Base Force Element Method Research Articles

Base Force Element Method for Finite Strain Problems Based on Artificial Neural Network

The combination of artificial intelligence and finite element method (FEM) is a hot topic in the field of computational mechanics. This study proposes a novel base force element method (BFEM) for finite strain problems based on the complementary energy principle. Using the back-propagation (BP) neural network in the field of artificial intelligence to construct the constitutive relationship of the BFEM for finite strain problems. First, a BFEM model for finite strain problems was derived. Second, using the BP neural network model and learning from test samples, a constitutive relationship for incompressible finite strain problems has been efficiently established. Third, the program has been upgraded using parallel computing and sparse matrices, which greatly improves the computational efficiency of this study. Finally, several finite strain examples were used to verify the correctness of the BFEM based on the BP neural network proposed in this study, as well as the efficiency of the parallel computing method. This study combines BP neural network with a new type of FEM — BFEM, which fills the gap in using complementary energy FEM to calculate the finite strain problem of incompressible hyperelastic materials.

A variable-node element model and its application to damage analysis of RAC using the 2D base force element method

The existing methods find it difficult to resolve the inconsistency in the nodal displacements of nodes at the interface of dense and sparse element models. Therefore, this paper proposes a new variable-node element model using the base force element method (BFEM) and successfully applies it to study the mechanical properties of recycled aggregate concrete (RAC). First, the variable-node element model with an arbitrary change of node number in the mid-edges was established, and the explicit expressions of the 2 × 2 nodal compliance matrix and nodal displacements were given. Subsequently, the triangular and quadrilateral elements of single-sides and double-sides of hanging element models were developed based on the variable-node element model. In addition, a double-notched model of RAC with different aggregate types but the same aggregate distribution position was established, and numerical simulations of uniaxial tension were performed. The results show that the compliance matrix and nodal displacement are independent of the element characteristic without Gaussian integration. The variable-node hanging element model has high numerical accuracy and applicability, and the nodes between the sparse and dense meshes do not require any construction measures. The variable-node elements ensure the coordination of the nodal displacement at the interfaces. The aggregate shape has a significant effect on the damage mode, maximum principal strain, principal stress distribution, and stress concentration, while has a negligible effect on RAC tensile strength when the aggregate distribution is the same.

基于基面力元法钢纤维轻骨料混凝土损伤分析

基于基面力元法钢纤维轻骨料混凝土损伤分析

Mesoscopic Analysis of Rounded and Hybrid Aggregates in Recycled Rubber Concrete.

Recycled rubber concrete (RRC), a sustainable building material, provides a solution to the environmental issues posed by rubber waste. This research introduces a sophisticated hybrid random aggregate model for RRC. The model is established by combining convex polygon aggregates and rounded rubber co-casting schemes with supplemental tools developed in MATLAB and Fortran for processing. Numerical analyses, based on the base force element method (BFEM) of the complementary energy principle, are performed on RRC's uniaxial tensile and compressive behaviors using the proposed aggregate models. This study identified the interfacial transition zone (ITZ) around the rubber as RRC's weakest area. Here, cracks originate and progress to the aggregate, leading to widespread cracking. Primary cracks form perpendicular to the load under tension, whereas bifurcated cracks result from compression, echoing conventional concrete's failure mechanisms. Additionally, the hybrid aggregate model outperformed the rounded aggregate model, exhibiting closer peak strengths and more accurate aggregate shapes. The method's validity is supported by experimental findings, resulting In detailed stress-strain curves and damage contour diagrams.

Analysis of Mechanical Properties and Failure Mechanism of Lightweight Aggregate Concrete Based on Meso Level.

