Mesh size sensitivity of the combined FEM/DEM fracture and fragmentation algorithms

In the context of the combined finite-discrete element method a number of algorithms aimed at modelling progressive failure, fracture and fragmentation of solids under extreme loading conditions have been proposed in the last few years. The fracture patterns obtained by recently proposed algorithms are impressive. However, sensitivity of these algorithms to both mesh size and mesh orientation remains an open question. The aim of this paper is to further investigate sensitivity to mesh size of the recently proposed so called combined single and smeared crack model. Sensitivity to mesh orientation is outside scope of this paper and is discussed only qualitatively.     

A coupled FEM/DEM approach for hierarchical multiscale modelling of granular media

A hierarchical multiscale framework is proposed to model the mechanical behaviour of granular media. The framework employs a rigorous hierarchical coupling between the FEM and the discrete element method (DEM). To solve a BVP, the FEM is used to discretise the macroscopic geometric domain into an FEM mesh. A DEM assembly with memory of its loading history is embedded at each Gauss integration point of the mesh to serve as the representative volume element (RVE). The DEM assembly receives the global deformation at its Gauss point from the FEM as input boundary conditions and is solved to derive the required constitutive relation at the specific material point to advance the FEM computation. The DEM computation employs simple physically based contact laws in conjunction with Coulomb's friction for interparticle contacts to capture the loading‐history dependence and highly nonlinear dissipative response of a granular material. The hierarchical scheme helps to avoid the phenomenological assumptions on constitutive relation in conventional continuum modelling and retains the computational efficiency of FEM in solving large‐scale BVPs. The hierarchical structure also makes it ideal for distributed parallel computing to fully unleash its predictive power. Importantly, the framework offers rich information on the particle level with direct link to the macroscopic material response, which helps to shed lights on cross‐scale understanding of granular media. The developed framework is first benchmarked by a simulation of single‐element drained test and is then applied to the predictions of strain localisation for sand subject to monotonic biaxial compression, as well as the liquefaction and cyclic mobility of sand in cyclic simple shear tests. It is demonstrated that the proposed method may reproduce interesting experimental observations that are otherwise difficult to be captured by conventional FEM or pure DEM simulations, such as the inception of shear band under smooth symmetric boundary conditions, non‐coaxial granular response, large dilation and rotation at the edges of shear band and critical state reached within the shear band. Copyright © 2014 John Wiley & Sons, Ltd.     

Fracture and fragmentation of ice: a fractal analysis of scale invariance

The fracture and fragmentation processes of ice are reviewed using fractal concepts. Numerous evidences for the scale invariance of fracture and fragmentation patterns in ice are given, including fracture networks at small (laboratory) and large (geophysical) scales, the distribution of fragment sizes in crushed ice or the distribution of sea ice floe sizes, or self-affine fracture surfaces. These observations strongly argue for the scale invariance of fracture and fragmentation processes in ice. This implies that the fracture mechanisms and the physical parameters revealed at the laboratory scale are still relevant at large scale. However, apparent scale effects can be observed for some parameters if the fractal geometry is ignored or neglected. Scale invariance also implies that the homogenization procedures used in the damage mechanics of ice have to be taken with caution.     

Finite element simulations of kidney stones fragmentation by direct impact: Tool geometry and multiple impacts

This paper analyses the fragmentation of kidney stones by direct impact with Swiss Lithoclast Master®. Based on a previous work, the impact of the probe of the Lithoclast is modeled with a displacement control of the nodes inside the impacted area. Different computations are carried out focusing the efforts on new tentative designs of the cross section of the probe, as well as the influence of multiple impacts. The results show that a hollowed probe could improve the results obtained with the existing massive probe. Likewise, it is shown that there is an optimal internal radius of the hollowed probe for which the damage caused to the kidney stone is maximized. Finally the results demonstrate the existence of a synergetic effect of the application of multiple impacts at a high frequency.     

