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A technique is proposed for reproducing particle size distributions in three‐dimensional simulations of the crushing and comminution of solid materials. The method is designed to produce realistic distributions over a wide range of loading conditions, especially for small fragments. In contrast to most existing methods, the new model does not explicitly treat the small‐scale process of fracture. Instead, it uses measured fragment distributions from laboratory tests as the basic material property that is incorporated into the algorithm, providing a data‐driven approach. The algorithm is implemented within a nonlocal peridynamic solver, which simulates the underlying continuum mechanics and contact interactions between fragments after they are formed. The technique is illustrated in reproducing fragmentation data from drop weight testing on sandstone samples. [ABSTRACT FROM AUTHOR]

This paper introduces a particle‐based framework for simulating the behavior of elastoplastic materials and the formation of fractures, grounded in Peridynamic theory. Traditional approaches, such as the Finite Element Method (FEM) and Smoothed Particle Hydrodynamics (SPH), to modeling elastic materials have primarily relied on discretization techniques and continuous constitutive model. However, accurately capturing fracture and crack development in elastoplastic materials poses significant challenges for these conventional models. Our approach integrates a Peridynamic‐based elastic model with a density constraint, enhancing stability and realism. We adopt the Von Mises yield criterion and a bond stretch criterion to simulate plastic deformation and fracture formation, respectively. The proposed method stabilizes the elastic model through a density‐based position constraint, while plasticity is modeled using the Von Mises yield criterion within the bond of particle paris. Fracturing and the generation of fine fragments are facilitated by the fracture criterion and the application of complementarity operations to the inter‐particle connections. Our experimental results demonstrate the efficacy of our framework in realistically depicting a wide range of material behaviors, including elasticity, plasticity, and fracturing, across various scenarios. [ABSTRACT FROM AUTHOR]

In engineering applications, the phenomenon of cracking is often accompanied by a coupled multiphysics effect. Peridynamics (PD) is an effective approach for solving cracking problems, but currently, no general PD model accounts for the coupling of multiple physical fields. In this work, we develop a PD model of coupled deformation, heat conduction, species diffusion, and chemical reactions. First, we establish the equations for mass, linear momentum, and energy. Then we establish fully coupled constitutive laws that interpret the interactions between the various fields and formulate evolution equations that govern the flux of species and heat. These laws and equations are developed based on the inequality of energy dissipation and the principles of chemical kinetics. Species diffusion and chemical reactions are treated as separate processes to study their effects on the Helmholtz free energy density of solids and the subsequent formation and propagation of cracks. In addition, certain coupling coefficients are calibrated by equating the corresponding physical quantities in the PD model with those in continuum mechanics. Four specific cases are simulated to validate the model, including redistribution of vacancies in ceramics, hydrogen traps, and embrittlement in metals. • A thermo-chemo-mechanically coupled peridynamics model is developed. • The expansion factor is defined to reveal its effect. • The chemical kinetics in a nonlocal form is derived. • The different effects of species diffusion and chemical reactions on cracks are investigated. [ABSTRACT FROM AUTHOR]

As a type of non-pneumatic wheel, mechanical elastic wheel (MEW) can is resistant to deformation and continue to be used when rubber is damaged by the bullet. In order to prove the deformation resistance ability of MEW, the model of rubber damaged by bullet based on the non-ordinary state-based peridynamic is proposed for the first time. By considering the two conditions with bullet penetrating and staying in rubber respectively, the model is simulated and predicted. The results show that the simulations about the model of rubber damaged by bullet is consistent with experiments, the validity of the model is verified. It explains the physical process of penetrating bullet hole being smaller than the bullet diameter, and explains the reasons for the rubber forming bulge after bullet staying in rubber. The MEW damaged by bullet still has the running ability, the damage wheel does not have obvious secondary damage after running, and MEW has the deformation resistance ability after bullet damage. It has reference significance for the research of rubber tearing problem.

