Simulation Of Dynamic Fracture Research Articles

Dynamic fracture simulation of brittle materials through a new tool: FEM equipped with continuous visibility

Dynamic fracture simulation of brittle materials through a new tool: FEM equipped with continuous visibility

Rate-dependent FDEM numerical simulation of dynamic tensile fracture and failure behavior in frozen soil

Considering that the dynamic fracture and failure behaviors of frozen soil play a crucial role in the safety and stability of engineering foundations in cold regions, this study aimed to reveal the dynamic tensile mechanical properties and damage failure mechanisms of frozen soil under impact loading. Dynamic Brazilian disk (BD) tests were conducted on frozen soil at different temperatures and loading velocities using a split Hopkinson pressure bar (SHPB) apparatus, followed by numerical simulations using the finite discrete element method (FDEM), focusing on the dynamic tensile deformation characteristics, failure patterns, tensile strength, and energy dissipation mechanisms of the frozen soil. The experimental results indicated that the dynamic tensile mechanical properties of frozen soil were influenced by both temperature and loading velocity. As the temperature decreased and loading velocity increased, the tensile strength of frozen soil significantly increased and showed a linear correlation with the loading velocity. At lower loading velocities, the cracks tended to propagate along the paths of least resistance, forming fewer but longer macrocracks. With increasing loading velocities, the number of cracks markedly increased, and their distribution became more diffuse, leading to a greater extent of failure in the frozen soil. An exponential damage cohesive interface model that considers rate effects was proposed to describe the dynamic tensile fracture mechanical behavior of frozen soil accurately. This model addresses the rate sensitivity of frozen soil and effectively accounts for the temperature effect by considering the volume of ice content and cryogenic suction. A comparison of the FDEM numerical simulation results with the experimental data indicated a good consistency in the overall trends, thus validating the effectiveness and applicability of the FDEM in simulating the dynamic tensile mechanical behavior of frozen soil.

High strain-rate fracture behavior of a hollow projectile

In this paper, a hollow projectile made of AISI4340 steel was fabricated based on an arbitrary warhead shape, and high-speed impact tests were performed according to various target encounter conditions including velocity and angle. In order to characterize the dynamic fracture behavior, tensile tests were performed on various notch specimens under three strain rates (10–3 s-1, 100 s-1, 103 s-1), and the stress state histories of the specimens were calibrated through a hybrid experimental-numerical analysis. In particular, for the intermediate (100 s-1) and high (103 s-1) strain rate conditions, the local temperature rose due to adiabatic heating until fracture was experimentally measured, and the thermal softening behavior determined from the inverse optimization technique was considered for the dynamic constitutive model. For the comparison with the high-speed impact test results, a rate-dependent ductile fracture model was utilized for numerical simulation. Considering that the model parameters were calibrated with the thermal softening effect, the proposed fracture model implicitly takes temperature into account. The deformation and fracture modes of the projectile from experimental and numerical study showed very good agreement under all impact conditions. It was confirmed that the softening of a material by adiabatic heating should be considered along with strain rate hardening in dynamic fracture simulation.

Peridynamic computations of wave propagation and reflection at material interfaces

Peridynamics describes the material in a non-local form and is very suited for the simulation of dynamic fracture. However, one significant effect regarding dynamic fracture is the correct handling of elastic deformation, like the pressure and tension waves inside a body, due to dynamic boundary conditions like an impact or impulse. Many peridynamic material formulations have been developed with differences in this regard. This study investigates the elastic wave propagation characteristics of bond-based, ordinary state-based, continuum kinematics-inspired peridynamics and a local continuum consistent correspondence formulation. Multiple parameters of a longitudinal pressure wave inside an elastic bar are studied. While all formulations demonstrate adequate wave propagation handling, all except the correspondence formulation are sensitive to incomplete horizons. The local continuum consistent formulation does not suffer from the surface effect and models the wave propagation with perfect accuracy.

Analytical modeling and simulations of dynamic mode-III fracture in pre-stressed dry sandy elastic continuum

A mathematical model has been developed to investigate the SIF (stress intensity factor) and COD (crack opening displacement) for the propagation of mode-III fracture influenced by propagating SH-wave in a pre-stressed dry sandy elastic continuum. The Wiener-Hopf mathematical method along with the Fourier integral transform (FIT) technique have been successively implemented to obtain the solution of the boundary value problem associated with the mathematical model. Furthermore, the closed form solutions of SIF and COD for non-static and static conditions of mode-III fracture have been obtained, and are found to be in well agreement with the existing results present in the literature. The sound effects of various affecting parameters viz. horizontal and vertical (compressive/tensile) pre-stresses, crack depth, and crack velocity on SIF and COD have been explored. In order to delineate the influences of these aforementioned parameters on SIF and COD graphically, numerical simulation has been accomplished.

