shape and path of continuous cracks, respectively.

A Degenerated Plane Truss Model of Base Force Element Method on Complementary Energy Principle

In order to study the performance of base force element method (BFEM), a new 2-node degenerated plane element model based on the BFEM of complementary energy principle is presented for linear elasticity problem and geometrically nonlinear problem respectively in this paper. The plane truss element model can easily be obtained by degenerating from a four-mid-node plane element of the BFEM based on complementary energy principle for linear elasticity problem or geometrically nonlinear problem. The compliance matrix of the rod element model is same as the compliance matrix of the four-mid-node plane element of the BFEM. According to the characteristics of analysis for truss structure, the nodal equilibrium conditions and the displacement coordination conditions of each rod at the nodes have been considered when the compliance matrix of structure is integrated. In order to verify the feasibility of the degenerated plane element model, several truss problems are analyzed and their solutions are compared to the analytical solutions and the numerical results which are calculated with the traditional displacement FEM. It is found that the model has shown high precision and good performance.

Application of Base Force Element Method on Complementary Energy Principle to Rock Mechanics Problems

The four-mid-node plane model of base force element method (BFEM) on complementary energy principle is used to analyze the rock mechanics problems. The method to simulate the crack propagation using the BFEM is proposed. And the calculation method of safety factor for rock mass stability was presented for the BFEM on complementary energy principle. The numerical researches show that the results of the BFEM are consistent with the results of conventional quadrilateral isoparametric element and quadrilateral reduced integration element, and the nonlinear BFEM has some advantages in dealing crack propagation and calculating safety factor of stability.

Application of 2D base force element method with complementary energy principle for arbitrary meshes

Purpose – 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. Design/methodology/approach – 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. Findings – 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. Research limitations/implications – 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. Practical implications – This paper presents a new idea and a new numerical method, and to explore new ways to solve the problem of arbitrary meshes. Originality/value – The paper presents a 2D model of the BFEM using the complementary energy principle for arbitrary mesh problems.

A 4-Mid-Node Plane Model of Base Force Element Method on Complementary Energy Principle

Using the base forces as fundamental variables to describe the stress state and the displacement gradients that are the conjugate variables of the base forces to describe the deformation state for the two-dimensional elasticity problems, a 4-mid-node plane model of base force element method (BFEM) based on complementary energy principle is proposed. In this paper, the complementary energy of an element of the BFEM is constructed by using the base forces. The equilibrium conditions are released by the Lagrange multiplier method, and a modified complementary energy principle described by the base forces is obtained. The formulation of the 4-mid-node plane element of the BFEM is derived by assuming that the stress is uniformly distributed on each edge of the plane elements. A procedure of the BFEM on complementary energy principle is developed using MATLAB language. The numerical results of examples show that this model of the BFEM has high precision and is free from mesh sensitivity. This model shows good performances.