In this work, we present a peridynamic-based simulation method for modeling quasi-static fracture propagation in isotropic and anisotropic rock within the framework of peridynamic least square minimization (PDLSM). The original isotropic elastic PDLSM is further extended to investigate fracture propagation in anisotropic materials in this study. The proposed AN-PDLSM model integrates an anisotropic model in fracture mechanics to analyze the failure process of anisotropic rocks. An important advancement in this research lies in the incorporation of the maximum energy release rate criterion (MERR) into the PDLSM framework for the first time. This enhancement enables accurately determining crack propagation and the associated crack angles. The proposed model utilizes the energy release rate calculated through the J-integral method to assess bond breakage, and it employs a mesh-independent, piecewise linear fracture model to describe crack propagation. The proposed method fully combines the merits of traditional fracture mechanics with the unique capabilities of peridynamics. To demonstrate the effectiveness of the proposed model, a simulation of fracture evolution in isotropic plates subjected to semi-circular bending tests is presented and compared with experimental results. It is shown that the proposed model accurately replicates fracture trajectories in isotropic specimens. In the context of anisotropic rock, the effect of a weak coefficient on crack morphology is discussed in order to obtain a suitable value. Additionally, the impact of bedding angles on fracture paths through our proposed model is also explored, revealing excellent agreement with experimental results. The findings in this research demonstrate that the proposed AN-PDLSM model is exceptionally proficient at capturing the intricate, oscillating crack paths observed in anisotropic rock materials. [ABSTRACT FROM AUTHOR]

The numerical simulation of crevice corrosion of a titanium alloy upon exposure to an aggressive marine environment is presented and discussed. The model parameters were calculated using the IR voltage theory and a one-dimensional calibration peridynamic model. The values of pH inside the crevice, having openings of 0.01, 0.05 and 0.1 mm, were calculated. A crevice corrosion simulation model, for a crevice of 0.01 in width and 4.95 mm in depth, was built, and a full-scale simulation was conducted using the model. Experiments were conducted to verify the simulation results. The chosen test pieces having crevice openings of 0.01, 0.05 and 0.1 mm were soaked in EXCO solution of 65 °C for 5, 10 and 15 days. The test results showed the pH inside the crevice initially decreased with depth and reached a minimum value when the titanium ions were saturated. Thereafter, the value of pH increased with depth. Comparing results of the simulation with experiment, results of corrosion depth within the crevice were in good consistence. Depth of pits as a direct consequence of crevice corrosion had an exponential relationship with distribution of pits. The IR voltage decrease was proven to be an important factor that exerts an influence on depth of corrosion due to crevice corrosion. [ABSTRACT FROM AUTHOR]

The stress of rock-like materials first increases and then decreases with an increase in the strain, and finally become damaged under tensile or compressive loads. It is not suitable to use the traditional bond-based peridynamics model to simulate the crack propagation of rock-like materials. Based on the bond-based peridynamics theory, a constitutive model has here been proposed that can reflect the characteristic of the stress with an increase in strain (i.e., that the stress of the rock-like materials first increases and then decreases, and finally fails). This makes up for the weakness with the traditional bond-based peridynamics theory, which fails to reflect the stress-strain change in rock-like materials. The strain energy density of the proposed constitutive model of rock-like materials has been derived and compared against the classical elasticity theory to obtain the model constants with respect to the elasticity moduli for plane stress conditions. Based on the here proposed constitutive model for rock-like materials, a numerical solution program for rock-like materials has been written using the Fortran language. For different loading conditions, the crack propagation process for an intact specimen has been simulated and compared with experimental results. This was also the situation for a specimen with a pre-existing flaw, a single non-straight flaw, and with three pre-existing flaws for plane stress conditions. The numerical simulation results were in good agreement with the corresponding experimental results. By using this proposed constitutive model, it was possible to simulate and predict the mechanical properties of rock-like materials, and the process of crack initiation, propagation, and coalescence under different loading conditions. The results from the present study can thus provide a reference for practical engineering. [ABSTRACT FROM AUTHOR]

Forecasting water content dynamics in heterogeneous porous media has significant interest in hydrological applications; in particular, the treatment of infiltration when in presence of cracks and fractures can be accomplished resorting to peridynamic theory, which allows a proper modeling of non localities in space. In particular, in this framework, we introduce a suitable influence function able to provide a nonlocal interaction between material particles; moreover, we make use of Chebyshev transform on the diffusive component of the equation and then we integrate forward in time using an explicit method. We prove that the proposed spectral numerical scheme provides a solution converging to the unique solution in some appropriate Sobolev space. We finally exemplify on several different soils, also considering a sink term representing the root water uptake. • We introduce a nonlocal form of Richards' equation using a non-standard influence function. • We compute the solution to the semi-discretized Richards' equation with Dirichlet boundary conditions with spectral methods. • We prove that the solution to the semi-discretize scheme converges, in a suitable Sobolev space, to the exact solution. [ABSTRACT FROM AUTHOR]

