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In this work, starting from an approach previously proposed by the Authors, we put forward an extension to the large deformation regime of the dimensionally-reduced formulation for peridynamic thin plates, including both hyperelasticity and fracture. In particular, the model, validated against numerical simulations, addresses the problem of the peeling in nonlocal thin films, which when attached to a soft substrate highlights how nonlocality of the peeled-off layer might greatly influence the whole structural response and induce some unforeseen mechanical behaviours that could be useful for engineering applications. Through a key benchmark example, we in fact demonstrate that de-localization of damage and less destructive failure modes take place, these effects suggesting the possibility of ad hoc conceiving specific networks of nonlocal interactions between material particles, corresponding to lattice-equivalent structure of the nonlocal model treated, of interest in designing new material systems and interfaces with enhanced toughness and adhesive properties.

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Material anisotropy caused by crystal orientation is an essential factor affecting the mechanical and fracture properties of crystal materials. This paper proposes an improved ordinary state-based peridynamic (OSB-PD) model to study the effect of arbitrary crystal orientation on the granular fracture in cubic crystals. Based on the periodicity of the equivalent elastic modulus of a cubic crystal, a periodic function regarding the crystal orientation is introduced into peridynamic material parameters, and a complete derivation process and expressions of correction factors are given. In addition, the derived parameters do not require additional coordinate transformation, simplifying the simulation process. Through convergence analysis, a regulating strategy to obtain the converged and accurate results of crack propagation paths is proposed. The effects of crystal orientations on crack initiation and propagation paths of single-crystal materials with different notch shapes (square, equilateral triangle, semi-circle) and sizes were studied. The results show that variations in crystal orientation can change the bifurcation, the number, and the propagation path direction of cracks. Under biaxial tensile loading, single crystals with semi-circular notches have the slowest crack initiation time and average propagation speed in most cases and are more resistant to fracture. Finally, the effects of grain anisotropy on dynamic fractures in polycrystalline materials under different grain boundary coefficients were studied. The decrease in grain anisotropy degree can reduce the microcracks in intergranular fracture and the crack propagation speed in transgranular fracture, respectively.

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In this work, we have developed a novel bond-associated non-ordinary state-based peridynamic (BA-NOSB PD) model for the numerical modeling and prediction of the impact response and fracture damage of quasi-brittle materials. First, the improved Johnson-Holmquist (JH2) constitutive relationship is implemented in the framework of BA-NOSB PD theory to describe the nonlinear material response, which also helps to eliminate the zero-energy mode. Afterwards, the volumetric strain in the equation of state is redefined by the introduction of the bond-associated deformation gradient, which can effectively improve the stability and accuracy of the material model. Then, a new general bond-breaking criterion is proposed in the BA-NOSB PD model, which is capable of covering various failure modes of quasi-brittle materials, including the tensile-shear failure that is not commonly considered in the literature. Subsequently, a practical bond-breaking strategy and its computational implementation are presented and discussed by means of energy convergence. Finally, the proposed model is verified by two benchmark numerical examples and demonstrated by the numerical simulation of edge-on impact and normal impact experiments on ceramics. The comparison between our results and references shows good capability and stability for impact problems of quasi-brittle materials. Numerical oscillations and unphysical deformation modes are effectively eliminated, showing strong robustness and bright prospects for relevant applications.

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In this paper, we propose a modeling method based on peridynamics for ductile fracture at high temperatures. We use a thermoelastic coupling model combining peridynamics and classical continuum mechanics to limit peridynamics calculations to the failure region of a given structure, thereby reducing computational costs. Additionally, we develop a plastic constitutive model of peridynamic bonds to capture the process of ductile fracture in the structure. Furthermore, we introduce an iterative algorithm for ductile-fracture calculations. We present several numerical examples illustrating the performance of our approach. More specifically, we simulated the fracture processes of a superalloy structure in 800 ℃ and 900 ℃ environments and compared the results with experimental data. Our comparisons show that the crack modes captured by the proposed model are similar to the experimental observations, verfying the validity of the proposed model.

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Due to the elastic nonlinearity of the material, high-amplitude surface acoustic waves undergo nonlinear evolution during propagation and may lead to material failure. To enable the acoustical quantification of material nonlinearity and strength, a comprehensive understanding of this nonlinear evolution is necessary. This paper presents a novel ordinary state-based nonlinear peridynamic model for the analysis of the nonlinear propagation of surface acoustic waves and brittle fracture in anisotropic elastic media. The relationship between seven peridynamic constants and second- and third-order elastic constants is established. The capability of the developed peridynamic model has been demonstrated by predicting surface strain profiles of surface acoustic waves after propagating in the silicon (111) plane and the 〈112¯ã€‰ direction. On this basis, the nonlinear wave-induced spatially localized dynamic fracture is also studied. The numerical results reproduce the main features of nonlinear surface acoustic waves and fracture observed in experiments.

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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.

