Peridynamics Research Articles

Peridynamics simulation of impact failure in glass plates

This paper aims at presenting numerical simulation of dynamic failure process of Duran 50 glass plates subjected to high-velocity impact loads using a bond-based peridynamics (PD). In simulation, several affecting parameters including impact velocity, impact angle, impact contact area, glass plate thickness, and porosity percentage in glass plate are considered. The effects of these parameters on the damage, reaction force, and coefficient of restitution are examined. The functional relationship among the reaction force on bullet, the bullet velocity and the plate thickness is established. In addition, the functional relationship among the damage percentage of plate, the bullet velocity and the plate thickness is constructed. Thus, the reaction force on the bullet and the damage percentage of the plate can be directly evaluated with the functional relationships in the practice applications. PD simulated results are validated by existing experimental data with a good agreement. Through the simulated results, the following conclusions are obtained (1) a strong correlation exists between the coefficient of restitution observed experimentally and the model predictions; (2) the sensitivity to the velocity and sheet thickness in large-sized bullets is more than that in small-sized ones; (3) the damage, maximum reaction force, and coefficient of restitution almost change linearly with increasing the velocity, plate thickness and impact contact area; and (4) the effect of the porosity percentage on damage and reaction force is negligible.

Simulations of Fractures of Heterogeneous Orthotropic Fiber-Reinforced Concrete with Pre-Existing Flaws Using an Improved Peridynamic Model.

The propagation and coalescence of cracks in fiber-reinforced concretes (FRCs) is the direct cause of instability in many engineering structures. To predict the crack propagation path and failure mode of FRCs, an orthotropic-bond-based peridynamic (PD) model was established in this study. A kernel function reflecting long-range force was introduced, and the fiber bond was used to describe the macroanisotropy of the FRC. The crack propagation process of the FRC plate with flaws was simulated under uniaxial tensile loading. The results showed that under homogeneous conditions, the cracks formed along the centerline of the isotropic concrete propagate in a direction perpendicular to the load. Under anisotropic conditions, the cracks propagate strictly in the direction of the fiber bond. The failure degree of the FRC increases with the increase in heterogeneity. When the shape parameter is 10 and the fiber bond is 0°, the failure mode changes from tensile to shear failure. When the fiber bond is 45°, the FRC changes from a state where outer cracks penetrate the entire specimen to a state where cracks coalesce at the middle. It was found that the improved model can effectively simulate the crack propagation processes of orthotropic FRC materials.

Numerical analysis of heat and mass transfer during hydrogen absorption in metal hydride beds with a novel peridynamic model

Numerical modelling and study of metal hydride bed with heat and mass transfer is a key to identify and predict the state of the storage device during absorption and desorption process. It is a great challenge to numerically study this problem considering cracks and volumetric expansion for conventional approaches due their limitations in treating discontinuities and large deformations. To effectively predict the hydrogen charging performance with the influences of cracks and volumetric expansion, a novel peridynamic (PD) model considering hydrogen absorption was proposed, which has not been used in most existing studies. The developed PD model was applied to simulate metal hydride reaction including depleted uranium (DU) and zirconium cobalt (ZrCo) in a thin-layer bed. The simulation results agreed well with both existing numerical solutions and experimental observations. The cracks were introduced to identify their influences on the performance of hydrogen absorption in a DU bed as a prototype. It is demonstrated that crack length and location had a significant influence on the absorption rate and average temperature evolution. With the increase in the crack length, the hydrogen absorption efficiency of the metal hydride bed (MHB) decreases dramatically due to the high bed temperature. The crack approaching the cooling boundary would greatly affect the temperature evolution, which causes the average H/M value to reach saturation later. Finally, the effects of the volumetric expansion were taken into consideration in the present PD model. Unlike ZrCo, the hydrogen kinetics performance would be overrated due to the neglection of the volumetric expansion in a DU bed.

Simulating concrete failure using the Microplane (M7) constitutive model in correspondence-based peridynamics: Validation for classical fracture tests and extension to discrete fracture

We begin the article by summarizing some key developments in the field of Peridynamics (PD) and arrive at a conclusion that two schools of PD are emerging in recent years. One school takes a more traditional view of PD as a model of a nonlocal continuum, while another approaches PD as a discretization methodology for local continua where the nonlocality is reduced under mesh refinement. Adhering to the latter viewpoint, we develop a PD formulation using the now classical, yet continuously evolving Microplane constitutive model (M7) developed for the failure analysis of concrete materials. We show how to incorporate the M7 model into correspondence-based PD (also known as the non-ordinary state-based PD) and validate the formulation using an extensive set of classical fracture tests. We also propose an extension of the M7 model to handle concrete fracture and fragmentation in the PD context.