Bi2Sr2Ca1Cu2O8+x (Bi-2212) wire is the potential material for the design of the high field superconducting magnet. However, compared with excellent current-carrying capacity, low mechanical strength can restrict the wide application of Bi-2212 wire. The superconducting filaments of Bi-2212 wire is sensitive to strain and is prone to fracture, which can lead to the degradation of critical current. Therefore, it is necessary to study the damage behavior of Bi-2212 round wire under external loads. In this paper, the three-dimensional mechanical damage and degradation of critical current in Bi-2212 composite wire under axial tensile load, radial compression load, bending and torsional loads are systematically investigated using ordinary state-based elastoplastic peridynamic (PD). The axial tensile simulations with the process of damage and thermal residual stress are in agreement with the experiment, and the critical current degradation with tensile strain is qualitatively predicted. The effect of plastic deformation of alloy on damage of filament bundles under radial compression load is explored. Finally, the simulations also reveal the damage characteristics of filament bundles in Bi-2212 round wire under torsional and bending loads. The above results are expected to provide a reference for application of Bi-2212 HTS round wire. [ABSTRACT FROM AUTHOR]

• A compensated critical energy density (CCED) criterion is proposed within peridynamics to optimize mixed-mode fracturing simulation in quasi-brittle materials. • CCED's robustness in modeling mode I, II, and mixed-mode fracturing is validated through benchmark tests. • A 90° approach angle between mechanically induced fractures and pre-existing natural fractures is commonly observed. This study integrates a compensated critical energy density criterion (CCED) into the ordinary state-based peridynamics framework to enable detailed analysis of mode I, mode II, and mixed-mode fracturing. The proposed bond failure criterion builds upon the advantages of the traditional critical energy density (CED) to enable precise calculation of strain energy density. Additionally, the critical bond rotation criterion (CR) is employed to account for shear bonds that the CED might overlook. Using the peridynamic differential operator (PDDO) format in formulating the entire computational framework enhances both accuracy and numerical stability. The model's validation is conducted through benchmark examples, including the mode I double cantilever beam test, the mode II compact shear test, and a mixed-mode mechanical fracturing test in pre-notched specimens with central borehole loading. Convergence studies, comparative analyses with finite element method simulations and theoretical solutions thoroughly examine the proposed model's performance and accuracy. [ABSTRACT FROM AUTHOR]

• A newly developed geometry-constraint-based non-ordinary state-based peridynamic theory is adopted. • The development of new cracks of flawed rock-like materials under compression-dominating stresses is numerically predicted. • The crack propagation mechanism of flawed rock-like materials is revealed based on the dynamic evolution of stress fields. • The tensile and shear failure modes of brittle materials can be reasonably modeled. Comprehending the cracking evolution and failure mechanism of flawed rocks under compression-dominating stresses is essential to evaluating the stability of rock engineering. In this work, a newly developed geometry-constraint-based non-ordinary state-based peridynamic (GC-NOSBPD) theory that can eliminate the numerical oscillation is applied to predict the development of new cracks of flawed rocks under compression-dominating stresses. The failure of bonds between particles is judged by the bond-associated stress-based fracture criteria. The cracking evolution trajectories of semi-disc and disc specimens containing flaws are traced. The effects of flaw inclination angle on the cracking trajectories are analyzed. The cracking evolution paths of rock-like specimens with two flaws under uniaxial and biaxial compression are molded. The effects of confining stress on the growth of new cracks are investigated. The confining stress restrains the propagation of tensile cracks, but it is easy to promote the growth of shear cracks. The concentration and transfer effects of stress can plainly revel the failure mechanism of flawed rocks. The present numerical method is reasonable to predict the tensile and shear failure modes of flawed specimens under compression-dominating stresses. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to provide a peridynamic (PD) model for the prediction of the viscoelastic creep deformation and failure model. The viscoelastic characteristic consists of several stages, namely primary creep, secondary creep, tertiary creep and fracture. A non-linear viscoelastic creep equation based on the internal state variable (ISV) theory covering four creep stages and PD equations are used. The viscoelastic equation is inserted into the PD equation to derive a PD model with two time parameters, i.e., numerical time and viscoelastic real time. The parameters of the viscoelastic equation are analyzed and optimized. A comparison between numerical and experimental data is performed to validate this PD model. The new PD model for nonlinear viscoelastic creep behavior is confirmed by an acceptable similarity between the numerical and experimental creep strain curves with an error of 15.85%. The nonlinearity of the experimental and numerical data is sufficiently similar as the error between the experimental and numerical curves of the secondary stage strain rate against the load is 21.83%. The factors for the errors are discussed and the variation of the constants in the nonlinear viscoelastic model is also investigated. [ABSTRACT FROM AUTHOR]

В настоящей работе доказывается единственность и существование решения задачи Коши для интегро-дифференциального уравнения, связанного с перидинамической моделью механики твёрдого тела с двумя пространственными переменными.

