Accurate numerical modeling of multifield piezoelectric materials is challenging because of the inherent electro-mechanical coupling effect and material anisotropic behaviors. The modeling becomes ...even more difficult especially for problems with non-smooth solutions like crack under dynamic loading. We present in this paper an extension of the extended isogeometric analysis (XIGA) for simulation of two-dimensional fracture mechanics problems in piezoelectric materials under dynamic and static coupled electromechanical loads. The discretization of problem domain is based on basis functions generated from NURBS, which are used for both geometric description and approximation of solution field variables. To capture the discontinuity across the crack-faces and the singularity at the crack-tip, the isogeometric approximation is locally enriched by discontinuous Heaviside function and asymptotic crack-tip branch functions. The sixfold enrichment functions particularly suitable for electromechanical crack-tip singularity of piezoelectric materials are used. To evaluate the generalized fracture parameters, a domain-form of electromechanical interaction integral is employed. For dynamic analysis, the implicit time integration scheme considering inertial effect is taken. Five numerical examples for single and mixed-modes of impermeable cracks are considered and the generalized fracture parameters under dynamic and static loads are analyzed. The accuracy and effectiveness of the proposed XIGA are illustrated through numerical investigations of the generalized dynamic and static fracture parameters. Numerical results are validated against the reference solutions derived from the boundary element methods. The effects of some numerical aspect ratios on generalized fracture parameters are also investigated. Additionally, we present some numerical results of quasi-static crack propagation in piezoelectric solids using the developed XIGA, taking fracture toughness anisotropy of polarized electroelastic materials into account, and employing the maximum modified hoop stress intensity factor criterion for predicting the growing direction of crack.
•XIGA dynamic and static fracture formulation in piezoelectricity is developed.•Crack growth modeling in brittle piezoelectric solids is presented.•Static generalized intensity factors of cracked piezoelectric solids are analyzed.•Transient dynamic responses of impermeable and permeable cracks are studied.•Effects of polarization, enrichments, meshes, loadings, etc. on GIFs are investigated.
•The influence of uncertainty on the dynamic fracture toughness of glass-filled epoxy composites is investigated.•An experimental investigation supported by data-driven approaches is proposed based ...on machine learning.•Different shapes of glass particles are considered with coupled stochastic variations in aspect ratio, dynamic elastic modulus and volume fraction.•An ANN based Monte Carlo simulation is carried out in conjunction with advanced experimental techniques like digital image correlation and scanning electron microscopy.•The outcomes based on experimental data essentially ascertain that quantification of uncertainty is of utmost importance for developing a reliable and practically relevant inclusive framework.
This paper presents an experimental investigation supported by data-driven approaches concerning the influence of critical stochastic effects on the dynamic fracture toughness of glass-filled epoxy composites using a computationally efficient framework of uncertainty quantification. Three different shapes of glass particles are considered including rod, spherical and flaky shapes with coupled stochastic variations in aspect ratio, dynamic elastic modulus and volume fraction. An artificial neural network based surrogate assisted Monte Carlo simulation is carried out here in conjunction with advanced experimental techniques like digital image correlation and scanning electron microscopy to quantify the uncertainty and sensitivity associated with the dynamic fracture toughness of composites in terms of stress intensity factor under dynamic impact. The study reveals that the pre-crack initiation time regime shows the most prominent effect of uncertainty. Additionally, rod shape and the aspect ratio are the most sensitive filler type and input parameter respectively for characterizing dynamic fracture toughness. Here the quantitative results based on large-scale data-driven approaches convincingly demonstrate using a computational mapping between the stochastic input and output parameter spaces that the effect of uncertainty gets pronounced significantly while propagating from the compound source level to the impact responses. Such outcomes based on experimental data essentially bring us to the realization that quantification of uncertainty is of utmost importance for developing a reliable and practically relevant inclusive analysis and design framework for the dynamic fracture of particulate composites. With limited literature available on the determination of fracture toughness considering inertial effects, the present work demonstrates a novel and insightful experimental approach for uncertainty quantification and sensitivity analysis of dynamic fracture toughness of particulate polymer composites based on surrogate modeling.
