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A linear tension softening model of concrete 300 In Fig. 11 σ c and ε c are the concrete's yield stress and strain in compression (at 28 days) 301
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Peridynamics has been increasingly used for the study of damage and failure behaviors of reinforced concrete (RC) structures, e.g., cracking, fragmentation, and interface debonding due to its strong capacity in analyzing discontinuous problems. This paper presents a practical bond-based peridynamics (BPD) modeling for simulating complicated nonline...
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A reliable crack width assessment is a basic part of the sustainability control of the reinforced concrete structures subjected to corrosion degradation. The uncertainty of the concrete cracking model based on a finite element method and nonlinear fracture mechanics is investigated. The parameters of numerical model, such as the finite element mesh...
Citations
... Zhang et al. developed a practical bond-based peridynamics (BPD) modeling for simulating complex nonlinear behaviors in reinforced concrete structures. They developed a novel ASI bond-slip model and implemented it in OpenSees, demonstrating its strong capacity for simulating damage behavior [144]. Saxena et al. developed a microstructure-sensitive and derivative-free continuum model for composite materials, incorporating microstructural information for accurate prediction of failure modes. ...
This study presents a comprehensive exploration of Peridynamic (PD) theory, with a specific focus on its theoretical foundations and practical implementations, including various PD formulations and PD operators. The objective is to highlight the unique attributes of each PD formulation and assess their suitability in the framework of material failure simulations by providing an extensive literature review. The research focuses on the bond-based (BB), ordinary state-based (OSB), and non-ordinary state-based (NOSB) PD formulations, offering a thorough understanding of their distinctive characteristics. Moreover, this study presents the importance of the PD operators on the solution of the differential equations. Numerical implementation is a central aspect of this research, providing a detailed flow chart of the computer codes for PD and PD operator models. In order to demonstrate the robustness of the PD formulations, this study presents numerical results, showcasing predictions generated by computer codes that can be accessed online.
... Yamghoobi et al. [20] proposed a micropolar PD method for modeling cracks in fiber-RC structures to accurately represent the composite response of notched fiber-RC beams. Zhang et al. [21,22] proposed a coupled axial-shear interaction (ASI) element to study the interaction between concrete and rebar. Despite its advantages, the PD model still has some limitations such as high computational costs resulting from the large number of DOF and elements, making it challenging to simulate the nonlinear response of large-scale structures. ...
This paper proposes a novel smart component model replacement (SCMR) approach that is not only efficient for large-scale nonlinear structural analysis, but also accurate in the refined simulation of components of interest. The method creates a FE model with a relatively coarse mesh to simulate the entire structure. During analysis, when a component is identified to predefined criteria defined by the users, its model will be replaced by another more refined "substructure" model that can simulate the damage and failure more accurately. A few "replace-ment" strategies are presented for smoothly transiting between different models: (1) A gradually transiting strategy is presented to avoid the possible jumps of responses due to the model differences to guarantee numerical stability; (2) The historical boundary conditions are applied to the substructure model to address the historical dependence of responses; (3) The boundary connection between main and substructure is considered by using a flexible client/server technology, to simplify the replacement. The SCMR approach is verified by three application examples. The results demonstrate that the proposed modeling approach can efficiently perform large-scale nonlinear structural analysis, while capturing the failure mechanism in RC structures well.
... Peridynamics has been used to simulate the failure of concrete structures. Zhang et al. proposed a novel coupled axial-shear interaction bond-slip model to simulate the damage behavior of reinforced concrete structures [36]. Song et al. developed a hybrid peridynamic and classical continuum mechanical model for the high-temperature damage and fracture analysis of concrete structures [37]. ...
How to simulate fracture mode and crack propagation path in a plate with multiple cracks is an attractive but difficult issue in fracture mechanics. Peridynamics is a recently developed nonlocal continuum formulation that can spontaneously predict the crack nucleation, branch and propagation in materials and structures through a meshfree discrete technique. In this paper, the peridynamic motion equation with boundary traction is improved by simplifying the boundary transfer functions. We calculate the critical cracking load and the fracture angles of the plate with multiple cracks under uniaxial tension. The results are consistent with those predicted by classical fracture mechanics. The fracture mode and crack propagation path are also determined. The calculation shows that the brittle fracture process of the plate with multiple cracks can be conveniently and correctly simulated by the peridynamic motion equation with boundary conditions.