Copyright of Chinese Journal of High Pressure Physics is the property of Chinese Journal of High Pressure Physics Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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. [ABSTRACT FROM AUTHOR]

• Uncovering the inherent limitations of peridynamic model in predicting dynamic crack velocity. • The influence mechanism of size and stiffness of the nonlocal region on crack velocity is elucidated. • Exposing wave speed degradation rules in peridynamic and formulating a prediction formula for limiting crack velocity. • The crack velocity is regulated by the local stiffness and point density. Peridynamic, an innovative solid mechanics method in continuum theory, offers unique advantages for discontinuity modeling such as fracture simulation. This study addressed a puzzling phenomenon observed in peridynamic dynamic fracture modeling, where the predicted normalized limiting crack velocity remained nearly constant across different material parameters input. Delving into the mechanism influencing predicted crack velocity in peridynamic model, we systematically explored the impacts of stiffness distribution of the nonlocal region around the crack tip, through numerical simulations and theoretical analyses. Additionally, the implicit wave velocity degradation in the damage zone of the peridynamic model was uncovered. A prediction formula for the limiting crack velocity was then derived based on these analyses. Furthermore, the wave velocity degradation scheme and the proposed prediction model were validated through numerical instances, involving convergence studies and material density degradation investigation. This work contributes to a further understanding of the peridynamic model and provides new insights for crack velocity prediction in dynamic fracture scenarios. [ABSTRACT FROM AUTHOR]

We study an inverse problem for the fractional wave equation with a potential by the measurement taking on arbitrary subsets of the exterior in the space-time domain. We are interested in the issues of uniqueness and stability estimate in the determination of the potential by the exterior Dirichlet-to-Neumann map. The main tools are the qualitative and quantitative unique continuation properties for the fractional Laplacian. For the stability, we also prove that the log type stability estimate is optimal. The log type estimate shows the striking difference between the inverse problems for the fractional and classical wave equations in the stability issue. The results hold for any spatial dimension n ∈ ℕ. [ABSTRACT FROM AUTHOR]

In this work, we modeled the brittle fracture of shell structure in the framework of Peridynamics Mindlin-Reissener shell theory, in which the shell is described by material points in the mean-plane with its drilling rotation neglected in kinematic assumption. To improve the numerical accuracy, the stress-point method is utilized to eliminate the numerical instability induced by the zero-energy mode and rank-deficiency. The crack surface is represented explicitly by stress points, and a novel general crack criterion is proposed based on that. Instead of the critical stretch used in common peridynamic solid, it is convenient to describe the material failure by using the classic constitutive model in continuum mechanics. In this work, a concise crack simulation algorithm is also provided to describe the crack path and its development, in order to simulate the brittle fracture of the shell structure. Numerical examples are presented to validate and demonstrate our proposed model. Results reveal that our model has good accuracy and capability to represent crack propagation and branch spontaneously. [ABSTRACT FROM AUTHOR]

Copyright of Bulletin of the Chinese Ceramic Society is the property of Bulletin of the Chinese Ceramic Society Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

• A non-local absorbing boundary conditions is constructed in peridynamic theory. • Motion equation of peridynamic theory is re-derived considering material damping. • Algorithm to realize the non-local absorbing boundary conditions in peridynamics is proposed. • Elastic wave propagation in semi-unbounded and unbounded solids are simulated. In order to simulate the elastic wave propagation in unbounded solids, this paper introduces a non-local method to construct absorbing boundary conditions in the bond-based peridynamic theory. To construct non-local absorbing boundary conditions in the form of absorbing layers with increasing damping, we first re-derived the particle motion equilibrium equation of the bond-based peridynamic theory, based on the principle of virtual work and Lagrange's equation on the premise of considering material damping. We also give the expression for the inter-particle damping force density which satisfies the balance laws of linear momentum and angular momentum. This paper also provides a process and algorithm for realizing the non-local absorbing boundary conditions in the bond-based peridynamic theory, and adopts the Fortran language for computer program compilation. Finally, we simulate the elastic wave propagation in semi-unbounded and unbounded solids as numerical examples. The results show that such non-local absorbing boundary conditions can stably absorb and attenuate incident elastic waves. Since it is derived in the time domain, this method does not require frequency-domain operations, such as Fourier and Laplace transformations, nor does it require wave field splitting. [ABSTRACT FROM AUTHOR]