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How to prescribe traction on boundary surface is still an open question in peridynamics. This problem is investigated in this paper. Through introducing the induced body force defined by boundary traction, the Silling's peridynamic motion equation is extended to a new formulation called the traction-associated peridynamic motion equation, which is verified to be compatible with the conservation laws of linear momentum and angular momentum. The energy conservation equation derived from the traction-associated peridynamic motion equation has the same form as that in the original peridynamics advanced by Silling. Therefore, the constitutive models of the original peridynamics can be directly applied to the traction-associated peridynamic motion equation. Some benchmark examples in the plane stress problems are calculated. The numerical solutions agree well with the classical elasticity solutions, and the volume correction and the surface correction are no longer needed in the numerical algorithm. These results show that the traction-associated peridynamic motion equation not only retains all advantages of the original peridynamics, but also can conveniently deal with the complex traction boundary conditions.

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Two nanomicas of similar composition, containing muscovite and quartz, but with different particle size distributions, have been used to prepare transparent epoxy nanocomposites. Their homogeneous dispersion, due to the nano-size, was achieved even without being organically modified, and no aggregation of the nanoparticles was observed, thus maximizing the specific interface between matrix and nanofiller. No exfoliation or intercalation has been observed by XRD, despite the significant dispersion of the filler in the matrix which produced nanocomposites with a loss in transparency in the visible domain of less than 10% in the presence of 1% wt and 3% wt of mica fillers. The presence of micas does not affect the thermal behavior of the nanocomposites, which remains similar to that of the neat epoxy resin. The mechanical characterization of the epoxy resin composites revealed an increased Young's modulus, whereas tensile strength was reduced. A peridynamics-based representative volume element approach has been implemented to estimate the effective Young's modulus of the nanomodified materials. The results obtained through this homogenization procedure have been used as input for the analysis of the nanocomposite fracture toughness, which has been carried out by a classical continuum mechanics-peridynamics coupling approach. Comparison with the experimental data confirms the capability of the peridynamics-based strategies to properly model the effective Young's modulus and fracture toughness of epoxy-resin nanocomposites. Finally, the new mica-based composites exhibit high values of volume resistivity, thus being excellent candidates as insulating materials.

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In this study, a series of three-point bending tests were carried out with notched beam structures made of polyvinyl alcohol (PVA) fiber-reinforced ultra-high-performance concrete (UHPC) to study the effect of volume fractions of PVA fibers on the fracture characteristics of the UHPC-PVAs. Furthermore, in order to meet the increasing demand for time- and cost-saving design methods related to research and design experimentation for the UHPC structures, a relevant hybrid finite element and extended bond-based peridynamic numerical modeling approach is proposed to numerically analyze the fracture behaviors of the UHPC-PVA structures in 3D. In the proposed method, the random distribution of the fibers is considered according to their corresponding volume fractions. The predicted peak values of the applied force agree well with the experimental results, which validates the effectiveness and accuracy of the present method. Both the experimental and numerical results indicate that, increasing the PVA fiber volume fraction, the strength of the produced UHPC-PVAs will increase approximately linearly.

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Plate-like structures can be characterized by a variety of abrupt geometric changes affecting the Lamb wave propagation, similarly to damage occurring in service. Therefore, a deep knowledge of phenomena involved in the interaction between guide waves and discontinuities is required. For this purpose, an experimental investigation is carried out considering an isotropic plate where an abrupt thickness change is present. The fundamental modes excitation is operated by a piezoelectric transducer while the signal sensing in multiple locations, also across the discontinuity, is performed by a scanning laser Doppler vibrometer. The investigation reveals mode conversion and highlights how the effects on the wave propagation depend upon the discontinuity geometrical characteristics. A peridynamics-based model representing the examined problem is also defined and its effectiveness to simulate the observed phenomena is proven.

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In this article, a numerical tool is proposed in the framework of bond-based peridynamics to simulate fatigue crack propagation in composite materials and structures. The cycle-dependent damage-cumulative model derived from Peerlings' law and applied to a bilinear constitutive law is used to evaluate the fatigue degradation of the bond stiffness. Several benchmark cases are studied to validate the proposed approach. Finally, static and fatigue crack propagations in composite systems with single or multi-inclusions are simulated to illustrate the capabilities and characteristics of the developed approach. This article is part of the theme issue 'Ageing and durability of composite materials'.

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Silicon carbide foam is a material that can be used as reinforcement of interpenetrated composites. This paper presents an analysis of such a foam subjected to low and fast compression. The analysis is performed using the peridynamics (PD) method. This approach allows for an evaluation of failure modes and such effects of microcracks nucleation, their growth, and, finally, fragmentation. Furthermore, the material appears to behave qualitatively and quantitatively differently while subjected to low- and high-speed steel piston movement. Under slow compression case, damage appears in the entire specimen, but the shape of the structure is not changing significantly, whereas during the fast compression the sample is dynamically fragmented.