Titanium alloy corrosion fatigue crack growth rates prediction: Peridynamics based numerical approach

This study presents a numerical approach for modelling the Corrosion Fatigue Crack Growth (CFCG) in conventional casting and additively manufactured Ti6Al4V alloys. The proposed numerical model, based on Peridynamics (PD), combines the PD Fatigue Crack Growth (FCG) model and PD diffusion model in order to couple the mechanical and diffusion fields existing in the material due to the impact of environmental fatigue. The mechanical field is responsible for the characterisation of the changes to the structure due to the fatigue loading conditions. The diffusion field is based on the modelling of the adsorbed-hydrogen Stress Corrosion Cracking (SCC), in particular, the Hydrogen Embrittlement (HE) model is considered. The proposed approach has been validated using experimental data available in the literature showing the capability of the tool to predict the CFCG rates.

Peridynamic Simulation of Particles Impact and Interfacial Bonding in Cold Spray Process.

Cold spray has recently emerged as a promising new technology for various coating, additive manufacturing, and on-site repair needs. One key challenge underlying cold spray is the proper simulation of the deposition process, for which numerous numerical studies have been carried out, but often fail to consider the interfacial adhesion. In this study, a new numerical approach on the base of peridynamics (PD) was developed to incorporate interfacial interactions as a part of the constitutive model to capture deformation, bonding, and rebound of impacting particles in one unified framework. Two models were proposed to characterize the adhesive contacts, i.e., a long-range Lenard-Johns type potential and a force-stretch relation of the interface directly derived from fracture properties of the bulk material. Using copper as the sample material, the deformation behaviors simulated by the PD-based approach were found to compare well with those from benchmark finite element method simulations. It was further demonstrated that this PD-based approach allows flexibility to realize different deposition scenarios, such as particle-substrate bonding and separation, by modulating adhesion energies. The approach provides a new numerical framework for more realistic cold spray impact simulations.

Peridynamic Simulation of Dynamic Fracture Process of Engineered Cementitious Composites (ECC) with Different Curing Ages.

The mechanical properties of engineered cementitious composites (ECC) are time-dependent due to the cement hydration process. The mechanical behavior of ECC is not only related to the matrix material properties, but also to the fiber/matrix interface properties. In this study, the modeling of fiber and fiber/matrix interactions is accomplished by using a semi-discrete model in the framework of peridynamics (PD), and the time-varying laws of cement matrix and fiber/matrix interface bonding properties with curing age are also considered. The strain-softening behavior of the cement matrix is represented by introducing a correction factor to modify the pairwise force function in PD theory. The fracture damage of ECC plate from 3 to 28 days was numerically simulated by using the improved PD model to visualize the process of damage fracture under dynamic loading. The shorter the hydration time, the lower the corresponding elastic modulus, and the smaller the number of cracks generated. The dynamic fracture process of early-age ECC is analyzed to understand the crack development pattern, which provides reference for guiding structural design and engineering practice.

Peridynamic-based investigation of the cracking behavior of multilayer thermal barrier coatings

Numerical simulations of the cracking behavior of the top layers of multilayer thermal barrier coatings (TBCs) can effectively reveal the failure mechanisms of the TBCs. Current finite element method (FEM)-based simulation means have been applied to solve certain simple cracking problems in TBCs; however, they cannot effectively describe complex cracking problems in TBCs such as coalescence, intersection, and interference among multiple cracks. Peridynamic (PD), a newly developed mechanical theory, has been widely studied to provide analysis for cracking problems in TBCs. In this paper, a numerical model of TBCs is built by the bond-based PD (BB-PD) theory. Complex cracking behaviors, such as spontaneous crack propagation at both interfacial and internal regions, coalescence, and interference among multiple cracks, are simulated under isothermal cooling and gradient cooling conditions. In addition, the effects of interfacial roughness and calcium–magnesium–alumina–silicate (CMAS) inclusions on the cracking behavior are discussed. The results show that the PD model accurately captures complex cracking behaviors observed via scanning electron microscopy (SEM). Given the ability of the model for analyzing discontinuities in TBCs, it can help to further clarify the fracture mechanisms of TBCs.