This article presents a new formulation of bond‐based peridynamic theory (PD) encompassing material texture heterogeneity through fractal geometry concepts and transforming all relevant variables from Euclidean space to fractal space. The heterogeneity incorporation is realized through the introduction of a linear transformation fractal coefficient (LTFC). By considering a mean value for all LTFCs of all spatial coordinates. For example, x, y, z, and using the relationship between fractal dimension Df and the Hurst exponent H. We present a fractal version of the bond‐based PD method that the equation of motion is conformed to fractal space. Validation of the formulation is accomplished in two steps: first, the effect of irregular mass distribution is characterized by the fractal dimension of the fracture surface roughness through experimental results of a series of single‐edge notched tensile tests of a ductile material. In the next step, the proposed formulation is calibrated with the fractal dimension obtained experimentally. The results are compared with the classical bond‐based PD formulation and the finite element analysis results. The obtained results in this article indicate that the irregular mass distribution of material can be introduced into particle‐based numerical methods using an adequate fractal exponent. The fractal version provides a good approximation of the fracture behavior of materials. [ABSTRACT FROM AUTHOR]

Partition of unity methods (PUM) are of domain decomposition type and provide the opportunity for multiscale and multiphysics numerical modeling. Here, we apply Peridynamic (PD) enrichment to propagate cracks in the PUM global–local enrichment scheme. We apply linear elasticity globally and PD over local zones where fractures occur. The elastic fields provide appropriate boundary data for local PD simulations on a subdomain containing the crack tip to grow the crack. Once the updated crack path is found the elastic field in the body and surrounding the crack is updated using the PUM basis with an elastic field enrichment near the crack. The subdomain for the PD simulation is chosen to include the current crack tip as well as features that influence crack growth. This paper is part II of this series and validates the combined PD/PUM simulator against the experimental results. The results of numerical simulation show that we attain good agreement between experiment and simulation with a local PD subdomain that is moving with the crack tip and adaptively chosen size. • A novel Multiscale Fracture Model using Peridynamic Enrichment of Finite Elements with an Adaptive Partition of Unity • Validation against three experimental data sets. • In addition to the experiments, we validate our hierarchical coupling technique approach with a concurrent coupling approach proposed by Ni et al. using the same experimental data. [ABSTRACT FROM AUTHOR]

• A novel dynamic damage constitutive model of rock-like materials based on peridynamics is proposed. • The relationship between the micro-modulus constant and elastic modulus has been derived. • Dynamic mechanical properties and energy dissipation of argillaceous sandstone with different internal flaws are obtained. • The dynamic failure process of argillaceous sandstone specimens are captured by numerical simulation. The original bond-based peridynamic model addresses brittle fracture rather than progressive fracture. It also does not account for the impact of strain rate on bond strength and fails to incorporate the impact of internal length on non-local long-range forces. As a result, it is inadequate for simulating the dynamic failure of rock-like materials under impact loading. To address these limitations, a new approach involves a sextic polynomial attenuation function. This function captures the impact of internal length on non-local long-range forces and leads to the derivation of a corresponding micro-modulus expression. A damage function and a new failure criterion are integrated to describe the nonlinear mechanical behavior and progressive failure of rock-like materials. The influence of strain rate on bond dynamic strength is considered to reflect the strain rate effect in rock materials. The outcome is a newly proposed dynamic damage constitutive model that overcomes the three shortcomings of the original bond-based peridynamic model when simulating the dynamic failure of rock-like materials. Numerical examples are simulated based on this model, and their results are compared with the experimental data. This comparison allows further exploration of the volumetric fracturing behavior and mechanical properties of rock specimens with internal flaws in three dimensions when subjected to impact loading. The findings demonstrate the effectiveness of the proposed model in accurately simulating crack propagation and mechanical properties across varying strain rates in rock-like materials. Notably, the internal flaw's depth significantly influences the specimen's mechanical properties and energy utilization efficiency at a specific flaw angle α = 90 °. Complex three-dimensional cracks, consisting of shell-like, wing, anti-wing, and shear cracks, emerge due to the interconnection of various crack types. The shape of these cracks is intricately linked to the flaw angle and depth. Ultimately, this model solves the challenge of capturing internal crack growth during dynamic impact processes that are often difficult to observe in experimental tests. [ABSTRACT FROM AUTHOR]