The relationship between the macroscopic mechanical properties of lightweight aggregate concrete and its microstructure is a hot topic in the discipline of concrete materials. It is very meaningful to provide an efficient numerical analysis method to conduct a meso-level analysis. This study proposes an automatic dissection algorithm and adapts the calculation program of the base force element method to conduct a non-linear damage analysis. In the numerical simulation, three groups of 100 mm × 100 mm × 100 mm specimens were selected for the uniaxial compression experiment and uniaxial tensile experiment, respectively. The average tensile strength of the numerical simulation for the uniaxial compression test was 21.86 MPa. The stress-strain softening curve, stress contour plot, strain contour plot, and damage plot of the light aggregate concrete were also analyzed. These research results provide data for analyzing the failure mechanism of light aggregate concrete and reveal the failure mechanism of light aggregate concrete. At the same time, the reliability of the proposed algorithm is verified. Our aim is to provide a more efficient and accurate analysis of meso-damage in lightweight aggregate concrete, which benefits industries involved in production, construction, and structural engineering.

Simulation study on the effect of the initial defect of recycled aggregate concrete based on BFEM

To study the effect of the initial defect on the mechanical properties and failure pattern of recycled aggregate concrete (RAC), several numerical models containing the initial defects were established and simulated under uniaxial compression. The recycled aggregate was simulated as an ellipse geometry, which can be constructed by compressing the circular geometry. The base force element method on the complementary energy principle was applied for the loading condition analysis. In addition, the stress–strain curves, deformation, and crack extension patterns of RAC were explored. Moreover, the maximum principal stress distribution and stress concentration were also investigated. The results demonstrate that the angle and length of the initial defect have a significant effect on the mechanical properties of the RAC. The initial defect interrupts the loading transfer path, forcing it into other continuous regions and forming a new transfer path. In addition, the longer the projection length of the initial defect in the loading direction, the most substantial influence on the mechanical properties, stress transfer, and damage mode.

Analysis of dynamic size effect of recycled concrete using base force element method

AbstractA 2D meso models of recycled concrete with different sizes is established using the base force element method. The specimens are loaded with different strain rates. The meso damage of recycled concrete is analyzed. In addition, the structural performance of specimens under the joint actions with strain rate and size are also studied. The simulation results find that the compressive strength has little difference when the values of strain rates are lower than 0.1 s−1. The greater the strain rates, the greater the difference of compressive strength between different sizes when strain rates are larger than 0.1 s−1. In addition, the Bažant statistical theory can be used to analysis the mechanical properties of recycled concrete. Besides, a modified formula in calculating the dynamic size effect of recycled concrete is also given based on the Bažant statistical size effect theory.

The base force element method based on the arc-length method for stability analysis

The Base Force Element Method (BFEM) is a simple and effective method for calculating large elastic deformation problems. In this paper, BFEM is further developed to make it useful for structural stability analysis. The generalized unbalanced displacement vector and composite tangent compliance matrix of the four-mid-node element and rod element of BFEM are proposed. BFEM can be combined with the Arc-Length Method (ALM) to analyze the stability of frame and truss structures. Through the calculation of several typical cases, the solution of this paper agrees well with the theoretical solution and the reference solution given by other methods. It is proved that the four-mid-node element and rod element of BFEM have high calculation accuracy in case of structural instability or post-buckling. In the calculation of the Lee frame, the calculation results of the four-mid-node element of BFEM are closer to the reference solutions than those of the CPS4 and CPS4R elements of general finite element software.

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

In this paper, a parallel homogenization model for recycled concrete was proposed. A new type of finite element method, the base force element method, based on the complementary energy principle and the parallel homogenization model, is used to conduct meso-level damage research on recycled concrete. The stress–strain softening curve and failure mechanism of the recycled concrete under uniaxial tensile load are analyzed using the nonlinear damage analysis program of the base force element method based on the parallel homogenization model. The tensile strength and destructive mechanisms of recycled concrete materials are studied using this parallel homogenization model. The calculation results are compared with the results of the experiments and meso-level random aggregate model analysis methods. The research results show that this parallel homogenization analysis method can be used to analyze the nonlinear damage analysis of recycled concrete materials. The tensile strength, stress–strain softening curve, and crack propagation process of recycled concrete materials can be obtained using the present method.