An explicit updated Lagrangian fragile points method for dynamic fracture simulations

Dynamic fracture is a prevalent phenomenon in engineering structures subjected to dynamic loads, and reliable and simple numerical simulations of such phenomenon has been an ongoing research topic of computational mechanics. Although the finite element method (FEM) has been widely used for fracture simulations, there are still challenges such as the crack introduction and the mesh distortion. In recent years, meshless methods have emerged as potential alternatives to overcome these issues. In this paper, an explicit updated Lagrangian Fragile Points Method (FPM) is proposed for dynamic fracture simulations. The FPM is a point-based discontinuous meshless method, thus it on one hand circumvents the mesh distortion, and on the other hand allows for a simple, explicit introduction of cracks. In this paper, the formulations of the explicit updated Lagrangian FPM are introduced. Then the method is applied to various dynamic fracture problems including the spalling fracture and the crack branching, and for each cases the FPM provides convincing results. This paper shows that the explicit updated Lagrangian FPM is an effective yet simple numerical tool for predicting dynamic fracture. Note that though only small deformation dynamic fracture examples are used in this paper, the proposed method is able to handle finite strain problems, verified by some simple examples, since it is developed in the updated-Lagrangian form.

Influence of rate-dependent damage phase-field on the limiting crack-tip velocity in dynamic fracture

This contribution explores three thermodynamically-consistent damage phase-field formulations for rate-dependent dynamic fracture in viscoelastic materials. By means of a numerical study on a uniform displacement strip benchmark, the formulations and modelling assumptions are compared, and the corresponding limiting crack-tip speeds are discussed. In essence, in addition to recalling the existing phase-field model for viscoelastic materials, a damage phase-field formulation for rate-dependent toughness is introduced as a function of the damage-rate at the crack-tip and is contrasted to existing strain-rate dependent toughness models. Dynamic fracture simulations have demonstrated the significant role of rate dependency in suppressing crack branching and accelerating the crack propagation. The rate dependency is analysed through two main mechanisms: (i) the viscous dissipation, which can promote fracture, and (ii) an increase in the energy required to evolve a crack, through rate-dependent toughness models. Depending on the specific choice of parameters, the numerical simulations show crack propagation at speeds that exceed the theoretical limit depicted by the Rayleigh wave speed. Indeed, these high speeds are attributed to the viscoelastic and viscoelastic-like (observed in the case of strain-rate dependent fracture toughness) stiffening at the crack-tip, which translates to faster running surface waves and enables supersonic crack-speeds; a never-seen-before result in damage phase-field simulations.

Study on non‐uniformity and dynamic fracture characteristics of GIL tri‐post insulators considering Al2O3 sedimentation

AbstractTri‐post insulators in gas‐insulated transmission line (GIL) are usually fabricated with high mass fraction of micron aluminum oxide (Al2O3), which will unavoidably settle under the action of gravity during the preparation process and seriously affect the uniformity. A model of filler sedimentation in epoxy resin composite materials was proposed based on the particle size analysis and Stokes' Law. Some scaled tri‐post insulators were prepared and tested by slicing. It is determined that the position of density concentration is the lower side of the two lower posts and the upper interface between the insulator and the conductor. The density ranges from 2.144 to 2.346 g/cm3. The dynamic fracture simulation model of insulator was established and it is found that the insulator fracture occurs at the interface of upper post/insert under radial load, which is verified by experiments. By comparing the influence of sprue position on the density distribution, it is found that the uniformity of insulators is increased by 13.7% by forward pouring compared with reverse pouring. This research develops an accurate method for simulating the filler sedimentation and the fracture process in epoxy‐based insulators, which is helpful for the improvement of mechanical reliability of GIL.