• Innovative Peridynamics (PD) framework to model laminated structures. • Two types of material points are utilized to simulate composite laminates. • Complex damage guidance techniques can be avoided in this new algorithm procedure. • The flaw of the conventional PD model in characterizing fiber direction is overcome. The study presents an improved peridynamic (PD) model for predicting the failure mode of composite laminates without any limitation to fiber orientation. In order to describe the directional dependency of composite laminae, the structural rotation angle is introduced into the PD framework to overcome the flaw that the fiber orientation is a specific value in conventional PD models. In improved PD model (IPM), two types of material points are used to model laminated structures, and a new force function mapping relationship is derived to achieve stable load transfer between in-plane and interlayer material points. As a result, the discrete grid of in-plane material points do not have to coincide with interlayer material points, and the technical difficulties in modeling multilayer laminates with general layups can be addressed. Since the IPM matches the microscopic configuration of practical composite structures, these damage characteristics, such as the damage path, crack initiation point, etc., correlate well with the experimental results. The numerical accuracy of the developed PD model are verified by simulating a series of examples of composite laminae with different fiber orientations, and the damage example further demonstrates the strong capability of the IPM in capturing failure modes of laminates with general layup. [ABSTRACT FROM AUTHOR]

Numerical simulations of rail wear during sliding contact pose significant challenges owing to the complex coupling between thermomechanical contact loads, material properties, and profile changes. This study proposes a modeling approach for rail wear during sliding contact, using nonlocal peridynamic (PD) thermomechanics and a bond damage criterion based on ratchet failure. To facilitate test verification, a two-dimensional PD model for twin-disc testing with elastoplastic materials was developed, and numerical simulations and corresponding twin-disc testing were performed during wheel idling under different loads, idling speeds, and idling times. The PD model accurately predicted rail wear under all operating conditions, exhibiting excellent agreement with the test results, and thus validating the proposed method and supporting the ratchet failure mechanism. Subsequently, thermomechanical modeling of sliding contacts with different creepages was performed. The PD model predicted continuous wear along the contact surface, with an increase in wear depth corresponding to higher creepage values. As the contact temperature increased with creepage, thermal stress and thermal softening caused slight and sharp increases in rail plastic strain, respectively. Therefore, thermal softening is the main factor responsible for the significant increase in wear rate with temperature. Finally, wear results of the PD model and classical Archard's wear model were compared. The PD models can capture variations in wear rates that are difficult to address using the Archard model. • A modeling approach for rail wear during sliding contacts using PD thermomechanics was proposed. • A 2D PD model for twin-disc testing with elastoplastic materials was developed. • Twin-disc testing was conducted to validate the PD model. • The performance of the PD model and classical Archard's wear model were compared. [ABSTRACT FROM AUTHOR]

The oxidation induced by coating cracking is a general failure mode of high-temperature composites such as C/C and C/SiC. However, this failure mode has not been fully investigated due to the lack of a method suitable for both crack simulation and oxidation interface capture. In this paper, a coupled thermo-mechanical-oxygenic peridynamic model is proposed for SiC-coated C/C composites in an oxidizing environment. The ordinary state-based peridynamics is extended to plane strain thermoelastic problems for orthotropic media to calculate the crack distribution. Cracks in the coating are modeled as oxygen diffusion channels and the peridynamic oxidation equation is developed to simulate the oxidation of the C/C substrate. Furthermore, the peridynamic non-Fourier heat transfer equation is employed to consider the finite thermal propagation speed and the model is validated by experimental results. Numerical examples are presented to investigate the oxidation failure after thermal shock, non-Fourier thermal shock fracture, and stress oxidation failure of SiC-coated C/C composites. [ABSTRACT FROM AUTHOR]

• Fracture failure simulation of single-phase and composite materials. • Dissipated energy: material degradation and frictional sliding along crack surfaces. • Critical stretch depending on the conditions characterising adjacent bonds. • Mixed-Mode failure analysis of experimental tests available in the literature. • Numerical simulation of global behaviour and crack pattern. A Peridynamic (PD) model is proposed for the fracture failure simulation of single-phase and composite materials with a quasi-brittle behaviour under Mixed-Mode loading. More precisely, the novelty of the proposed model consists in taking into account the dissipated energy related to both the damage produced by material degradation and the damage produced by frictional sliding along rough crack surfaces. More precisely, the frictional sliding is taken into account within the model by a novel bond force-stretch relationship, where the rupture stretch related to a generic bond under tension is made depend on the level of compression of the adjacent bonds. Such a PD model is employed to simulate some experimental tests available in the literature. [ABSTRACT FROM AUTHOR]

