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The scaling-dependent behaviors of rocks are significant to the stability and safe operation of the structures built in or on rock masses for practical engineering. Currently, many size effect models are employed to connect laboratory measurements at small scales and engineering applications at large scales. However, limited works consider the strain rate effect. In this study, an fractal-statistical scaling model incorporating strain rate is proposed based on a weakest-link approach, fractal theory and dynamic fracture mechanics. The proposed scaling model consists of 8 model parameters with physical meaning, i.e. rate-dependent parameter, intrinsic material parameter, dynamic strain rate, quasi-static strain rate, quasi-static fracture toughness, micro-crack size, micro-crack intensity and fractal dimension, enabling the proposed scaling model to model the scaling behaviors under different external conditions. Theoretical predictions are consistent with experimental data on red sandstone, proving the reliability and effectiveness of the proposed scaling model. Thus, the scaling behaviors of rocks under dynamic loading conditions can be captured by the proposed fractal-statistical scaling model. The sensitivity analysis indicates that the nominal strength difference becomes more obvious with a higher strain rate, larger fractal dimension, smaller micro-crack size or lower micro-crack intensity. Therefore, the proposed scaling model has the potential to capture the scaling behaviors considering the thermal effect, weathering effect, anisotropic characteristic etc., as the proposed scaling model incorporated model parameters with physical meaning. The findings of this study are of fundamental importance to understand the scaling behaviors of rock under dynamic loading condition, and thus would facilitate the appropriate design of rock engineering.

This work presents concepts and algorithms for the simulation of dynamic fractures with a Lattice Boltzmann method (LBM) for linear elastic solids. This LBM has been presented previously and solves the wave equation, which is interpreted as the governing equation for antiplane shear deformation. Besides the steady growth of a crack at a prescribed crack velocity, a fracture criterion based on stress intensity factors has been implemented. This is the first time that crack propagation with a mechanically relevant criterion is regarded in the context of LBMs. Numerical results are examined to validate the proposed method. The concepts of crack propagation introduced here are not limited to mode III cracks or the simplified deformation assumption of antiplane shear. By introducing a rather simple processing step into the existing LBM at the level of individual lattice sites, the overall performance of the LBM is maintained. Our findings underline the validity of the LBM as a numerical tool to simulate solids in general as well as dynamic fractures in particular. [ABSTRACT FROM AUTHOR]

In this paper, we prove the existence of solutions for a class of viscoelastic dynamic systems on time-dependent cracking domains. [ABSTRACT FROM AUTHOR]

We prove an existence result for the fractional Kelvin–Voigt's model involving Caputo's derivative on time-dependent cracked domains. We first show the existence of a solution to a regularized version of this problem. Then, we use a compactness argument to derive that the fractional Kelvin–Voigt's model admits a solution which satisfies an energy-dissipation inequality. Finally, we prove that when the crack is not moving, the solution is unique. [ABSTRACT FROM AUTHOR]

In this paper, we formulate and study the system of elastodynamics on domains with arbitrary growing cracks. This includes homogeneous Neumann conditions on the crack sets and mixed general Dirichlet–Neumann conditions on the boundary. The only assumptions on the crack sets are to be (n - 1) -rectifiable with finite surface measure, and increasing in the sense of set inclusions. In particular, they might be dense; hence, the weak formulation must fall outside the usual context of Sobolev spaces and Korn's inequality. We prove existence of a solution for both the damped and undamped systems, while in the damped case we are also able to prove uniqueness and an energy balance. [ABSTRACT FROM AUTHOR]

In this paper, we prove the existence of solutions for a class of viscoelastic dynamic systems on time-dependent cracked domains, with possibly degenerate viscosity coefficients. Under stronger regularity assumptions, we also show a uniqueness result. Finally, we exhibit an example where the energy-dissipation balance is not satisfied, showing there is an additional dissipation due to the crack growth. [ABSTRACT FROM AUTHOR]

We propose a phase–field model of dynamic fracture based on the Ambrosio–Tortorelli's approximation, which takes into account dissipative effects due to the speed of the crack tips. By adapting the time discretization scheme contained in Larsen et al. (Math Models Methods Appl Sci 20:1021–1048, 2010), we show the existence of a dynamic crack evolution satisfying an energy–dissipation balance, according to Griffith's criterion. Finally, we analyze the dynamic phase–field model of Bourdin et al. (Int J Fract 168:133–143, 2011) and Larsen (in: Hackl (ed) IUTAM symposium on variational concepts with applications to the mechanics of materials, IUTAM Bookseries, vol 21. Springer, Dordrecht, 2010, pp 131–140) with no dissipative terms. [ABSTRACT FROM AUTHOR]