... Based on the radial movement of material points, the relative rotation of the material point pairs is considered, and the micropolar peridynamic model is proposed. Zhang et al. [22] proposed a new bond-slip model and demonstrated its powerful ability to simulate the damage behavior of reinforced concrete structures. Yaghoobi et al. [23,24] introduced the semi-discrete method into the micropolar PD model to study the effect of reinforcing fibers on the analysis of cracks in cementitious materials. ...
A reinforced concrete shear wall is an important building structure. Once damage occurs, it not only causes great losses to various properties but also seriously endangers people's lives. It is difficult to achieve an accurate description of the damage process using the traditional numerical calculation method, which is based on the continuous medium theory. Its bottleneck lies in the crack-induced discontinuity, whereas the adopted numerical analysis method has the continuity requirement. The peridynamic theory can solve discontinuity problems and analyze material damage processes during crack expansion. In this paper, the quasi-static failure and impact failure of shear walls are simulated by improved micropolar peridynamics, which provides the whole process of microdefect growth, damage accumulation, crack initiation, and propagation. The peridynamic predictions are in good match with the current experiment observations, filling the gap of shear wall failure behavior in existing research.
... Peridynamics has also attracted considerable research attention as a new non-local theory [11,12], and has been applied to many engineering problems, such as the stress analysis in the vicinity of the crack tip [13], fracture modelling of reinforced concrete [14,15], and the inelastic fracture [16], etc. The governing equations in peridynamics are integral-differential equations rather than partial differential equations. ...
In this study, we propose the first unified implementation strategy for peridynamics in commercial finite element method (FEM) software packages based on their application programming interface using the peridynamics-based finite element method (PeriFEM). Using ANSYS and ABAQUS as examples, we present the numerical results and implementation details of PeriFEM in commercial FEM software. PeriFEM is a reformulation of the traditional FEM for solving peridynamic equations numerically. It is considered that the non-local features of peridynamics yet possesses the same computational framework as the traditional FEM. Therefore, this implementation benefits from the consistent computational frameworks of both PeriFEM and the traditional FEM. An implicit algorithm is used for both ANSYS and ABAQUS; however, different convergence criteria are adopted owing to their unique features. In ANSYS, APDL enables users to conveniently obtain broken-bond information from UPFs; thus, the convergence criterion is chosen as no new broken bond. In ABAQUS, obtaining broken-bond information is not convenient for users; thus, the default convergence criterion is used in ABAQUS. The codes integrated into ANSYS and ABAQUS are both verified through benchmark examples, and the computational convergence and costs are compared. The results show that, for some specific examples, ABAQUS is more efficient, whereas the convergence criterion adopted in ANSYS is more robust. Finally, 3D examples are presented to demonstrate the ability of the proposed approach to deal with complex engineering problems.
... The reason lies in that, without considering compaction of shear dilation, the unloading and reloading stiffness of UHPC is too strong to be re-compacted during the rebound stage. Therefore, the compaction of shear dilation, i.e., degeneration of stiffness, is essential for accurately reproducing the residual deflection of reinforced UHPC beams/columns subjected to lateral low-velocity impact loading, which is similar to the findings of numerical works [31,56] conducted on reinforced concrete structures. Table 4 lists the test scenarios, and The FEM of reinforced UHPC under field explosion is identical to Ref. [33], including the element type and size, material model for steel reinforcement and support, as well as the contact between reinforced UHPC panel and support. ...