• We developed a peridynamic model based on generalized thermoelastic theory. • The TSIFs and crack propagation under non-Fourier thermal shock are studied. • The generalized thermoelastic response of oblique crack is investigated. • The effect of thermal relaxation time on crack propagation is analyzed. In this paper, a peridynamic model based on generalized thermoelastic theory is derived by irreversible thermodynamics. This model avoids the spatial derivative and can be easily applied to generalized thermoelastic problems with discontinuities. The transient temperature response is captured using the non-Fourier CattaneoVernotte (C-V) model. The interaction integral is employed to calculate the transient thermal stress intensity factors (TSIFs). Numerical examples are presented for analyzing the effects of crack orientation angle and multi-crack distribution on transient thermoelastic response. And the crack propagation behavior under non-Fourier thermal shock is further discussed in detail. It is found that with the increase of the angle between inner crack and heating boundary, the sensitivity of mode-I TSIFs to the non-Fourier effect increases, while the sensitivity of mode-II TSIFs to the non-Fourier effect decreases. This peridynamic model may be useful for understanding the crack behaviors of thermal protection materials under thermal shock. [ABSTRACT FROM AUTHOR]

• Fracture of brittle glass under quasi-static and dynamic flexure loads is modeled by peridynamic. • A novel peridynamic model incorporating the rate-dependency of glass is proposed. • The inhomogeneity of glass is established by modifying the critical strength based on Weibull distribution. • The accuracy of the improved peridynamic predictions is verified by describing the peak strength and failure behavior of glass. This study presents a novel rate-dependent bond-based peridynamic model for predicting the mechanical behavior of brittle aluminosilicate glass under quasi-static and dynamic flexure loading. To achieve this, the damage criterion is modified with reference to the concept of strain rate in the classical continuum mechanics (CCM). Additionally, a peridynamic (PD) model with inhomogeneous critical stretch based on the Weibull distribution is proposed to account for the randomly distributed defects in glass and investigate their effect on crack initiation and propagation. The accuracy and rationality of the improved PD model are verified by comparing the calculated strength and fracture modes with the experimental results under quasi-static Ball-On-Ring (BOR) and dynamic low-velocity impact tests. The results show that the rate effect increases the damage threshold of glass, enhancing strength and damage ratio. Notably, flexural failures induced by tensile stress are observed under both static and dynamic loading. The rate-dependent inhomogeneous PD model indicates that glass inhomogeneity reduces strength while increasing crack propagation velocity (CPV). The introduction of pre-existing defects alters the symmetrical crack propagation pattern typically observed in homogeneous materials, resulting in a more randomized crack propagation path. Overall, the results can provide a promising approach for predicting the mechanical behavior of brittle materials. [ABSTRACT FROM AUTHOR]

This study proposes a novel method for predicting the microcrack propagation in composites based on coupling the local and non-local micromechanics. The special feature of this method is that it can take full advantages of both the continuum micromechanics as a local model and peridynamic micromechanics as a non-local model to achieve composite fracture simulation with a higher level of accuracy and efficiency. Based on the energy equivalence, we first establish the equivalent continuum micromechanics model with equivalent stiffness operators through peridynamic micromechanics model. These two models are then coupled into a closed equation system, and a transition region is introduced to achieve a smooth transition between them. A composite strength-induced adaptive algorithm is introduced to solve the unified model. Numerical examples for particle reinforced composites are considered to show the accuracy and performance of the present method. The micromechanics-based coupling method has the potential to efficiently simulate the microcrack propagation in various complex composite materials. [ABSTRACT FROM AUTHOR]

This study presents a peridynamic model to predict void formation and growth in metal lines due to electromigration. The nonlocal form of the nonlinear governing equations and boundary conditions for electromigration are derived by using the peridynamic differential operator (PDDO). The equation of motion includes the effect of diffusion strain due to electromigration. Coupled governing equations of atomic concentration and deformation are solved in the Ansys framework with native elements through implicit algorithms. The numerical results show that the current approach can accurately predict the distribution of the deformation, atomic concentration, and hydrostatic stress. Also, the void growth predictions agree well with the experimental predictions. • Void formation and growth in metal lines due to electromigration. • Peridynamic form of fully coupled governing equations for atomic concentration and deformation. • Peridynamic interactions and simulations in Ansys framework. • Verification based on published experimental measurements and simulations. [ABSTRACT FROM AUTHOR]

Peridynamic is a promising nonlocal continuum theory that reconstructs the equations of motion of solid mechanics using spatial integral equations, rendering it suitable for describing objects with discontinuities such as cracks. In this study, a novel extended ordinary state-based peridynamic model was developed for nonlinear deformation and fracture analysis, which established a general relationship with continuum-based parameters and permitted the selection of different influence functions. Based on the principle of virtual displacement, the complete derivations of the peridynamic parameters were presented for two and three-dimensional conditions. After that, the specific numerical scheme and algorithm implementation were summarized. The capability and accuracy of the proposed nonlinear model were verified by comparing with the experimental and finite element simulation results. Finally, several other numerical examples were provided to further demonstrate the applicability and robustness of the proposed model and its implementation. [ABSTRACT FROM AUTHOR]