We prove an existence result for a model of dynamic fracture based on Griffith's criterion in the case of a prescribed crack path with a kink. [ABSTRACT FROM AUTHOR]

After a brief review of atomistic theories of defect dynamics in solids, a summary of Slepyan's first computation of dynamic fracture in a lattice is presented. Some of the main extensions and clarifi- cations of the original physical picture are then summarized. Many molecular dynamics simulations of fracture would benefit if Slepyan's work were better known. This article is part of the theme issue 'Modelling of dynamic phenomena and localization in structured media (part 1)'. [ABSTRACT FROM AUTHOR]

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In this work, the lattice Boltzmann method is applied to study the dynamic behaviour of linear elastic solids under antiplane shear deformation. In this case, the governing set of partial differential equations reduces to a scalar wave equation for the out of plane displacement in a two dimensional domain. The lattice Boltzmann approach developed by Guangwu (J Comput Phys 161(1):61-69, 2000) in 2006 is used to solve the problem numerically. Some aspects of the scheme are highlighted, including the treatment of the boundary conditions. Subsequently, the performance of the lattice Boltzmann scheme is tested for a stationary crack problem for which an analytic solution exists. The treatment of cracks is new compared to the examples that are discussed in Guangwu’s work. Furthermore, the lattice Boltzmann simulations are compared to finite element computations. Finally, the influence of the lattice Boltzmann relaxation parameter on the stability of the scheme is illustrated. [ABSTRACT FROM AUTHOR]

Abstract The paper presents a nonlinear approach to investigate the behavior of composite sandwich structures with transversely compressible core, under static and dynamic loading conditions. The proposed model, formulated in the 2D framework, incorporates moving mesh cohesive modeling, crack initiation and nucleation at core/skin interfaces. Interface elements are used to predict debonding mechanisms, whereas shear deformable beams and two-dimensional plane stress elements identify skin and core behavior, respectively. In this framework, interfacial crack onset, layer kinematic and debonding propagation effects are correctly simulated. The moving mesh technique, combined with a multilayer formulation, ensures a reduction of the computational costs, required to predict crack onset and progressive evolution of debonding phenomena. Cohesive models for sandwich core/skin interfaces are calibrated by means of comparisons with numerical and experimental data with respect mode I and mode II configurations. Moreover, a parametric study to address the influence of the loading rate and sandwich characteristics on both static and dynamic frameworks is proposed. [ABSTRACT FROM AUTHOR]

A coupled thermoelastic radial integration boundary element method is applied to analyze the dynamic fracture mechanics of functionally graded materials (FGMs) subjected to the thermal shock loadings. The dynamic stress intensity factor (DSIF) of the crack tip is defined by the crack open displacement (COD) near the crack tip. The effects of material gradating direction versus crack direction and the coupling effects on the stress intensity factor are studied for two- and three-dimensional crack structures. The results demonstrate that the present method is very accuracy and efficiency to analyze the dynamic fracture mechanics for the cracked FGMs. The research also provides a theoretical basis for engineering design, and can extend the application range of the boundary element method. [ABSTRACT FROM AUTHOR]

In the numerical manifold method (NMM), the mathematical patches composing the mathematical cover can take on any shape in addition to finite elements. In this study, the influence domains of those scattered nodes in the moving least squares (MLS) approximation serve as the mathematical patches. And accordingly, the MLS based NMM, designated by MLS-NMM, is derived, which owns the advantages of both NMM and MLS. Then, MLS-NMM is applied to analyze cracked bodies under dynamic loading, and a mass lumping scheme fit for MLS-NMM is proposed. The dynamic analyses of some typical cracked bodies are carried out, indicating MLS-NMM equipped with the proposed mass lumping scheme has more excellent numerical properties than that with the consistent mass formulation in the analysis of the time domain as well as the frequency domain. [ABSTRACT FROM AUTHOR]