Based on the framework of elastic-plastic-hydrocode concrete model, this study established a novel constitutive model of ultra-high performance concrete (UHPC) for impact and blast loadings considering the compaction of shear dilation. First, the established UHPC model is introduced, including five parts: (i) the dynamic failure strength surface, which is divided into tensile, compressive, and tensile-to-compressive regions and considers the Lode-dependence and strain rate effect; (ii) equation of state (EOS) that accounts for the nonlinear volumetric compaction; (iii) damage of strength, which contains independently described tensile and compressive strength hardening or softening formulae; (iv) damage of stiffness for depicting the compaction of shear dilation; (v) plastic flow rule, where the radial return algorithm is adopted for updating stress and an independent plastic potential function is employed to model the shear dilation. Then, parameters of the established UHPC model are systematically calibrated according to tests and empirical suggestions, and are further validated by conducting single element tests under varying loading paths. Through simulating the tests of reinforced UHPC beams/columns and UHPC filled steel tubes under drop hammer impact and reinforced UHPC panels under field explosion, it demonstrates that both the damage patterns and deflection-time histories of UHPC members are precisely reproduced by the established UHPC model. Furthermore, based on comparative simulations, it shows the compaction of shear dilation is critical for predicting the structural residual deflection of reinforced UHPC members. This study discloses a possibility to establish a constitutive model of concrete suitable for impact and blast scenarios with a wide range of strain rate and hydrostatic pressure.
... It is demonstrated that the method can accurately represent the composite response of notched fiber-RC beams. Zhang et al. [26] have developed a coupled axial-shear interaction (ASI) element to simulate the bond-slip and interface damages between the concrete and rebar. The element can be used to well capture the bond-slip behaviors and crack development in two-dimensional PD models. ...
... The strains and stresses of the RC specimen at section 4-4 with different slip displacements are investigated in Fig. 23 and Fig. 24, where the strain is calculated by an estimation method mentioned in [26]. When strain gradually increases from zero, the stress first increases from zero (i.e., in elastic state shown in white color) to the peak strength (shown in red/blue color in tensile/compressive state), and then decreases to zero again (when completed damage and shown in black color). ...
Peridynamic (PD) theory can effectively model discontinuous problems, but it remains a challenging task for refined three-dimensional (3D) simulation of bond-slip behaviors in pull-out tests, particularly when the rib of rebar is considered. The mesh size of the model needs to be small enough (e.g., decimillimetre or 0.1 mm) to simulate various shapes of ribs. Therefore, the scale of the PD model is usually significantly large and the computational efficiency is low. This paper proposes an enhanced bond-based PD (BPD) model to perform a refined 3D simulation of bond-slip behaviors in the ribbed bar pull-out test. In order to reduce the computation scale and improve efficiency, a practical 3D coupled element is developed to couple the fine PD model and coarse finite element (FE) model, where the PD is used to model the regions in concrete and rebar that are close to the interface, while FE model is used to simulate the regions far away from the interface. A computational framework is developed for implicit and static analyses of the coupled PD-FE model. A parallel computing strategy is adopted to improve the computational efficiency, and enhanced concrete and steel BPD models are presented to accurately simulate the nonlinear behaviors and damage of concrete and ribbed rebars. The enhanced PD modeling approach is implemented in an open-source finite element software framework, OpenSees, and verified by a cantilever beam under uniaxial loading conditions and a pushover analysis of an RC column. Based on the enhanced PD, a refined 3D simulation of ribbed rebar pull-out tests is performed. The bond-slip behaviors are studied in detail, e.g., the crack propagation with different types of ribs, concrete strengths, and rebar properties. The enhanced PD modeling approach provides an effective tool for refined simulation of the complicated bond-slip behaviors in RC structures.
... Yang et al. [24] studied the mode-I crack problem of concrete by introducing a trilinear constitutive relationship in pairwise force function. Zhang et al. [25] and Gu et al. [26] simulated the uniaxial tension, uniaxial compression, and impact responses of concrete using the bond-based PD (BBPD) theory; Chen et al. [27] proposed a new thermo-mechanical coupling model by improving the PD differential operator, and the experimental results of concrete cracking verify the numerical accuracy. Li and Guo [28] employed a dual-horizon PD model (DH-PD) for debonding damage analysis in fiber-reinforced polymer (FRP)-to-concrete bonded joints. ...