Improved peridynamics approach for the progressive fracture of marine concrete

Crack initiation and propagation in marine concrete play a significant role in the security and durability of concrete in ocean construction. Peridynamics (PD), which reformulates classical continuum mechanics in terms of spatial integral equations instead of partial differential equations, has been used successfully to match the fracture patterns observed in experiments. However, the classical bond-based peridynamics (BPD) describe brittle fracture instead of quasi-brittle fracture; this includes the failure of quasi-brittle solid marine concrete. Further, the models have significant surface effects, and the effect of the internal length on nonlocal long-range forces is not reflected. The current work proposes an improved BPD approach to overcome the three drawbacks of fracture analyses of marine concrete. A novel kernel function is incorporated, an effective PD surface effect correction method is used, and the BPD bond stiffness at the boundary is modified. Then, the constitutive force function of the BPD is established based on the linear and nonlinear mechanical behaviours of the progressive fracture of ocean concrete materials, and a corresponding failure criterion is given. The validity and accuracy of the proposed method are demonstrated via numerical analyses and experiments. The proposed method can fully capture the nonlinear deformation and progressive fracture of marine concrete.

Peridynamic simulationons of RCF crack growth in laser quenched rail material

Laser quenching (LQ) is a promising technology which could be applied on rails to improve their anti-wear properties. However, severe rolling contact fatigue (RCF) damages tend to occur on the LQ treated rail materials. The peridynamics (PD) simulation is a novel method, which is good at addressing issues on discontinuous materials. Thus, the present study aims at exploring the growth mechanism of RCF cracks in the LQ treated rail material using the PD simulation. Meanwhile, rolling-sliding contact experiments were conducted to verify the simulation results. The results indicated that the RCF crack initiated closely to the front edge of the quenching region. During one wheel/rail contact cycle, the crack growth mode was dominated by the sliding mode when the wheel was close to the crack, and by the opening mode when the wheel was above the crack. The crack growth process in the LQ treated rail could be divided into four stages: crack initiation in the quenching region; crack propagation in depth; branch cracks generation at the bottom of quenching region and crack growth along the boundary between the quenching and substrate regions; crack growth into the substrate or back to the surface. The crack growth rate was increased significantly with the increase in crack length in the quenching region, then decreased gradually in the boundary and substrate regions.

Thermomechanical Coupling Analysis of the Lining Structure of the Tunnel Entrance in Cold Regions Based on Peridynamics

To explore the effect of frost heaving of the tunnel entrance in cold regions, this paper carries out a thermomechanical coupling analysis based on peridynamics (PD), combines PD with finite-element method (FEM) into a numerical model, and verifies the feasibility of the proposed model. On this basis, we selected frost heave amount as the quantitative index, discussed the evolution law of the energy field in the lining structure of the tunnel entrance in cold regions, and analyzed the stress of the lining structure, as well as the expansion and distribution laws of lining cracks, under different frost heave amounts. The results show that: The difference of frost heave amount indirectly brings changes to the system’s energy field. With the growth of frost heave amount, the thermal potential and strain would increase. During the changes, the thermal potential and strain energy of the system are both positively correlated with frost heave amount. The degradability of tunnel lining increases with the frost heave amount of the lining. A high density of cracks can be observed at the foot and waist of the arch, most of which are tensile cracks. With frost heave amount as the main temperature reference, this research explores the degradation state of the tunnel entrance in cold regions, which greatly facilitates the maintenance, repair, and safe operation of tunnels.

Failure modeling of concrete: A peri-dynamical approach with bond-based correspondence to bi-scalar damage model

Concrete is a special quasi-brittle material, in which both the tensile and compressive nonlinearity play an important role, especially when working with steels. To capture the failure behavior of concrete, a peridynamic (PD) approach that shows great advantages in modeling discontinuities and cracks is employed in the present paper. Based on the simplest PD model, a bond-based correspondence framework is established instead of reconstructing the constitutive relations, which provides a general and direct way for classical constitutive models incorporation. To derive the mapping function, the strain energy density equivalence is conducted and further simplified for computational efficiency. Under the correspondence framework, a thermodynamically consistent damage model, namely the bi-scalar plasticity-damage model is incorporated in for concrete failure modeling. Corresponding to the separate consideration of tensile and compressive behavior in the model, the topologic damage is developed accordingly, which combines both the advantages of PD and damage mechanics. The proposed model is then demonstrated by the simulation of experiment, including both the plain concrete and reinforced concrete cases. The results indicate that the proposed model retains the original simplicity but greatly improves the capability for concrete failure modeling, with which different failure modes of concrete can be well reproduced.