Effects of Recycled Aggregate Replacement Rate on Compression Mechanical Behavior of Concrete Based on Base Force Element Method

A meso-analysis method which is derived from the base force element method (BFEM) was proposed for recycled aggregate concrete (RAC). A simple algorithm was used to generate the convex recycled concrete aggregate (RCA) model. Uniaxial compression numerical simulations were carried out on the numerical specimens with different replacement rates of RCA. The model predictions were in a good agreement with the test results. The proposed method is very promising. It can totally predict the full stress-strain curve of RAC, as well as the failure process and failure mode, including strain softening and strain localization.

Geometrical nonlinear problems of truss beam by base force element method

AbstractThe base force element method (BFEM), formulated according the principle of complementary energy, is a new finite element method (FEM) that deals with nonlinear problems. Using the BFEM, the linear elastic model and large elastic deformation model of the plane truss element are derived, and the large elastic deformation model is expanded into a three‐dimensional setting in this study. The rotating part of the element should be considered when deriving the large elastic deformation model. Accordingly, it is necessary to determine whether base force can be used as a fundamental unknown variable. Nonlinear numerical calculation is performed in combination with large elastic deformations of the truss beam and frame. The calculated results conform with the theoretical results of a solid beam with equivalent deflection. In this study, the U.L and T.L formats are used to solve the governing equations iteratively. The calculated results in the T.L format are compared with those of the T2D2 and LINK1 elements in the finite element software. Only a single loading of the T.L format is necessary, rendering it a simple and convenient approach that can improve calculation efficiency. Moreover, the arc‐length method is first applied to the BFEM to solve the snap‐through problem.

3‐D base force element method on meso‐damage analysis for recycled concrete

AbstractThe 3‐D base force element method (BFEM) for damage problems is proposed, which is applied to analyze the damage mechanism of recycled aggregate concrete (RAC). A piecewise curve damage constitutive model is given to simulate the constitutive relationships of RAC phases. A spatial random aggregate model of RAC is proposed. 3‐D numerical simulations of RAC under uniaxial mechanical stress are carried out. The macroscopic stress–strain relationship and failure process of RAC under uniaxial stress based on the 3‐D BFEM are obtained. The numerical results show a good consistency with the experimental results. This illustrates that the numerical simulation can reflect the nonlinearity deformation, stress redistribution, and crack propagation process of RAC. In addition, the influence of recycled aggregate replacement percentage on strength and elastic modulus is investigated. The results show that the content proportion of recycled aggregate has a great effect on RAC, which have to be considered in the analysis and the application of RAC.

Five-phase sphere equivalent model of recycled concrete and numerical simulation based on the base force element method

Purpose 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. Design/methodology/approach 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. Findings 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. Originality/value 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.

Mesoscopic numerical simulation of fracture process and failure mechanism of cement mortar

AbstractCement mortar is an important part of building material and a typical cement matrix composite material. In current work, the mechanical properties and failure mechanism of cement mortar under static compression are studied by using the Base Force Element Method (BFEM). The static compression damage program of cement mortar is compiled grounded on the BFEM of the potential energy principle. An elastic polyline damage constitutive model is put forward to express the meso‐damage and evolution process of cement mortar. A 2D random circular aggregate model of cement mortar was established. The numerical simulation of the uniaxial static compression is carried out, the stress–strain curve, damage process, and damage model are obtained. The strength of the interfacial transition zone and the failure process of hardened cement mortar were discussed. A mesoscopic equivalent model is proposed to analyze the mechanical properties of cement mortar by considering the effect of initial porosity.

