High-resolution brittle fracture simulation with boundary elements

We present a method for simulating brittle fracture under the assumptions of quasi-static linear elastic fracture mechanics (LEFM). Using the boundary element method (BEM) and Lagrangian crack-fronts, we produce highly detailed fracture surfaces. The computational cost of the BEM is alleviated by using a low-resolution mesh and interpolating the resulting stress intensity factors when propagating the high-resolution crack-front. Our system produces physics-based fracture surfaces with high spatial and temporal resolution, taking spatial variation of material toughness and/or strength into account. It also allows for crack initiation to be handled separately from crack propagation, which is not only more reasonable from a physics perspective, but can also be used to control the simulation. Separating the resolution of the crack-front from the resolution of the computational mesh increases the efficiency and therefore the amount of visual detail on the resulting fracture surfaces. The BEM also allows us to re-use previously computed blocks of the system matrix

Strain injection techniques in dynamic fracture modeling

A computationally affordable modeling of dynamic fracture phenomena is performed in this study by using strain injection techniques and Finite Elements with Embedded strong discontinuities (E-FEM). In the present research, classical strain localization and strong discontinuity approaches are considered by injecting discontinuous strain and displacement modes in the finite element formulation without an increase of the total number of degrees of freedom. Following the Continuum Strong Discontinuity Approach (CSDA), stress–strain constitutive laws can be employed in the context of fracture phenomena and, therefore, the methodology remains applicable to a wide number of continuum mechanics models. The position and orientation of the displacement discontinuity is obtained through the solution of a crack propagation problem, i.e. the crack path field, based on the distribution of localized strains. The combination of the above mentioned approaches is envisaged to avoid stress-locking and directional mesh bias phenomena. Dynamic simulations are performed increasing the loading rate up to the appearance of crack branching, and the variation in terms of failure modes is investigated as well as the influence of the strain injection together with the crack path field algorithm. Objectivity of the presented methodology with respect to the spatial and temporal discretization is analyzed in terms of the dissipated energy during the fracture process. The dissipation at the onset of branching is studied for different loading rate conditions and is linked to the experimental maximum velocity observed before branching takes place.Fil: Lloberas Valls, Oriol. Universidad Politecnica de Catalunya; España. Centre Internacional de Metodes Numerics en Enginyeria; EspañaFil: Huespe, Alfredo Edmundo. Centre Internacional de Metodes Numerics en Enginyeria; España. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Centro de Investigaciones en Métodos Computacionales. Universidad Nacional del Litoral. Centro de Investigaciones en Métodos Computacionales; ArgentinaFil: Oliver, J.. Centre Internacional de Metodes Numerics en Enginyeria; España. Universidad Politecnica de Catalunya; EspañaFil: Dias, I.F.. Laboratório Nacional de Engenharia Civil; Portuga

Micro computed tomography based finite element models of calcium phosphate scaffolds for bone tissue engineering

Bone is a living tissue that is able to regenerate by itself. However, when severe bone defects occur, the natural regeneration may be impaired. In these cases, bone graft substitutes can be used to induce the natural healing process. As a scaffold for tissue engineering, these bone graft substitutes have to meet specific requirements. Among others, the material must be biocompatible, biodegradable and have a porous structure to allow vascularization, cell migration and formation of new bone. Additionally, the mechanical properties of the scaffold have to resemble the ones of native tissue. The goal of this project is to create a computational model of the calcium phosphate scaffolds that are produced by rapid-prototyping by the Biomaterials, Biomechanics, and Tissue Engineering group at the Technical University of Catalonia. These models are based on finite element analysis and micro computed tomography images in order to consider the actual architecture of the scaffolds. The generated FE-models allow the computation of both local strains, which act as mechanical stimuli on attached cells, as well as the behaviour of the entire scaffold. When considering this information, the scaffold can be optimized for tissue differentiation by tuning both the scaffold architecture and the scaffold material bulk properties.Incomin