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The mechanical properties of quasi-brittle materials, which are widely used in engineering applications, are often affected by the thermal condition of their service environment. Moreover, the materials appear brittle when subjected to tensile loading and show plastic characteristics under high pressure. These two phenomena manifest under different circumstances as completely different mechanical behaviors in the material. To accurately describe the mechanical response, the material behavior, and the failure mechanism of quasi-brittle materials with the thermo-mechanical coupling effect, the influence of the thermal condition is considered in calculating bond forces in the stretching and compression stages, based on a new bond-based Peridynamic (BB-PD) model. In this study, a novel bond-based Peridynamic, fully coupled, thermo-mechanical model is proposed for quasi-brittle materials, with a heat conduction component to account for the effect of the thermo-mechanical coupling. Numerical simulations are carried out to demonstrate the validity and capability of the proposed model. The results reveal that agreement could be found between our model and the experimental data, which show good reliability and promise in the proposed approach.

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The conventional bond-based peridynamics (BB-PD) model is suitable for simulating the failure mode of homogeneous elastic-brittle materials. However, the strain hardening and subsequent strain softening characteristics of rocks under loading cannot be reflected. In addition, the fracture mechanisms of rock materials under tension and compression are completely different. To solve these problems, this paper proposes an improved BB-PD model using different fracture criteria in the tensile and compression stages of the bond based on previous improved models, and a critical failure condition obeying the Weibull distribution is introduced to reflect the heterogeneity of the rock. The crack propagation processes of an intact rock specimen, rock specimen with a single pre-existing flaw and rock specimens with two and three pre-existing flaws under compressive loading are simulated using the model, and its feasibility is verified by comparing with the results of previous laboratory tests. Next, the effects of the inclination angle and length on the wing crack propagation length are studied. Finally, the changes in the crack aggregation modes under different rock bridge inclination angles are simulated. Eight types of crack aggregation modes are found, and the conditions under which they may occur are analysed. The improved model proposed can effectively simulate the crack propagation and coalescing processes and has a wide application prospect for rock fracture simulations.

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This work investigates quasi-static crack propagation in specimens made of brittle materials by combining local and non-local elasticity models. The portion of the domain where the failure initiates and then propagates is modeled via three-dimensional bond-based peridynamics (PD). On the other hand, the remaining regions of the structure are analyzed with high order one-dimensional finite elements based on the Carrera unified formulation (CUF). The coupling between the two zones is realized by using Lagrange multipliers. Static solutions of different fracture problems are provided by a sequential linear analysis. The proposed approach is demonstrated to combine the advantages of the CUF-based classical continuum mechanics models and PD by providing, in an efficient manner, both the failure load and the shape of the crack pattern, even for three-dimensional problems.

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Crack initiation and propagation is a long-standing difficulty in solid mechanics, especially for elastic brittle materials. A new type of transparent sandwich structure, with a magnesium-aluminum spinel ceramic glass as the outer structure, was proposed in this paper. Its dynamic response was studied by high-speed impact experiments and numerical simulations of peridynamics under impact loads, simultaneously. In the experiments, a light gas cannon was used to load the projectile to 180 m/s, and the front impacted the transparent sandwich structure. In the numerical simulations, the discontinuous Galerkin peridynamics method was adopted to investigate the dynamic response of the transparent sandwich structure. We found that both the impact experiments and the numerical simulations could reproduce the crack propagation process of the transparent sandwich structure. The radial cracks and circumferential cracks of the ceramic glass layer and the inorganic glass layer were easy to capture. Compared with the experiments, the numerical simulations could easily observe the damage failure of every layer and the splashing of specific fragments of the transparent sandwich structure. The ceramic glass layer and the inorganic glass layer absorbed the most energy in the impact process, which is an important manifestation of the impact resistance of the transparent sandwich structure.

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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.

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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.

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Bone remodelling is a complex biomechanical process, which has been studied widely based on the restrictions of local continuum theory. To provide a nonlocal bone remodelling framework, we propose, for the first time, a peridynamic formulation on the macroscale. We illustrate our implementation with a common benchmark test as well as two load cases of the proximal femur. On the one hand, results of our peridynamic model with diminishing nonlocality measure converge to the results of a local finite element model. On the other hand, increasing the neighbourhood size shows to what extent the additional degree of freedom, the nonlocality, can influence the density evolution.

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Due to the complexity of the composite structure, analyzing the material failure process of carbon fiber reinforced polymers (CFRP) is fairly difficult, particularly for the machining process. Peridynamic theory, a new branch of solid mechanics, is a useful tool for dealing with discontinuities. This study presents an ordinary state-based peridynamic (OSB-PD) model for unidirectional CFRP material in the cutting process. In this model, angle tolerance is used to overcome the fiber angle limitation in a classical OSB-PD laminate method, and the short-range force approach is utilized to simulate the contact of the cutting tool and workpiece. The effectiveness of the supplied models is validated by tension and cutting tests. Finally, it can be indicated that the OSB-PD model is capable of predicting machined surface damage and cutting force, based on the comparison of simulation and experimental data.