Numerical simulations of dynamic fracture and fragmentation problems by a novel diffusive damage model

In this paper, we report numerical simulations for dynamic fracture and fragmentation problems in brittle materials using a recently developed split strain energy diffusive mass-field damage model in terms of standard finite element method (FEM). The enhanced constitutive laws for mass source and mass flux by means of strain energy decomposition are adopted to overcome certain drawbacks of the original non-split model. We present theoretical formulations in a more general way that is suitable and valid for both small and finite deformation regimes. The coupled system of equations is derived in which the momentum is governed to describe the time-dependent deformation of brittle solids whereas the mass-diffusion balance equations are for the evolution of mass density. We also develop simple techniques for determining crack velocity and estimating amount of mass loss. Numerical examples are considered for both small and finite deformations. The accuracy and performance of the developed theory for dynamic brittle fracture are illustrated through comparison and verification, which are to compare the computed results with respect to experimental data and other numerical methods in terms of crack path trajectories, dynamic response, energy dissipation, and other relevant numerical aspects.

Simulation of dynamic compression and fracture of propellant charge in bore

After many years of research, the main reason of breech blow caused by propellant charge is the large scale fracture which leaded by the compression of propellant. The description of the dynamic compression and fracture process involves not only the large motion of granular system consisting of large numbers of propellant particles, but also the deformation and fracture of every propellant particle. Hence, it has become a big problem all over the world. The discrete element method is used to study the compression and fracture process of propellant charge in bore in this paper. The results show that the fragmentation degree of the propellant charge at the bottom of projectile is the highest when launching, and the mechanism of breech blow caused by propellant charge is proved.

Simulation of dynamic fracture in quasi-brittle materials using a finite element modeling approach enhanced by moving mesh technique and interaction integral method

This work presents an efficient modeling approach for predicting dynamic crack propagation mechanisms in quasi-brittle materials. The proposed method consists of a standard Finite Element code enhanced by Moving Mesh (MM) technique consistent with the Arbitrary Lagrangian-Eulerian (ALE) formulation. The MM is used to reproduce the geometry evolution caused by dynamically growing cracks. More precisely, the nodes of the computational mesh around the crack tip change position during the simulation consistently with the growth of the crack front. In such a context, the ALE formulation ensures an effective re-location of mesh nodes inside the computational domain, reducing the overall amount of remeshing events. The motion of the computational mesh takes place according to previsions dictated by classic fracture criteria, which define crack initiation conditions, the direction of propagation, and the velocity of the advancing crack front. Such conditions depend on Dynamic Stress Intensity Factors at the crack front. Hence, accurately predicting these fracture variables is mandatory to ensure consistent mesh motions. To this end, the proposed approach implements the ALE formulation of the M-integral, which enables computing fracture variables on moving elements without losing accuracy. The validity of the proposed modeling strategy has been assessed through comparisons with numerical data and analytical formulations reported in the literature.

A continuum consistent discrete particle method for continuum–discontinuum transitions and complex fracture problems

In numerical simulations where complex fracture behavior plays a prominent role in the material’s mechanical behavior, particle methods are an attractive computational tool since they adequately accommodate arbitrary discontinuities. However, existing particle methods are either limited in their constitutive flexibility, like the Discrete Element Method (DEM), or prone to instabilities, like Smoothed Particle Hydrodynamics (SPH) and Peridynamics. In this paper we present an alternative particle formulation, referred to as the Continuum Bond Method (CBM). The method has the same constitutive flexibility as conventional continuum methods like the Finite Element Method (FEM), while still being able to incorporate arbitrary discontinuities as in particle methods like DEM, SPH and Peridynamics. In CBM, the continuum body is divided into a series of material points where each material point carries a fraction of the body’s mass. A triangulation procedure establishes the bonds between the particles that interact with each other. The deformation gradient tensor is determined via a volume weighted averaging procedure over the volumes spanned by pairs of nearest neighboring particles. The obtained approximation of the continuum deformation field on the particles allows for a straightforward implementation of continuum constitutive laws. To assess this property in CBM, simulation outcomes for an elastic nonlinear plastic tensile bar are compared to FEM and SPH results. While the stress–strain curves obtained by FEM, CBM and SPH coincide quite accurately, it is found that the local plastic strains obtained by CBM are much closer to the FEM reference solution than the SPH results. The ability of CBM to account for arbitrary discontinuities is demonstrated via a series of dynamic fracture simulations. It is shown that, without the need of additional crack tracking routines, CBM can account for fracture instability phenomena like branches. In conclusion, CBM is suitable for the implementation of continuum constitutive behavior while maintaining the advantageous discontinuous fracture properties of particle methods.