A variational model of fracture for tearing brittle thin sheets

Tearing of brittle thin elastic sheets, possibly adhered to a substrate, involves a rich interplay between nonlinear elasticity, geometry, adhesion, and fracture mechanics. In addition to its intrinsic and practical interest, tearing of thin sheets has helped elucidate fundamental aspects of fracture mechanics including the mechanism of crack path selection. A wealth of experimental observations in different experimental setups is available, which has been often rationalized with insightful yet simplified theoretical models based on energetic considerations. In contrast, no computational method has addressed tearing in brittle thin elastic sheets. Here, motivated by the variational nature of simplified models that successfully explain crack paths in tearing sheets, we present a variational phase-field model of fracture coupled to a nonlinear Koiter thin shell model including stretching and bending. We show that this general yet straightforward approach is able to reproduce the observed phenomenology, including spiral or power-law crack paths in free standing films, or converging/diverging cracks in thin films adhered to negatively/positively curved surfaces, a scenario not amenable to simple models. Turning to more quantitative experiments on thin sheets adhered to planar surfaces, our simulations allow us to examine the boundaries of existing theories and suggest that homogeneous damage induced by moving folds is responsible for a systematic discrepancy between theory and experiments. Thus, our computational approach to tearing provides a new tool to understand these complex processes involving fracture, geometric nonlinearity and delamination, complementing experiments and simplified theories.Fil: Li, Bin. Universidad Politécnica de Catalunya; España. Sorbonne Université; Francia. Centre National de la Recherche Scientifique; FranciaFil: Millán, Raúl Daniel. Universidad Nacional de Cuyo. Facultad de Ciencias Aplicadas a la Industria; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza; Argentina. Universidad Politécnica de Catalunya; EspañaFil: Torres Sánchez, Alejandro. Universidad Politécnica de Catalunya; EspañaFil: Roman, Benoît. Centre National de la Recherche Scientifique; Francia. Sorbonne Université; FranciaFil: Arroyo Balaguer, Marino. Universidad Politécnica de Catalunya; Españ

Voronoi cell finite element modelling of the intergranular fracture mechanism in polycrystalline alumina

The mechanisms of fracture in polycrystalline alumina were investigated at the grain level using both the micromechanical tests and finite element (FE) model. First, the bending experiments were performed on the alumina microcantilever beams with a controlled displacement rate of 10 nm s–1 at the free end; it was observed that the intergranular fracture dominates the failure process. The full scale 3D Voronoi cell FE model of the microcantilever bending tests was then developed and experimentally validated to provide the insight into the cracking mechanisms in the intergranular fracture. It was found that the crystalline morphology and orientation of grains have a significant impact on the localised stress in polycrystalline alumina. The interaction of adjacent grains as well as their different orientations determines the localised tensile and shear stress state in grain boundaries. In the intergranular fracture process, the crack formation and propagation are predominantly governed by tensile opening (mode I) and shear sliding (mode II) along grain boundaries. Additionally, the parametric FE predictions reveal that the bulk failure load of the alumina microcantilever increases with the cohesive strength and total fracture energy of grain boundaries

Quasicontinuum simulation of fracture at the atomic scale

We study the problem of atomic scale fracture using the recently developed quasicontinuum method in which there is a systematic thinning of the atomic-level degrees of freedom in regions where they are not needed. Fracture is considered in two distinct settings. First, a study is made of cracks in single crystals, and second, we consider a crack advancing towards a grain boundary (GB) in its path. In the investigation of single crystal fracture, we evaluate the competition between simple cleavage and crack-tip dislocation emission. In addition, we examine the ability of analytic models to correctly predict fracture behaviour, and find that the existing analytical treatments are too restrictive in their treatment of nonlinearity near the crack tip. In the study of GB-crack interactions, we have found a number of interesting deformation mechanisms which attend the advance of the crack. These include the migration of the GB, the emission of dislocations from the GB, and deflection of the crack front along the GB itself. In each case, these mechanisms are rationalized on the basis of continuum mechanics arguments