An improved bond-based peridynamic model with shear bonds for eliminating rigid body rotation

Peridynamics (PD) is a kind of nonlocal theory based on displacement calculation of material particles around a horizon. The calculation of bond force, which determines the distribution of displacement field, is the key to damage and fracture simulation. Due to introduction of tangential stiffness, the bond-based PD models with shear bonds (PDS models), put forward higher requirements for the calculation of bond force. Because PDS models cannot remove the false shear deformation of bonds caused by rigid body rotation, the calculation of bond force may be inaccurate. To eliminate the influence of rigid body rotation on the calculation of bond force, an improved PDS model is proposed. Based on the principle of minimum energy and the nonlocality of peridynamics, the formula of rigid body rotation is derived. By deducting the influence of rigid body rotation, the improved PDS model ensures the accuracy of bond force calculation. In addition, a new failure criterion, strain-based failure criterion, is developed to improve the accuracy of PD model in calculating fracture energy. The results of deformation and fracture examples with finite rigid body rotation illustrate the necessity of removing the effects of rigid body rotation, and prove that the improved PDS model has high precision in the calculation of elastic displacement and prediction of cracking process. Finally, verification of the developed strain-based failure criterion was tackled with dynamic crack examples.

Coupled peridynamic model for geometrically nonlinear deformation and fracture analysis of slender beam structures

AbstractSlender beam structures can experience large displacements, large rotations and fractures, even if the structures are only subjected to small loads. A coupling model of peridynamics (PD) and classical continuum mechanics (CCM) for beam fracture analysis in geometrically nonlinear deformations is developed in this study. Firstly, the formulations of virtually nonlinear strain energy density of each incremental step are obtained by using the updated Lagrangian (UL) formulation and von Karman beam theory, then the nonlinear PD beam parameters are established on the geometrically nonlinear micro‐beam bonds via the principle of virtual work and homogenization. Secondly, the coupling model of PD and CCM for geometrically nonlinear beams is proposed, for which the morphing method is applied to create a balance between the stiffness of geometrically nonlinear CCM beam model and the weighted coefficients of geometrically nonlinear PD beam model. Thirdly, a new fracture criterion for PD beam models considering the effect of geometrical nonlinearity is adopted. Finally, the large deformation and fracture analysis of straight beam, spiral slender beam and complex frame subjected to different loading conditions illustrate the validity and accuracy of the proposed PD‐CCM coupling model.

A nonlocal interface approach to peridynamics exemplified by continuum‐kinematics‐inspired peridynamics

AbstractIn this contribution, we present a novel approach on how to treat material interfaces in nonlocal models based on peridynamics (PD) and in particular continuum‐kinematics‐inspired peridynamics (CPD), a novel variationally consistent peridynamic formulation. Our method relies on a nonlocal interface where the material subdomains overlap. Within this region, a kinematic coupling of the two constituents is enforced. The contact is purely geometrical as interaction forces act only between points of the same material. We provide a detailed description of the computational implementation within the framework of CPD, that is in principle applicable to all formulations of PD. A variety of numerical examples for modeling bimaterial interfaces illustrate the utility of the technique for both two‐dimensional and three‐dimensional problems, including examples at large deformations. Our model approaches a local model when the nonlocality parameter, the horizon size, is decreased. The proposed methodology offers a viable alternative to previous approaches in PD, which are essentially imposing mixture rules for the interfacial material parameters.

An extended peridynamic model for dynamic fracture of laminated glass considering interfacial debonding

In this work, an extended peridynamic (PD) model considering interfacial debonding is proposed to investigate the dynamic fracture behavior of laminated glass under low-velocity and high-velocity impacting loads. The interaction between different materials is described by adding an interfacial force term into the governing equations, which is derived from the energy density function of the interfacial bonds. A potential function term sourced from the cohesive zone model (CZM) is reconstructed and then introduced into the peridynamic model to describe the cohesive interfaces. The failure criterion of interfacial debonding is determined by the calculation of interface fracture energy and interfacial energy density. Two benchmark examples, a through-cracked tensile test and a drop-weight test, have been conducted to establish the validity of the proposed model. The proposed model and approach are then employed to investigate the dynamic fracture mechanism of laminated glass under high-velocity impacting loads.