Peridynamic simulation of dynamic fracture in functionally graded materials subjected to impact load

Dynamic crack propagation assessment in functionally graded materials (FGMs) with micro-cracks is accomplished using bond-based Peridynamics (PD). The dynamic fracture behaviour of various FGMs’ material models is studied in Kalthoff–Winkler experiment. Dynamic crack growth predictions and associated material damage of the specimen under dynamic loading conditions are considered. The effect of micro-cracks near macro-crack tips on the toughening mechanism is evaluated in terms of crack propagation velocities. Stochastically pre-located micro-cracks are modelled to obtain the toughening effect in the material. In addition, the velocities and time required for fracture are compared in different FGM cases. It is frankly found that if a crack propagates in the harder region of the specimen, velocities decrease and toughness increase in contrast to the softer region. Furthermore, micro-cracks around a macro-crack decelerate the crack propagation and enhance toughening mechanism in FGM body depending on gradation of material properties.

Quasi-static and dynamic fracture modeling by the nonlocal operator method

In this paper, a phase field model is developed and applied to the simulation of quasi-static and dynamic fracture using the nonlocal operator method (NOM). The phase field’s nonlocal weak and associated strong forms are derived by a variational principle. The NOM requires only the definition of the energy. Its differential operators replace the shape functions in methods such as FEM which drastically simplifies the implementation. We present both a nonlocal implicit phase field model and a nonlocal explicit phase field model for fracture; the first approach is better suited for quasi-static fracture problems while the key application of the latter one is dynamic fracture. To demonstrate the performance of the underlying approach, several benchmark examples for quasi-static and dynamic fracture are solved.

Dynamic Fracture Simulation of Functionally Graded Engineered Cementitious Composite Structures Based on Peridynamics

Dynamic Fracture Simulation of Functionally Graded Engineered Cementitious Composite Structures Based on Peridynamics

P.009 MDK gene expression is correlated with human brain activity during acceptance of monetary rewards

Computationally efficient methods for bridging length scales, from highly resolved micro/meso-scale models that can explicitly model crack growth, to macro-scale continuum models that are more suitable for modeling large parts, have been of interest to researchers for decades. In this work, an improved brittle damage model is presented for the simulation of dynamic fracture in continuum scale quasi-brittle metal components. Crack evolution statistics, including the number, length, and orientation of individual cracks, are extracted from high-fidelity, finite discrete element method (FDEM) simulations and used to generate effective material moduli that reflect the material’s damaged state over time. This strategy allows for the retention of small-scale physical behaviors such as crack growth and coalescence in continuum scale hydrodynamic simulations. However, the high-fidelity simulations required to generate the crack statistics are computationally expensive. Thus, steps were taken to produce a flexible constitutive model to reduce the number of costly high-fidelity simulations needed to produce accurate results. A new stress based degradation criterion is introduced for the degradation of individual material zones. This allows for the development of a heterogeneous damage distribution within the bulk material. Then a flow stress model is added to the hydrodynamic simulation to account for plasticity in quasi-brittle materials. As a result, the effective moduli model can be applied to a larger range of materials. The effective moduli constitutive model is used to simulate beryllium flyer plate experiments. The results from the continuum scale simulations using statistics from a single high-fidelity simulation are found to be in excellent agreement with numerical and experimental velocity interferometer data. The same set of crack statistics are used to extrapolate the results of a higher rate flyer plate case using the effective moduli model. The extension of this model to higher rate cases shows promise for further reducing the number of costly high-fidelity simulations needed to generate crack statistics.

Combining XFEM and time integration by α-method for seismic analysis of dam-foundation-reservoir

Extended finite element method (XFEM) and time integration by α-method are coupled in the direct integration scheme to study the 2D dynamic fracture of concrete gravity dam-foundation-reservoir interaction. The advantages of XFEM for the strong displacement discontinuity description of a crack and α-method for the time integration in dynamic analysis to dissipate the shockwaves after crack growth are combined together. The proposed method can improve the computation efficiency and can avoid numerical instability to judge the crack propagation orientation of XFEM. Obtained results show by increasing the value of α in time integration, the shock waves after crack growth are decreased and the stability of numerical solution is increased. In addition the accuracy of the dynamic fracture simulation using the proposed method is investigated in comparison with other reported in the literature.To apply the interaction in finite element model, zero thickness six-nodal contact elements are used in which the dam, foundation and reservoir are formulated with Lagrangian approach. Also, to predict dynamic fracture behavior of a cracked dam, dynamic stress intensity factors (DSIFs) are used. The interaction integral (conservation integral) originally proposed to evaluate SIFs to incorporate dynamic effects is utilized to evaluate DSIFs. Effective parameters in problem-solving such as the contribution of each distinct term in the interaction integral, crack tip element, length of crack growth, integration radius, location of initial crack, angle of initial crack, internal damping ratio of the dam, and fracture energy based on proposed method are discussed.