Peridynamics (PD), as a nonlocal theory, is well-suited for solving problems with discontinuities, such as cracks. However, the nonlocal effect of peridynamics makes it computationally expensive for ...dynamic fracture problems in large-scale engineering applications. As an alternative, this study proposes a multi-time-step (MTS) coupling model of PD and classical continuum mechanics (CCM) based on the Arlequin framework. Peridynamics is applied to the fracture domain of the structure, while continuum mechanics is applied to the rest of the structure. The MTS method enables the peridynamic model to be solved at a small time step and the continuum mechanical model is solved at a larger time step. Consequently, higher computational efficiency is achieved for the fracture domain of the structure while ensuring computational accuracy, and this coupling method can be easily applied to large-scale engineering fracture problems.
•MTS method is used to enable the different integration time-step in a coupled model.•Subdomains with different integration time-steps are coupled by Arlequin framework.•The model capture the characteristics of dynamic brittle fracture successfully.•The parallel implementation of the algorithm is executed on GPU using the CUDA.
The focus of this paper is on application of peridynamics (PD) to propagation of elastic waves in unbounded domains. We construct absorbing boundary conditions (ABCs) derived from a semi-analytical ...solution of the PD governing equation at the exterior region. This solution is made up of a finite series of plane waves, as fundamental solutions (modes), which satisfy the PD dispersion relations. The modes are adjusted to transmit the energy from the interior region (near field) to the exterior region (far field). The corresponding unknown coefficients of the series are found in terms of the displacement field at a layer of points adjacent to the absorbing boundary. This is accomplished through a collocation procedure at subregions (clouds) around each absorbing point. The proposed ABCs offer appealing advantages, which facilitate their application to PD. They are of Dirichlet-type, hence their implementation is relatively simple as no derivatives of the field variables are required. They are constructed in the time and space domains and thus application of Fourier and Laplace transforms, cumbersome for nonlocal models, is not required. At the discrete level, the modes satisfy the same numerical dispersion relations of the near field, which makes the far-field solution compatible with that of the near field. We scrutinize the performance of the proposed ABCs through several examples. Our investigation shows that the proposed ABCs perform stably in time with an appropriate level of accuracy even in problems characterized by highly-dispersive propagating waves, including crack propagation in semi-unbounded brittle solids.
•Development of absorbing boundary conditions for 2D bond-based peridynamics.•Introduction of easy-to-implement, Dirichlet-type absorbing boundary conditions.•Approximation of the far-field solution in consistency with the near-field solution.•Construction of the absorbing boundary conditions in the time and space domains.•Solution of propagating cracks in a half-space.
The fracture behaviour and crack propagation features of coal under coupled static-dynamic loading conditions are important when evaluating the dynamic failure of coal. In this study, coupled ...static-dynamic loading tests are conducted on Brazilian disc (BD) coal specimens using a modified split Hopkinson pressure bar (SHPB). The effects of the static axial pre-stress and loading rate on the dynamic tensile strength and crack propagation characteristics of BD coal specimens are studied. The average dynamic indirect tensile strength of coal specimens increases first and then decreases with the static axial pre-stress increasing. When no static axial pre-stress is applied, or the static axial pre-stress is 30% of the static tensile strength, the dynamic indirect tensile strength of coal specimens shows an increase trend as the loading rate increases. When the static axial pre-stress is 60% of the static tensile strength, the dynamic indirect tensile strength shows a fluctuant trend as the loading rate increases. According to the crack propagation process of coal specimens recorded by high-speed camera, the impact velocity influences the mode of crack propagation, while the static axial pre-stress influences the direction of crack propagation. The failure of coal specimens is a coupled tensile-shear failure under high impact velocity. When there is no static axial pre-stress, tensile cracks occur in the vertical loading direction. When the static axial pre-stress is applied, the number of cracks perpendicular to the loading direction decreases, and more cracks occur in the parallel loading direction.
Being able to seamlessly deal with complex crack patterns like branching, merging and even fragmentation, the phase-field model, amongst several alternatives, is promising in the computational ...modeling of dynamic fracture in solids. This paper presents an extension of our recently introduced phase-field cohesive zone model for static fracture to dynamic fracture in brittle and quasi-brittle solids. The model performance is tested with several benchmarks for dynamic brittle and cohesive fracture. Good agreement is achieved with existing findings and experimental results; and particularly the results are independent to the discretization resolution and the incorporated length scale parameter. The latter is in contrast to existing phase-field models.