Partition of unity methods are of domain decomposition type and provide the opportunity for multiscale and multiphysics numerical modeling. Different physical models can exist within a partition of unity method scheme for handling problems with zones of linear elasticity and zones where fractures occur. Here, the peridynamic model is used in regions of fracture and smooth partition of unity methods is used in the surrounding linear elastic media. Our method is novel in that we evolve the crack path using peridynamics and apply the partition of unity method to compute the elastic fields in the neighborhood of the crack tip. Earlier work uses the peridynamic fields, e.g displacement, at the crack tip to approximate enrichment functions for the partition of unity methods. The method is a so-called global–local enrichment strategy. The elastic fields of the undamaged media provide appropriate boundary data for the localized peridynamic simulations. The geometry of the crack path in the damaged media is transferred to partition of unity method. Here, Heaviside and Westergaard functions are used to model the crack. We do not transfer information of the peridynamic fields to the partition of unity method, solely the crack geometry. The first steps for a combined peridynamic and partition of unity method simulator are presented. We show that the local peridynamic approximation can be utilized to enrich the global partition of unity method approximation to capture the true material response with high accuracy efficiently. Test problems are provided demonstrating the validity and potential of this numerical approach. • Novel global–local scheme using peridynamics within a partition of unity method • Reduce peridynamic cost while maintaining peridynamic resolution in global response. • Natural peridynamic crack growth in computationally cheap continuum mechanics model. • Foundation for an automatic, combined PD/PUM simulator. [ABSTRACT FROM AUTHOR]

An improved stabilized peridynamic correspondence material model (IS-PD-CMM) is proposed in this paper to simulate the crack propagation of nearly incompressible hyperelastic materials. A shape-associated micromodulus as the correction coefficient (penalty factor) is introduced into the modified force state in the IS-PD-CMM to control the deformation caused by nonuniform deformation vector state. Different from the conventional stabilization method, the penalty factor in the IS-PD-CMM is only related to the material properties and does not require the parameter calibration. In addition, an equivalent strain function is introduced into the IS-PD-CMM as the failure criterion for the nearly incompressible hyperelastic material, where the nonlocal damage of the model is determined by calculating the ratio of bond breakages of material particles. The high accuracy and adaptability of the IS-PD-CMM are demonstrated by three representative examples including the infinitesimal deformation of linear elastic materials and the finite deformation of hyperelastic materials. Finally, the in-plane tensile fracture behavior and the out-of-plane tearing fracture behavior are simulated and analyzed to illustrate the good performance of the IS-PD-CMM in predicting the crack propagation of nearly incompressible hyperelastic materials. • An IS-PD-CMM is proposed to predict the fracture of nearly incompressible hyperelastic materials. • A new modified force state is derived to eliminate the zero-energy mode oscillation. • An equivalent strain criterion is introduced to reasonably characterize the failure behavior. • Numerical examples demonstrate the high accuracy and adaptability of the IS-PD-CMM. [ABSTRACT FROM AUTHOR]

• A smeared fatigue-induced damage model for ductile materials without needing to know the location and length of the crack. • An approach to correlate the strain energy calculated away from the crack tip to the propagation rate predicted by Paris Law. • Prediction of mixed-mode damage within peridynamic and energy-based framework without knowing a priori the mixity mode ratio. • Improvements in the peridynamic elastoplastic theory aiming higher accuracy and computational time reduction. In recent years a considerable effort has been dedicated to the development of analysis tools that enable the design of damage tolerant structures, particularly in aerospace applications where weight reduction is a crucial requirement. One of these tools developed in recent years is the peridynamic theory, employed to solve numerically complex elastodynamics problems. One of its advantages reported in the literature is the natural ability to simulate the initiation and crack growth without the need for additional numerical procedures commonly employed in other numerical approaches, like in the conventional finite element formulation. Within this context, this paper presents a novel elastoplastic fatigue-induced damage model whose formulation is based on a strain energy framework combined with a smeared crack approach to simulate the damage process without the need of knowing the location of the crack tip and its length within the domain. The proposed model also can predict the mixed-mode damage propagation in ductile materials without knowing a priori the mixity mode ratio. This approach incorporates an analytical methodology based on the material properties that correlate the strain energy calculated away from the crack tip to the expected propagation rate predicted by the Paris Law. The accuracy of the proposed model is verified by comparing the results obtained using an in-house peridynamic FORTRAN code with the experimental results available in the open literature. Some improvements for the peridynamic material parameters are also presented in this paper, which is also verified by using the in-house code. [ABSTRACT FROM AUTHOR]