The difficulties in dealing with steel skeleton frames and low computational efficiency are the major obstacles for applying peridynamics (PD) to model reinforced concrete (RC) structures. This paper proposes a new reinforced concrete model, named PDROD, in which the concrete is modeled by PD theory and the reinforcement is modeled by rod elements. A bonding formulation is derived to characterize the interaction between the concrete and reinforcements, guaranteeing the consistence of load transfer between the two mediums. Thanks to the new bonding model, the discretization of the concrete and reinforcements does not necessarily need to be coincident, facilitating the application of PDROD in modeling RC structures whose skeleton frames are with complex geometries. The PDROD model not only gives full play to the advantages of PD theory in damage problems without additional failure criteria and stiffness degradation model, but also significantly increases the numerical efficiency of computation, which extends the applicability of PD to modeling real-scale RC structures. The accuracy and efficiency of the PDROD model are demonstrated by simulating a series of examples of concrete plates with reinforcing bars. Good agreements have been observed between the results from PDROD and the classical FEM predictions. The challenging benchmarks on the Stuttgart Shear Tests were also simulated to demonstrate the capability of the PDROD model in quasi-brittle fracture problems of large-scale RC structures.
... responses of compressive force versus displacement in the uniaxial tensile/compressive strength test of concrete specimens under the cyclic compressive loading) or the parameters of steel bond, the sti®ness E N , strength N and hardening ratio B are taken as that in the one-dimensional (1D) tensile test of rebars. The parameters of the ASI model are calibrated in a similar manner as the concrete bond model, as documented in detail by Zhang et al. 33,34 The RC shear wall is subjected to cyclic loading conditions by imposing a displacement history at the top using the static displacement control with a uniformly distributed vertical load (i.e. 378kN corresponding to the axial force ratio of 0.07) applied at the top. ...
... The Newton algorithm is used to solve the PD equation in Eq. (16). A gradually fadinḡ ctitious element (GFFE) approach is employed when the Newton algorithm does not converge, 33,34 particularly when the damage is severe such that a signi¯cant number of bonds begin to yield. ...
Peridynamics (PD) has gained increasing usage in simulating the nonlinear damage behavior of reinforced concrete (RC) structures due to its extraordinary capacity in solving discontinuous problems. This paper presents an enhanced bond-based peridynamic (BPD) modeling method for simulating the complex nonlinear behavior of RC shear walls, such as strength deterioration and cracking propagation, under cyclic loading conditions. In the proposed BPD method, a novel concrete bond model is presented that can consider the stiffness degradation, strength deterioration, and residual plastic deformation. A steel model and a coupled axial-shear model are adopted to simulate the nonlinear behavior of rebar and reinforcement-concrete interaction. The enhanced PD is implemented in an open-source finite element software framework, OpenSees, and can perform implicit or explicit, dynamic or static analyses in a parallel manner. Two RC shear walls under cyclic loading conditions are used as verification examples. The nonlinear damage behavior is studied in detail for the RC shear walls, e.g. the strength deterioration, pinch effect, and cracking behavior. The results demonstrate that the enhanced BPD modeling approach is capable of simulating the nonlinear damage behavior of RC shear walls under cyclic loading conditions.
... Huang et al. [22] and Yang et al. [23] established a PD model of crack propagation in concrete structures and simulated the propagation process of type I crack in concrete slabs. Then, Zhang et al. [24] and Chen et al. [25] used the PD method to simulate reinforced and fiber-reinforced concrete structures. Zhou et al. [26] developed a novel PD method for investigating the start, propagation, and merging of cracks in the rock under pressure. ...
The numerical simulation results utilizing the Peridynamics (PD) method reveal that the initial crack and crack propagation of the tunnel concrete lining structure agree with the experimental data compared to the Japanese prototype lining test. The load structure model takes into account the cracking process and distribution of the lining segment under the influence of local bias pressure and lining thickness. In addition, the influence of preset cracks and lining section form on the crack propagation of the concrete lining model is studied. This study evaluates the stability and sustainability of tunnel structure by the Peridynamics method, which provides a reference for the analysis of the causes of lining cracks, and also lays a foundation for the prevention, reinforcement and repair of tunnel lining cracks.