• A non-deterministic virtual modelling integrated phase field framework is proposed for 3D dynamic brittle fracture. • Virtual model fracture prediction is proven effective against physical finite element results. • Accurate virtual model prediction is achieved by novel X-SVR method with T-spline polynomial kernel. • Structural safety and reliability assessment can be potentially developed with the proposed framework. A non-deterministic phase field (PF) virtual modelling framework is proposed for three-dimensional dynamic brittle fracture. The developed framework is based on experimental observations, accurate numerical modelling, and virtually foreseeable dynamic fracture prediction module through the machine learning algorithm. The uncertain system inputs, including variabilities of material properties, are incorporated into dynamic fracture analysis. Phase field method is implemented to simulate the dynamic fracture behaviours of 3D cracked structures with variabilities and then to create the training database for virtual damage model. The virtual damage model omits the physical finite element approximation process and reveals the virtual governing relationship between the variational system inputs and fracture responses. This advantage enables the virtual model to provide reliable crack propagation prediction based on either experiment-based or numerical simulation and greatly improves the computational efficiency of dynamic fracture analysis. To establish the accurate virtual model in the training process, a newly developed extended support vector regression (X-SVR) method with T-spline polynomial kernel functions is adopted for its outstanding performance in handling complex high-dimensional problems. Based on different real-world engineering scenarios, multiple fracture failure criteria, both strength-based and serviceability-based, are selected and demonstrated in numerical investigations to visualise the proposed framework's workflow. The effectiveness as well as accuracy are verified by these examples, and it is observed that the computational efficiency of dynamic fracture analysis is greatly improved. With the proposed framework, a continuously updating dynamic fracture surveillance system can be potentially built for practical applications. [Display omitted] [ABSTRACT FROM AUTHOR]

Part I of this study was an extensive fractographic investigation that covered the topics local crack arrest, and cleavage fracture-inducing mechanisms under dynamic loading situations. Also, it produced data regarding the origin of cleavage fracture. Now, this data is used for the numerical part of this study. First, the development of temperature and strain rate increase at the origin of cleavage fracture is conducted, and linked to discrepancies regarding experiments and the Master Curve concept in a phenomenological way. Then, cleavage fracture controlling mechanical field variables at the origin of fracture are analyzed, whereas very similar conditions regarding crack initiation and propagation are found when compared to quasi-static data. The influence of wave phenomena is examined as well. Finally, micromechanical simulations showed that a local temperature increase at the particle–matrix interface does not influence fracture behavior either, and that conclusively, the actual physical mechanism of cleavage fracture initiation (crack initiation and instability) takes place under the same conditions at elevated loading rates as under quasi-static conditions. Ultimately, the mechanisms responsible for the shortcomings of the Master Curve concept under dynamic loading conditions are identified, and current local approach concepts need to be adjusted to consider local crack arrest to be reliable. [ABSTRACT FROM AUTHOR]

The fracture toughness of ferritic steels under dynamic loading conditions on the one hand shows decreasing values with elevated loading rates but on the other hand the shape of the temperature dependent fracture toughness curve has turned out to be different from the static Master Curve according to ASTM E 1921. This difference is often explained by adiabatic heating in the crack tip region, yet it is not clear if there are other additional mechanisms under dynamic loading conditions that contribute to these changes. This work is dedicated to systematically identifying and quantifying additional mechanisms regarding cleavage fracture under dynamic loading conditions. In part I of this study an extensive fractographic analysis of the fracture surfaces was conducted for various crack tip loading rates and testing temperatures. The primary fracture-inducing mechanism was found to be identical to the dominant one under quasi-static conditions (carbide cracking). Yet, the dynamic loading conditions appear to change the origin of fracture, promote local crack arrest, and cause multiple fracture initiation sites that lead to global failure. These results also question the reliability of current local approach concepts if used to assess fracture probability at elevated loading rates. The fractographic results are used in, and complemented by, part II of this study which deals with the numerical analysis of other additional mechanisms such as inertia. [ABSTRACT FROM AUTHOR]

• Photoelastic method, DIC method and strain gauge method are used simultaneously. • The stress field, displacement field and strain field are collected synchronously. • The causes of errors in DSIFs obtained by three methods are discussed. The photoelastic, digital image correlation (DIC), and strain gauge measurement methods are extensively used for studying dynamic fracture mechanics. However, few studies on dynamic fracture focus on combining these methods. In this study, a simultaneous measurement system for in situ investigation on dynamic fractures using the photoelastic, DIC, and strain gauge measurement methods was established for the first time. To reveal the performance of the system, impact experiments were conducted on three-point bending beam specimens fabricated using epoxy resin; consistent results were obtained from the three methods. The developed system provides rich experimental data, including full-field information of the stress, displacement, and strain fields. [ABSTRACT FROM AUTHOR]

