Fragmentation of a Circular Disc by Impact on a Frictionless Plate

The break-up of a two-dimensional circular disc by normal and oblique impact on a hard frictionless plate is investigated by molecular dynamics simulations. The disc is composed of numerous unbreakable randomly shaped convex polygons connected together by simple elastic beams that break when bent or stretched beyond a certain limit. It is found that for both normal and oblique impacts the crack patterns are the same and depend solely on the normal component of the impact velocity. Analysing the pattern of breakage, amount of damage, fragment masses and velocities, we show the existence of a critical velocity which separates two regimes of the impact process: below the critical point only a damage cone is formed at the impact site (damage), cleaving of the particle occurs at the critical point, while above the critical velocity the disc breaks into several pieces (fragmentation). In the limit of very high impact velocities the disc suffers complete disintegration (shattering) into many small fragments. In agreement with experimental results, fragment masses are found to follow the Gates-Gaudin-Schuhmann distribution (power law) with an exponent independent of the velocity and angle of impact. The velocity distribution of fragments exhibit an interesting anomalous scaling behavior when changing the impact velocity and the size of the disc.Comment: submitted to J. Phys: Condensed Matter special issue on Granular Medi

A quadtree-polygon-based scaled boundary finite element method for image-based mesoscale fracture modelling in concrete

A quadtree-polygon scaled boundary finite element-based approach for image-based modelling of concrete fracture at the mesoscale is developed. Digital images representing the two-phase mesostructure of concrete, which comprises of coarse aggregates and mortar are either generated using a take-and-place algorithm with a user-defined aggregate volume ratio or obtained from X-ray computed tomography as an input. The digital images are automatically discretised for analysis by applying a balanced quadtree decomposition in combination with a smoothing operation. The scaled boundary finite element method is applied to model the constituents in the concrete mesostructure. A quadtree formulation within the framework of the scaled boundary finite element method is advantageous in that the displacement compatibility between the cells are automatically preserved even in the presence of hanging nodes. Moreover, the geometric flexibility of the scaled boundary finite element method facilitates the use of arbitrary sided polygons, allowing better representation of the aggregate boundaries. The computational burden is significantly reduced as there are only finite number of cell types in a balanced quadtree mesh. The cells in the mesh are connected to each other using cohesive interface elements with appropriate softening laws to model the fracture of the mesostructure. Parametric studies are carried out on concrete specimens subjected to uniaxial tension to investigate the effects of various parameters e.g. aggregate size distribution, porosity and aggregate volume ratio on the fracture of concrete at the meso-scale. Mesoscale fracture of concrete specimens obtained from X-ray computed tomography scans are carried out to demonstrate its feasibility

Fragmentation processes in impact of spheres

We study the brittle fragmentation of spheres by using a three-dimensional Discrete Element Model. Large scale computer simulations are performed with a model that consists of agglomerates of many particles, interconnected by beam-truss elements. We focus on the detailed development of the fragmentation process and study several fragmentation mechanisms. The evolution of meridional cracks is studied in detail. These cracks are found to initiate in the inside of the specimen with quasi-periodic angular distribution. The fragments that are formed when these cracks penetrate the specimen surface give a broad peak in the fragment mass distribution for large fragments that can be fitted by a two-parameter Weibull distribution. This mechanism can only be observed in 3D models or experiments. The results prove to be independent of the degree of disorder in the model. Our results significantly improve the understanding of the fragmentation process for impact fracture since besides reproducing the experimental observations of fragment shapes, impact energy dependence and mass distribution, we also have full access to the failure conditions and evolution

What Is the Exact Contribution of PITX1 and TBX4 Genes in Clubfoot Development? An Italian Study