Simulating the pervasive fracture of materials and structures using randomly close packed Voronoi tessellations

Under extreme loading conditions most often the extent of material and structural fracture is pervasive in the sense that a multitude of cracks are nucleating, propagating in arbitrary directions, coalescing, and branching. Pervasive fracture is a highly nonlinear process involving complex material constitutive behavior, material softening, localization, surface generation, and ubiquitous contact. A pure Lagrangian computational method based on randomly close packed Voronoi tessellations is proposed as a rational and robust approach for simulating the pervasive fracture of materials and structures. Each Voronoi cell is formulated as a finite element using the Reproducing Kernel Method. Fracture surfaces are allowed to nucleate only at the intercell faces, and cohesive tractions are dynamically inserted. The randomly seeded Voronoi cells provide a regularized random network for representing fracture surfaces. Example problems are used to demonstrate the proposed numerical method. The primary numerical challenge for this class of problems is the demonstration of model objectivity and, in particular, the identification and demonstration of a measure of convergence for engineering quantities of interest. Sandia is a multi-program laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy’s National Nuclear Security Administration under Contract DE-AC04-94AL85000.     

Detonation gas model for combined finite‐discrete element simulation of fracture and fragmentation

The equation of state for expansion of detonation gas together with a model for gas flow through fracturing solid is proposed and implemented into the combined finite‐discrete element code. The equation of state proposed enables gas pressure to be obtained in a closed form for both reversible and irreversible adiabatic expansion, while the gas flow model proposed considers only 1D compressible flow through cracks, hence avoiding full 2D or 3D gas flow through the fracturing solid. When coupled with finite‐discrete element algorithms for solid fracture and fragmentation, the model proposed enables gas pressure to be predicted and energy balance to be preserved. Copyright © 2000 John Wiley & Sons, Ltd.     

Numerical comparison of some explicit time integration schemes used in DEM,FEM/DEM and molecular dynamics

Discontinua simulations are becoming an important part of Computational Mechanics to the extent that Computational Mechanics of Discontinua is becoming a separate subdiscipline of Computational Mechanics. Among the most widely used methods of Computational Mechanics of Discontinua are Discrete Element Methods, Molecular Dynamics Methods, Combined Finite‐Discrete Element Methods, DDA, Manifold Methods, etc. The common feature of all these methods is time discretization of the governing equations and the resulting mostly explicit time integration schemes. A wide range of time integration schemes is available in the literature. In this paper a comparative study of some of the most commonly used explicit time integration schemes is made in terms of accuracy, stability and CPU efficiency. The study has been performed using numerical experiments based on a one degree of freedom mass‐spring system. The results are presented as charts that can be used when deciding which scheme to use for a particular discontinua problem. Copyright © 2004 John Wiley & Sons, Ltd.     

Scaled boundary polygons with application to fracture analysis of functionally graded materials

This study presents a framework for the development of polygon elements based on the scaled boundary FEM. Underpinning this study is the development of generalized scaled boundary shape functions valid for any n‐sided polygon. These shape functions are continuous inside each polygon and across adjacent polygons. For uncracked polygons, the shape functions are linearly complete. For cracked polygons, the shape functions reproduce the square‐root singularity and the higher‐order terms in the Williams eigenfunction expansion. This allows the singular stress field in the vicinity of the crack tip to be represented accurately. Using these shape functions, a novel‐scaled boundary polygon formulation that captures the heterogeneous material response observed in functionally graded materials is developed. The stiffness matrix in each polygon is derived from the principle of virtual work using the scaled boundary shape functions. The material heterogeneity is approximated in each polygon by a polynomial surface in scaled boundary coordinates. The intrinsic properties of the scaled boundary shape functions enable accurate computation of stress intensity factors in cracked functionally graded materials directly from their definitions. The new formulation is validated, and its salient features are demonstrated, using five numerical benchmarks. Copyright © 2014 John Wiley & Sons, Ltd.     