In this paper, the edge-based smoothed extended finite element method (ES-XFEM) is applied to the dynamic fracture analysis of two-dimensional elastic solids. The dynamic stress intensity factor (DSIF) is deduced from J -integral with the train smoothing method. With the deduced DSIF, the implementation of numerical integration and sub-smoothing regions are numerically verified in dynamic fracture behaviors of linear elastic solids. The analysis shows that ES-XFEM is an efficient numerical approach to simulate the dynamic fracture problems. [ABSTRACT FROM AUTHOR]

This publication discusses a material or configurational force approach based crack propagation scheme for dynamic fracture, in which the formulation of the material forces is derived from a Lagrangian density where inertia effects are taken into account. In dynamics, the crack driving force can generally be much larger than in the static case. In order to study the capability of the method, an algorithm based on the principle of local symmetry (PLS) is introduced into an implicit solution scheme which requires an additional iterative algorithm to seek for energy minimization. By other explicit approaches, it is not possible to study the crack bifurcation phenomenon, which is well known in dynamic fracturing. It is observed that many micro branches evolve from the main crack in case of fast crack propagation. Thus, the energy flow into the main crack tip is divided between the main crack and the micro-branches. To introduce the micro-cracking effect to the fracture toughness, a fracture criterion as a function of the crack velocity is used in the model, in order to represent realistically the resistance of the cracked structure. In conclusion, it is shown that the proposed method based on the implicit description of energy minimization, is capable of explaining the physics behind the branching phenomenon and it offers a mesh objective solution for a structure even with a coarse mesh. [ABSTRACT FROM AUTHOR]

In the present work, three different enrichment schemes are proposed in conjunction with XFEM to investigate the dynamic response of cracked structures. In the proposed enrichment schemes, only two additional degrees of freedom are added at each node of the crack tip element to reduce the matrix size. In the first enrichment scheme, only Heaviside function is used to model the crack tip. In the second enrichment scheme, the crack tip element is modeled by Heaviside function along with a linear ramp function whereas in third enrichment scheme, Heaviside function is combined with a cubic ramp function to model the crack tip. Newmark time integration scheme is adopted to obtain the dynamic response, and the values of dynamic stress intensity factor are computed by interaction integral approach. To check the accuracy and effectiveness of the enrichment schemes, several stationary and moving crack problems in homogeneous and bi-materials are solved. The numerical results obtained by XFEM are compared with available analytical results, and it is observed that the Heaviside function along with cubic ramp function provides slightly better results as compared to other enrichment schemes. [ABSTRACT FROM AUTHOR]

Dynamic delamination in curved composite laminates is investigated experimentally and numerically. The laminate is 12-ply graphite/epoxy woven fabric L-shaped laminate subject to quasi-static loading perpendicular to one arm. Delamination initiation and propagation are observed using high speed camera and load–displacement data is recorded. The quasi-static shear loading initiates delamination at the curved region which propagates faster than the shear wave speed of the material, leading to intersonic delamination in the arms. In the numerical part, the experiments are simulated with finite element analysis and a bilinear cohesive zone model. Cohesive interface elements are used between all plies with the interface properties obtained from tests. The simulations predict a single delamination initiating at the corner under pure mode-I stress field propagating to the arms under pure mode-II stress field. The crack tip speeds transition from sub-Rayleigh to intersonic in conjunction with mode change. In addition to intersonic mode-II delamination, shear Mach waves emanating from the crack tips in the arms are observed. The simulations and experiments are found to be in good agreement at the macro-scale, in terms of load-displacement behavior and failure load, and at the meso-scale, in terms of delamination initiation location and crack propagation speeds. Finally, a mode dependent crack tip definition is proposed and observation of vibrations during delamination is presented. This paper presents the first conclusive evidence of intersonic delamination in composite laminates triggered under quasi-static loading. [ABSTRACT FROM AUTHOR]