A three dimension lattice-spring model with rotational degree of freedom and its application in fracture simulation of elastic brittle materials

Applying parameter mapping theory, this paper establishes a new three dimension lattice-spring model with rotational degree of freedom (3D-LSMR). This 3D-LSMR contains nearest neighbor, next nearest neighbor and third nearest neighbor which highly increases the accuracy of system. Compared with the general lattice spring model, 3D-LSMR adds the rotational and tangential degrees of freedom, whose spring parameters are obtained by finite element parameter mapping. The traditional lattice spring model only considers the normal interaction between two points (the Poisson’s ratio is fixed), which limits the application of the lattice spring model in a wider range of materials. Some scholars proposed to add shear spring into the traditional model to solve the problem of fixed Poisson’s ratio, but the rotation invariance could not be maintained. The main reason is that the shear spring can’t distinguish the difference of tangential velocity (or displacement) between the two particles due to the common rotation or shear. Therefore, the rotation of the whole rigid body may cause incorrect generation of additional strain energy inside the shear spring. 3D-LSMR model is able to maintain rotation invariance and reproduces different Poisson’s ratios because of the spring parameters with rotational degrees of freedom and the rotation effect of lattice points. In this paper, the finite element stiffness matrix with rotational freedom is derived by using 3D-LSMR as the basic mechanical model, and the parameter mapping theory of spring stiffness coefficient is introduced. By means of numerical simulation, the large deflection of slender cantilever beam, elastic symmetrical collision and the simulation of dynamic fracture for concrete L-specimen are checked and calculated respectively, and then the correctness of the model is verified.

A coupling model of XFEM/peridynamics for 2D dynamic crack propagation and branching problems

Peridynamics (PD) and extended finite element method (XFEM) are coupled in the explicit integration scheme to study the 2D dynamic fracture problems. The advantages of PD for the crack propagation and XFEM for the strong displacement discontinuity description of the crack are combined together. The proposed method can improve the computation efficiency in comparison of the pure PD, and can avoid using macroscopic criteria to judge the crack propagation orientation of XFEM. The coupling scheme for the stiffness and mass matrices of PD and XFEM is given in the coupling region. The horizon length δ is examined to study their influences on the convergence of the proposed method. The accuracy of the dynamic fracture simulation using the proposed method is also validated in comparison of experimental and other numerical methods.

Scale bridging damage model for quasi-brittle metals informed with crack evolution statistics

Computationally efficient methods for bridging length scales, from highly resolved micro/meso-scale models that can explicitly model crack growth, to macro-scale continuum models that are more suitable for modeling large parts, have been of interest to researchers for decades. In this work, an improved brittle damage model is presented for the simulation of dynamic fracture in continuum scale quasi-brittle metal components. Crack evolution statistics, including the number, length, and orientation of individual cracks, are extracted from high-fidelity, finite discrete element method (FDEM) simulations and used to generate effective material moduli that reflect the material’s damaged state over time. This strategy allows for the retention of small-scale physical behaviors such as crack growth and coalescence in continuum scale hydrodynamic simulations. However, the high-fidelity simulations required to generate the crack statistics are computationally expensive. Thus, steps were taken to produce a flexible constitutive model to reduce the number of costly high-fidelity simulations needed to produce accurate results. A new stress based degradation criterion is introduced for the degradation of individual material zones. This allows for the development of a heterogeneous damage distribution within the bulk material. Then a flow stress model is added to the hydrodynamic simulation to account for plasticity in quasi-brittle materials. As a result, the effective moduli model can be applied to a larger range of materials. The effective moduli constitutive model is used to simulate beryllium flyer plate experiments. The results from the continuum scale simulations using statistics from a single high-fidelity simulation are found to be in excellent agreement with numerical and experimental velocity interferometer data. The same set of crack statistics are used to extrapolate the results of a higher rate flyer plate case using the effective moduli model. The extension of this model to higher rate cases shows promise for further reducing the number of costly high-fidelity simulations needed to generate crack statistics.