Congenital clubfoot is a common pediatric malformation that affects approximately 0.1% of all births. 80% of the cases appear isolated, while 20% can be secondary or associated with complex syndromes. To date, two genes that appear to play an important role are PTIX1 and TBX4, but their actual impact is still unclear. Our study aimed to evaluate the prevalence of pathogenic variants in PITX1 and TBX4 in Italian patients with idiopathic clubfoot. PITX1 and TBX4 genes were analyzed by sequence and SNP array in 162 patients. We detected only four nucleotide variants in TBX4, predicted to be benign or likely benign. CNV analysis did not reveal duplications or deletions involving both genes and intragenic structural variants. Our data proved that the idiopathic form of congenital clubfoot was rarely associated with mutations and CNVs on PITX1 and TBX4. Although in some patients, the disease was caused by mutations in both genes; they were responsible for only a tiny minority of cases, at least in the Italian population. It was not excluded that other genes belonging to the same TBX4-PITX1 axis were involved, even if genetic complexity at the origin of clubfoot required the involvement of other factors

Evaluation of Mode I Fracture Toughness Assisted by the Numerical Determination of K-Resistance

The fracture toughness of a rock often varies depending on the specimen shape and the loading type used to measure it. To investigate the mode I fracture toughness using semi-circular bend (SCB) specimens, we experimentally studied the fracture toughness using SCB and chevron bend (CB) specimens, the latter being one of the specimens used extensively as an International Society for Rock Mechanics (ISRM) suggested method, for comparison. The mode I fracture toughness measured using SCB specimens is lower than both the level I and level II fracture toughness values measured using CB specimens. A numerical study based on discontinuum mechanics was conducted using a two-dimensional distinct element method (DEM) for evaluating crack propagation in the SCB specimen during loading. The numerical results indicate subcritical crack growth as well as sudden crack propagation when the load reaches the maximum. A K-resistance curve is drawn using the crack extension and the load at the point of evaluation. The fracture toughness evaluated by the K-resistance curve is in agreement with the level II fracture toughness measured using CB specimens. Therefore, the SCB specimen yields an improved value for fracture toughness when the increase of K-resistance with stable crack propagation is considered

A Review of Computational Methods in Materials Science: Examples from Shock-Wave and Polymer Physics

This review discusses several computational methods used on different length and time scales for the simulation of material behavior. First, the importance of physical modeling and its relation to computer simulation on multiscales is discussed. Then, computational methods used on different scales are shortly reviewed, before we focus on the molecular dynamics (MD) method. Here we survey in a tutorial-like fashion some key issues including several MD optimization techniques. Thereafter, computational examples for the capabilities of numerical simulations in materials research are discussed. We focus on recent results of shock wave simulations of a solid which are based on two different modeling approaches and we discuss their respective assets and drawbacks with a view to their application on multiscales. Then, the prospects of computer simulations on the molecular length scale using coarse-grained MD methods are covered by means of examples pertaining to complex topological polymer structures including star-polymers, biomacromolecules such as polyelectrolytes and polymers with intrinsic stiffness. This review ends by highlighting new emerging interdisciplinary applications of computational methods in the field of medical engineering where the application of concepts of polymer physics and of shock waves to biological systems holds a lot of promise for improving medical applications such as extracorporeal shock wave lithotripsy or tumor treatment

Discrete element method to simulate continuous material by using the cohesive beam model

The mechanical behavior of materials is usually simulated by the continuous mechanics approach. However, simulation of non-continuous phenomena like multi fracturing is not well adapted to a continuous description. In this case, the discrete element method (DEM) is a good alternative because it naturally takes into account discontinuities. Many researchers have shown interest in this approach for wear and fracture simulation. The problem is that, while DEM is well adapted to simulate discontinuities, it is not suitable to simulate continuous behavior. In problems of wear or fracture, material is composed of continuous parts and discontinuous interfaces. The aim of the present work is to improve the ability of DEM to simulate the continuous part of the material using cohesive bond model. Continuous mechanics laws cannot be used directly within a DEM formulation. A second difficulty is that the volume between the discrete elements creates an artificial void inside thematerial. This paper proposes a methodology that tackles these theoretical difficulties and simulates, using a discrete element model, any material defined by a Young’s modulus, Poisson’s ratio and density, to fit the static and dynamic mechanical behavior of the material. The chosen cohesive beam model is shown to be robust concerning the influence of the discrete element sizes. This method is applied to a material which can be considered as perfectly elastic: fused silica