The conventional extended finite element method (XFEM) is enhanced in this paper to simulate dynamic crack branching, which is a top challenge issue in fracture mechanics and finite element method. XFEM uses the enriched shape functions with special characteristics to represent the discontinuity in computation field. In order to describe branched cracks, it is necessary to set up the additional enrichment. Here we have developed two kinds of branched elements, namely the 'element crossed by two separated cracks' and 'element embedded by a junction'. Another series of enriched degrees of freedom are introduced to seize the additional discontinuity in the elements. A shifted enrichment scheme is used to avoid the treatment of blending element. Correspondingly a new mass lumping method is developed for the branched elements based on the kinetic conservation. The derivation of the mass matrix of a four-node quadrilateral element which contains two strong discontinuities is specially presented. Then by choosing crack speed as the branching criterion, the branching process of a single mode I crack is simulated. The results including the branching angle and propagation routes are compared with that obtained by the conventionally used element deletion method. [ABSTRACT FROM AUTHOR]

This research aimed at developing an experimental procedure to characterize the dynamic fracture toughness of a fast running crack in advanced epoxies enriched with thermoplastic particles and demonstrating quasi-brittle fracture. A strain gauge method was defined to determine the dynamic stress intensity factor KIDKID for the mode I crack opening with various crack speeds. This strain gauge measurement was associated with high speed cinematography on a three point bending test dedicated to the fracture of notched specimens made of the Hexply®M21 epoxy resin. Results demonstrate that the crack propagation speed has a large influence on the dynamic fracture toughness of advanced epoxy resins. [ABSTRACT FROM AUTHOR]

This article studies the problem of a finite crack in a finite piezoelectric medium subjected to transient electric and mechanical loads. Unlike past studies that mainly focused on the infinitesimal cracks, the current article considers the effect of the medium boundaries on the transient fracture behavior of piezoelectric materials. A system of singular integral equations is formulated in terms of the crack surface displacement and electric potential. Effects of crack length and medium size on the crack-tip field intensity factors are investigated in detail. Numerical results for the time-dependent stress and electric displacement intensity factors are obtained. Electrically impermeable crack assumption, electrically permeable crack assumption, and notch of finite height are investigated. Some new conclusions are drawn. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the recently developed singular edge-based smoothed finite element method (sES-FEM) is further developed for dynamic crack analysis in two-dimensional elastic solids. The objective of this work is to provide an efficient and accurate numerical simulation tool for the dynamic fracture behaviors of linear elastic solids in the framework of the strain smoothing approaches. Following this approach, the strains are smoothed and the system stiffness matrix is thus performed using the strain smoothing technique over the smoothing domains associated with the element edges. In order to accurately capture the singular fields at the crack-tip, a two-layer singular 5-node crack-tip element is employed. The governing dynamic equations are transformed into a weakened weak (W2) form, which is then discretized into a sES-FEM system of time-dependent equations to be solved by the unconditionally stable implicit Newmark time integration method. To analyze the fracture behaviors of linear elastic solids, mixed-mode dynamic stress intensity factors (DSIFs) are evaluated using the domain forms of the interaction integrals in terms of the smoothing technique. Four test examples including pure mode-I and mixed-modes are studied to validate the accuracy of the proposed method. The computed results for the normalized DSIFs are compared with analytical and other numerical reference solutions in a wide range of benchmark dynamic crack problems which shows high accuracy of the sES-FEM. [Copyright &y& Elsevier]

Abstract: In this paper dual boundary element method for analysis of cracked stiffened panels under dynamic loading is presented for the first time. A continuously attached stiffener is considered. The time-dependent solutions are obtained by the Laplace transformed method. The stress intensity factors are presented for an inclined central crack in a plate with two symmetrically placed stiffeners either side of the crack. The dynamic stress intensity factors are found to be around 2.5 times higher than their respective static values. The stiffeners are shown to be effective in reducing the stress intensity factors. [Copyright &y& Elsevier]

A dynamic model to predict crack growth phenomena in z-pinned reinforced composite structures is proposed. The formulation is based on a novel technique, which is able to couple Fracture Mechanics concepts with a strategy based on a moving mesh methodology. The former is utilized to predict the crack growth, whereas the latter defines the way to take into account the geometry changes on the basis of the invoked fracture parameters. The presence of the z-pins is simulated by means of a large-scale bridging approach, introducing along the delaminated interfaces normal and tangential traction forces depending on the dynamic characteristics of the pull-out mechanism. In order to evaluate the fracture parameters, which govern the crack evolution, the J-integral decomposition procedure is utilized, providing new expressions in the framework of a large-scale bridging crack growth. A numerical modeling based on the finite element procedure is implemented and comparisons with experimental results are reported to validate the proposed formulation. Moreover, a parametric study is developed to investigate the influence of z-pins on the crack growth mechanisms. [ABSTRACT FROM AUTHOR]