Simulation of highly nonlinear materials based on a stabilized non-ordinary state-based peridynamic model

Peridynamics (PD) is an effective method to solve discontinuity problems that involve cracking or crushing behaviors. In the non-ordinary state-based PD (NOSBPD), the so called zero-energy mode may cause inaccuracy particularly when the material is highly nonlinear. This paper proposed a novel stabilized NOSBPD modeling method to mitigate the inaccuracy and instability of NOSBPD solutions. A correction force for a PD point is defined as the difference between an internal force obtained by stress equilibrium equation and that obtained by the force states of the points within its horizon. The correction force is applied on the PD points to be corrected, e.g., that on the boundary of a PD model. Three examples are presented demonstrating the proposed method's effectiveness in static and dynamic analyses of both linear or highly nonlinear models, i.e., 3D cap plasticity concrete model and 2D multi-yield surface soil model. The predicted responses (e.g., displacements, stresses, strains at representative points) are analyzed and compared with those without force correction for both linear and highly nonlinear cases. The proposed method is demonstrated to be an effective method for mitigating the inaccuracy and instability of the NOSBPD solutions.

Eulerian peridynamic modeling of microjetting from a grooved aluminum sample under shock loading

The micro jetting from a grooved aluminum surface under impact loading is investigated by using Eulerian peridynamics (PD). The simulation results are compared with the published experimental data and the spike velocity model, exhibiting qualitative agreement. The governing mechanism accounting for the formation of micro jetting is elucidated from the perspective of the shock wave interaction with the surface groove. The PD simulation results indicate that the incident shock wave induces progressive groove collapse along the direction of shock wave propagation. The rarefaction waves reflected from the groove edges cause the variation of the velocity vector of PD material points, leading to the material points above and below the symmetric axis of the groove converging toward the symmetric axis and colliding with each other. Then, those collided material points are driven by the incident shock wave propagating along the horizontal symmetric axis and eventually ejected from the groove. The effects of the groove dimensions and the impact velocity on the spike velocity and the ejected mass are discussed. The results show that spike velocity decreases with an increasing groove angle but increases with increasing impact velocity. Furthermore, the ejected mass increases with increasing impact velocity. However, when the depth of the surface groove is fixed and the groove angle increases, the ejected mass first increases and then decreases with the turning point at ∼120°. As the depth of the surface groove increases, the ejected mass increases. The simulation results provide a mechanistic understanding of the micro jetting phenomena and instructive guidance for developing better ejecta models.

An adaptive peridynamics material point method for dynamic fracture problem

An adaptive peridynamics material point method (APDMPM) is proposed for modeling dynamic fracture problems to fully take advantage of both the peridynamics (PD) and material point method (MPM). The PD is used to model the crack region of a continuum, while the MPM is used to model the remaining regions of the continuum. A hand-shake region is employed to transfer the interaction between the PD and MPM particles. The simulation region is initially discretized by MPM particles, which will be adaptively converted to PD particles based on their stress condition or connect relation to make the PD sub-region fit the damage area automatically. Several numerical examples, including spallation of Hopkinson bar, plate with a pre-existing crack and plate with a circular cutout under velocity boundary conditions, are studied to verify the proposed method. The numerical results show that the APDMPM can successfully predict the initiation and propagation of cracks without explicitly tracking crack surface, meanwhile improve the calculation efficiency and accuracy of the rest of the region.

Peridynamic Simulation of Cracking Behavior in Thermal Barrier Coatings

Abstract Cracking-induced fracture in thermal barrier coatings (TBCs) is one of the most severe failure mechanisms among TBCs failure cases. Current numerical simulation of cracking behavior in TBCs are mostly developed by FEM-based methods, which have their own disadvantages. The concept of peridynamic (PD) is proposed and developed these years to deal with discontinuous problems, providing new ideas to simulate crack initiation and propagation in TBCs. In this paper, a PD-based numerical model of TBCs is built to discuss cracking behavior in the top coat (TC) layer. Simulation results validate the effectiveness and accuracy of PD in TBCs cracking analysis, compared with SEM observations. And effects of pre-existed cracks in TC, which could obviously interfere original crack propagation path, are also proved and discussed. It could be concluded that PD would be a powerful tool in TBCs crack propagation predictions if provided with more supportive experiment data.