Detection of fibre fracture and ply fragmentation in thin-ply UD carbon/glass hybrid laminates using acoustic emission

This paper investigates the link between acoustic emission (AE) events and the corresponding damage modes in thin-ply UD carbon/glass hybrid laminates under tensile loading. A novel configuration was investigated which has not previously been studied by AE, where the laminates were fabricated by embedding thin carbon plies between standard thickness translucent glass plies to produce progressive fragmentation of the carbon layer and delamination of the carbon/glass interface. A criterion based on amplitude and energy of the AE event values was established to identify the fragmentation failure mode. Since the glass layer was translucent, it was possible to quantitatively correlate the observed fragmentation during the tests and the AE events with high amplitude and energy values. This new method can be used as a simple and advanced tool to identify fibre fracture as well as estimate the number and sequence of damage events that are not visible e.g. in hybrid laminates with thick or non-transparent layers as well as when the damage is too small to be visually detected.     

Investigation of the fracture and fragmentation of explosively driven rings and cylinders

Cylinders and rings fabricated from AerMet^® 100 alloy and AISI 1018 steel have been explosively driven to fragmentation in order to determine the fracture strains for these materials under plane-strain and uniaxial-stress conditions. The phenomena associated with the dynamic expansion and subsequent break up of the cylinders are monitored with high-speed diagnostics. In addition, complementary experiments are performed in which fragments from the explosively driven cylinders are recovered and analyzed to determine the statistical distribution associated with the fragmentation process as well as to determine failure mechanisms. The data are used to determine relevant coefficients for the Hancock–McKenzie (Johnson–Cook) fracture model. Metallurgical analysis of the fragments provides information on damage and failure mechanisms.     

Bound theorem and implementation of dual finite elements for fracture assessment of piezoelectric materials

Owing to the complexity of piezoelectric crack problems, derivation of closed-form solutions is virtually impossible and numerical solutions are largely resorted to. Hence, the upper and lower bound estimation for piezoelectric fracture parameters are of theoretical and practical values. An alternative assessment approach for electromechanical coupling cracked system is suggested in the paper. The dual path-independent integrals and the related bound theorems are presented. Consequently, the dual piezoelectric finite elements are formulated and implemented in bound analysis.     

Fracture analysis of anisotropic materials using enriched crack tip elements

Enriched finite element methodology, which employs special crack tip elements, is extended for cracks in anisotropic materials. Enrichment formulation is described briefly and three validation examples using single crystal, directionally solidified, and orthotropic material properties are presented to demonstrate the accuracy and effectiveness of the methodology. In addition to validation examples, the effect of material anisotropy on stress intensity factors is investigated using the common compact tension specimen and the results are compared to the ASTM solution for isotropic materials. It is shown that the effect of anisotropy on the computed stress intensity factors can be significant, depending on the degree of anisotropy, material orientation, and a/W ratio in the compact tension specimen geometry.     

Reliable stress and fracture mechanics analysis of complex components using a h–p version of FEM

We develop effective approaches with which complex three-dimensional components may be analysed with a high and virtually guaranteed accuracy. The main computational tool is a h-p version of FEM practically realized with the p-version program STRIPE having a mesh generator for automatic mesh refinement at edges and vertices. Use of advanced extraction methods and new theoretical approaches give exponential convergence rates for accuracies in all engineering data of interest. New methods for reliable calculation of local stresses and stress intensity data at edges and vertices to be used for fatigue dimensioning at fillets, damage tolerance assessment of three-dimensional flaws, etc., are given. A complex real-life problem is reliably analysed in order to demonstrate the practical usefulness of the procedures advocated. The technical details will be given in forthcoming papers.     

Application of the X‐FEM to the fracture of piezoelectric materials

This paper presents an application of the extended finite element method (X‐FEM) to the analysis of fracture in piezoelectric materials. These materials are increasingly used in actuators and sensors. New applications can be found as constituents of smart composites for adaptive electromechanical structures. Under in service loading, phenomena of crack initiation and propagation may occur due to high electromechanical field concentrations. In the past few years, the X‐FEM has been applied mostly to model cracks in structural materials. The present paper focuses at first on the definition of new enrichment functions suitable for cracks in piezoelectric structures. At second, generalized domain integrals are used for the determination of crack tip parameters. The approach is based on specific asymptotic crack tip solutions, derived for piezoelectric materials. We present convergence results in the energy norm and for the stress intensity factors, in various settings. Copyright © 2008 John Wiley & Sons, Ltd.     