Modeling interfacial transition zone of RAC based on a degenerate element of BFEM

To study the properties of the interfacial transition zone (ITZ) of recycled aggregate concrete (RAC), a RAC model was presented that can mesh directly inside the aggregate. The characteristics of the ITZ can be accurately identified and simulated based on this model. Additionally, as for comparative specimens, several projection mesh models of RAC were also set up to prove the accuracy and efficiency of this model. Further, a two-dimensional (2D) element was introduced to simulate the ITZ element, which is degenerated from a three-dimensional (3D) element on the base force element method (BFEM). Hereafter, these RAC models were subjected to a displacement loading to simulate the uniaxial compression and tension tests based on the BFEM. The effect of ITZ thickness on the compressive strength, tensile strength, peak/ultimate strain, and crack development was studied. Besides, the influence of the relative properties between ITZs and the corresponding mortar was also investigated. The obtained results demonstrate that the present model is an efficient way to analyze the influence law of ITZ. Besides, the multiple influencing factors can be fixed via this model; therefore, their effects can be studied by varying one single factor at a time. The degenerate element is a new approach to investigate the element with a large aspect ratio with sufficient accuracy and efficiency.

Mesoscale fracture analysis of recycled aggregate concrete based on digital image processing technique

AbstractSince recycled aggregate concrete (RAC) is valuable for green concrete and global sustainability, it has attracted many numerical research studies as a five‐phase material in mesolevel. In this study, the digital image processing (DIP) technique is used to obtain the real aggregate and mortar distribution of recycled concrete specimens. By applying the DIP MATLAB model, the real mesoheterogeneity of RAC is well represented. Based on the base force element method (BFEM), a mesomechanical model is constructed to simulate the uniaxial tension and compression tests of recycled concrete specimens subjected to displacement loads. The damage and the cracking mechanisms of RAC are analyzed in the mesolevel. Moreover, the failure process and the failure mode are investigated. Results indicate the nonlinearity deformation, stress redistribution, and cracks propagation of RAC. The stress–strain curve, fracture energy, and fracture distribution are also figured. The comparative analysis between the simulation and the experimental results of in situ RAC samples shows the applicability of the model; therefore, the failure mechanism is revealed. It also extends the application of the BFEM in the field of failure mechanism analysis of RAC as a heterogeneous composite material.

Mesoscopic numerical analysis of dynamic tensile fracture of recycled concrete

Purpose 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. Design/methodology/approach 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. Findings The failure strength and failure pattern of RAC have strong rate-dependent characteristics because of the inhomogeneity and the inertial effect of the material. Originality/value The dynamic base force element method has been successfully applied to the study of recycled concrete.

Numerical Studies on Damage Behavior of Recycled Aggregate Concrete Based on a 3D Model.

This paper develops a 3D base force element method (BFEM) based on the potential energy principle. According to the BFEM, the stiffness matrix and node displacement of any eight-node hexahedral element are derived as a uniform expression. Moreover, this expression is explicitly expressed without a Gaussian integral. A 3D random numerical model of recycled aggregate concrete (RAC) is established. The randomness of aggregate was obtained by using the Monte Carlo random method. The effects of the recycled aggregate substitution and adhered mortar percentage on the elastic modulus and compressive strength are explored under uniaxial compression loading. In addition, the failure pattern is also studied. The obtained data show that the 3D BFEM is an efficient method to explore the failure mechanism of heterogeneous materials. The 3D random RAC model is feasible for characterizing the mesostructure of RAC. Both the substitution of recycled aggregate and the percentage of adhering mortar have a non-negligible influence on the mechanical properties of RAC. As the weak points in the specimen, the old interfacial transition zone (ITZ) and adhered mortar are the major factors that lead to the weakened properties of RAC. The first crack always appears in these weak zones, and then, due to the increase and transfer of stress, approximately two-to-three continuous cracks are formed in the 45°direction of the specimen.

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

SummaryThe 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.

Research on softening curve of recycled concrete using base force element method in meso-level

PurposeBased 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.Design/methodology/approachThe 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.FindingsThe 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.Originality/valueThe results show that the base force element method has been successfully applied to the study of softening curve of recycled concrete under uniaxial tension.