Abstract: The transient response of cracked composite materials made of piezoelectric and piezomagnetic phases, when subjected to in-plane magneto-electro-mechanical dynamic loads, is addressed in this paper by means of a mixed boundary element method (BEM) approach. Both the displacement and traction boundary integral equations (BIEs) are used to develop a single-domain formulation. The convolution integrals arising in the time-domain BEM are numerically computed by Lubich’s quadrature, which determines the integration weights from the Laplace transformed fundamental solution and a linear multistep method. The required Laplace-domain fundamental solution is derived by means of the Radon transform in the form of line integrals over a unit circumference. The singular and hypersingular BIEs are numerically evaluated in a precise and efficient manner by a regularization procedure based on a simple change of variable, as previously proposed by the authors for statics. Discontinuous quarter-point elements are used to properly capture the behavior of the extended crack opening displacements (ECOD) around the crack-tip and directly evaluate the field intensity factors (stress, electric displacement and magnetic induction intensity factors) from the computed nodal data. Numerical results are obtained to validate the formulation and illustrate its capabilities. The effect of the combined application of electric, magnetic and mechanical loads on the dynamic field intensity factors is analyzed in detail for several crack configurations under impact loading. [Copyright &y& Elsevier]

Existence and convergence results are proved for a regularized model of dynamic brittle fracture based on the Ambrosio–Tortorelli approximation. We show that the sequence of solutions to the time-discrete elastodynamics, proposed by Bourdin, Larsen & Richardson as a semidiscrete numerical model for dynamic fracture, converges, as the time-step approaches zero, to a solution of the natural time-continuous elastodynamics model, and that this solution satisfies an energy balance. We emphasize that these models do not specify crack paths a priori, but predict them, including such complicated behavior as kinking, crack branching, and so forth, in any spatial dimension. [ABSTRACT FROM AUTHOR]

Abstract: Most magnetoelectroelastic composites were developed in the form of a composite laminate by alternating the ferromagnetic layers and ferroelectric layers during stacking. Presence of interfacial crack may influence the magneto-electro-mechanical coupling behavior of magnetoelectroelastic materials considerably. This paper describes a method to analyze the transient response of a layered magnetoelectroelastic medium of finite size with an interface crack. Based on Fourier and Laplace transforms, the boundary value problem is reduced to a system of generalized singularity integral equations in the Laplace transform domain. By utilized numerical Laplace inversion, the time-dependent full field solutions are obtained in the time domain. Effects of medium size, crack-face electric and magnetic boundary conditions on the dynamic crack tip fields are studied. By investigating an interface notch of finite gap thickness, the electric and magnetic properties of the medium inside the notch are included in the analytical model so that the applicability of crack-face electric and magnetic boundary conditions on the transient response of the magnetoelectroelastic medium can be investigated. [Copyright &y& Elsevier]

This paper addresses the question of rate effects in the propagation of delamination cracks in Composite Fiber-Reinforced Plastics (CFRPs). In order to make use of a simple loading device, a mode-II case is used as the basis of the experimental study. The position of the crack is recorded quantitatively by means of a high-speed camera and dedicated image processing techniques. The delamination process is modeled by means of an interfacial Continuum Damage Model (CDM), similar to Cohesive Zone Model (CZM) approaches. In order to make suitable comparison between test and explicit finite element simulation of the test, criterai of proper temporal and spatial discretization have been derived. They ensure a fine description of the process zone and a proper description of the degradation evolution of the interface. Using such simulations and direct comparisons with the tests results, it is shown that the experimental results cannot be reproduced numerically without introducing rate effects. Then, it is proposed and identified by means of comparison between experiments and numerical simulation a bounded-damage-rate interfacial model. The main consequence of the proposed rate-dependent model is that it introduces a maximum crack velocity which is a function of the maximum damage rate. The dependence of the critical energy release rate on the crack’s velocity is analyzed, which leads to the identification of an equivalent rate-dependent fracture mechanics criterion. [ABSTRACT FROM AUTHOR]