•Dynamic fracture is modeled by a phase-field regularized cohesive zone model.•Both brittle fracture and quasi-brittle failure under dynamic loadings are considered.•The results are independent of the length scale parameter regularizing the sharp cracks.•Numerical results are in good agreement with existing computational/experimental findings.
•The dynamic experiment of rock with different crack inclination angles was carried out by using the drop hammer system.•The dynamic propagation behavior of boundary cracks in elliptical surrounding ...rock is analyzed by experiment and numerical simulation.•The universal function is used to modify the static stress intensity factor to solve the dynamic stress intensity factors of mode I and I / II composite cracks.
Elliptical cross-section underground holes are widely present, and the shock waves generated during construction can disturb the existing cracks and defects around them, affecting the surrounding rock’s stability. A series of impact experiments were executed utilizing crack propagation gauges to analyze the behavior of boundary cracks in the surrounding rock that contains elliptical holes under dynamic loading conditions. The fracture time and the crack propagation velocity for the elliptical hole model were determined across a spectrum of prefabricated crack angles. A good agreement was achieved between the simulation and experimental results. It was concluded that for crack angles α equal to 0° and 90°, the initiation time for crack formation in the specimens is extended compared to the initiation time observed in mode I/II composite cracks, concurrent with an accelerated crack propagation rate. For a crack angle of α at 30°, there is a heightened propensity for tensile failure to manifest along both sides of the short half-axis of the elliptical hole. In contrast, when the crack angle is inclined at 60°, the region at the base of the longer semi-axis of the elliptical hole becomes more vulnerable to tensile failure.
•First publicly available COMSOL implementation of phase field models for static and dynamic fracture in 2D and 3D.•Validated COMSOL code for phase field model for fracture.
The phase-field model ...(PFM) represents the crack geometry in a diffusive way without introducing sharp discontinuities. This feature enables PFM to effectively model crack propagation compared with numerical methods based on discrete crack model, especially for complex crack patterns. Due to the involvement of “phased field”, phase-field method can be essentially treated a multifield problem even for pure mechanical problem. Therefore, it is supposed that the implementation of PFM based on a software developer that especially supports the solution of multifield problems should be more effective, simpler and more efficient than PFM implemented on a general finite element software. In this work, the authors aim to devise a simple and efficient implementation of phase-field model for the modelling of quasi-static and dynamic fracture in the general purpose commercial software developer, COMSOL Multiphysics. Notably only the tensile stress induced crack is accounted for crack evolution by using the decomposition of elastic strain energy. The width of the diffusive crack is controlled by a length-scale parameter. Equations that govern body motion and phase-field evolution are written into different modules in COMSOL, which are then coupled to a whole system to be solved. A staggered scheme is adopted to solve the coupled system and each module is solved sequentially during one time step. A number of 2D and 3D examples are tested to investigate the performance of the present implementation. Our simulations show good agreement with previous works, indicating the feasibility and validity of the COMSOL implementation of PFM.
•3D FEM of CNT pull-out deformation is established considering the loading rates.•The atomistic behavior of CNT-matrix interface is captured for rate-dependent CZM.•A viscoelastic-viscoplastic ...constitutive law is used to model the matrix behavior.•The effects of CNT on fracture energy are studied at different pull-out speeds.
Carbon nanotubes (CNTs) enhance the fracture toughness of polymer-based matrix composites by dissipating the fracture energy through the pull-out deformation damage mechanism. The rate-dependent behavior of the matrix phase and the CNT/matrix interface affects the contribution of CNTs in enhancing the fracture toughness under dynamic loading and rapid crack growth. A continuum-based finite element (FE) model is utilized in this research to analyze the CNT pull-out damage mechanism. The influence of CNTs on the dynamic fracture behavior of polymer-based composites is studied taking into account the crack opening speed and loading rate effects. The matrix phase is treated as a viscoelastic-viscoplastic material and a new rate-dependent cohesive zone model (CZM) is proposed for modeling the behavior of interface between the CNTs and matrix. The rate-dependent traction-separation laws for the cohesive zone elements are established at different pull-out or crack opening speeds. The proposed rate-dependent FE model of pull-out mechanism facilitates the investigation of the effective factors of CNTs, including length, orientation, and waviness, on fracture energy dissipation at different pull-out speeds. Developed model is very suitable for very long CNTs where atomistic-based molecular dynamics and molecular mechanics methods are associated with difficulties and are more costly and time-consuming.
PDF