Fracture and fragmentation of thin shells using the combined finite–discrete element method

A model for fracture and fragmentation of multilayered thin shells has been developed and implemented into the combined finite–discrete element code. The proposed model incorporates an extension of the original combined single and smeared fracture approach to multilayered thin shells; it then combines these with an interaction algorithm that is based on the original distributed potential contact force approach. The developed contact kinematics preserves both energy and momentum balance, whereas the developed fracture model is capable of modelling complex fracture patterns such as fracture of laminated glass under impact. Copyright © 2013 John Wiley & Sons, Ltd.     

Anisotropic dynamic damage and fragmentation of rock materials under explosive loading

This paper describes the development of a constitutive model for predicting dynamic anisotropic damage and fragmentation of rock materials under blast loading. In order to take account of the anisotropy of damage, a second rank symmetric damage tensor is introduced in the present model. Based on the mechanics of microcrack nucleation, growth and coalescence, the evolution of damage is formulated. The model provides a quantitative method to estimate the fragment distribution and fragment size generated by crack coalescence in the dynamic fragmentation process. It takes account of the experimental facts that a brittle rock material does not fail if the applied stress is lower than its static strength and certain time duration is needed for fracture to take place when it is subjected to a stress higher than its static strength. Numerical results are compared with those from independent field tests.     

Three-dimensional reconstruction and homogenization of heterogeneous materials using statistical correlation functions and FEM

In this study, a previously developed reconstruction methodology is extended to three-dimensional reconstruction of a three-phase microstructure, based on two-point correlation functions and two-point cluster functions. The reconstruction process has been implemented based on hybrid stochastic methodology for simulating the virtual microstructure. While different phases of the heterogeneous medium are represented by different cells, growth of these cells is controlled by optimizing parameters such as rotation, shrinkage, translation, distribution and growth rates of the cells. Based on the reconstructed microstructure, finite element method (FEM) was used to compute the effective elastic modulus and effective thermal conductivity. A statistical approach, based on two-point correlation functions, was also used to directly estimate the effective properties of the developed microstructures. Good agreement between the predicted results from FEM analysis and statistical methods was found confirming the efficiency of the statistical methods for prediction of thermo-mechanical properties of three-phase composites.     

Modal analysis of carbon nanotubes and nanocones using FEM

Modal analysis of single-walled carbon nanotubes (SWCNTs) and nanocones (SWCNCs) was performed using a finite element method (FEM) with ANSYS. The vibrational behaviors of fixed beam and cantilever SWCNTs with different section types of a circle and an ellipse were modeled using three-dimensional elastic beams of carbon bonds and point masses. Also, the vibrational behaviors of fixed beam and cantilever SWCNCs with different disclination angles of 120°, 180°, and 240° were modeled using the same method. The beam element natural frequencies were calculated by considering the mechanical characteristics of the covalent bonds between the carbon atoms in the hexagonal lattice. Each mass element of the carbon atoms was assigned as a point mass at the nodes of the FEM elements. The natural frequencies of zigzag and armchair SWCNTs and SWCNCs were also computed. There were some differences between the findings obtained in this study and the molecular structural mechanics data available in the literature. The natural frequencies of SWCNCs were estimated depending on the geometrical type and disclination angle with different boundary conditions. The natural frequencies of the SWCNCs with disclination angles of 120°, 180°, and 240° increased significantly at higher modes of vibration.     

Development of a new model for representing elastoplastic deformation and fracture behaviors of solid fats

A new simulation model, namely, ADEM Ductile Fracture model (ADF model) is developed to represent elastoplastic deformation and fracture behaviors of solid fats. Experimental measurement of the coefficient of plastic starting distance and the yield point affecting the deformation behavior has been obtained by compression test. The fracture distance affecting the fracture behavior has been measured by cutting test. The ADF model shows a good match with the experimentally determined compression and cutting behaviors of the solid fats, and load–strain curves as a function of plate thickness. This confirms that the ADF model could represent the elastoplastic deformation and fracture behaviors of the solid fats.