Related papers: Quasi-Static Fractures in Disordered Media and Ite…
The method of iterated conformal maps is developed for quasi-static fracture of brittle materials, for all modes of fracture. Previous theory, that was relevant for mode III only, is extended here to mode I and II. The latter require…
The dynamics of a single crack moving through a heterogeneous medium is studied in the quasi-static approximation. Equations of motion for the crack front are formulated and the resulting scaling behaviour analyzed. In a model scalar system…
Fracture in quasi-statically driven systems is studied by means of a discrete spring-block model. Developed from close comparison with desiccation experiments, it describes crack formation induced by friction on a substrate. The model…
We study size effects in the fracture strength of notched disordered samples using numerical simulations of lattice models for fracture. In particular, we consider the random fuse model, the random spring model and the random beam model,…
Fracture involves interaction across large and small length scales. With the application of enough stress or strain to a brittle material, atomistic scale bonds will break, leading to fracture of the macroscopic specimen. From the…
We investigate the fracture behavior of pre-cracked triangular beam-lattices whose elements have failure stresses drawn from a Weibull distribution. Through a statistical analysis and numerical simulations, we identify and verify the…
Materials with network-like microstructure, including polymers, are the backbone for many natural and human-made materials such as gels, biological tissues, metamaterials, and rubbers. Fracture processes in these networked materials are…
We study three quasicontinuum approximations of a lattice model for crack propagation. The influence of the approximation on the bifurcation patterns is investigated. The estimate of the modeling error is applicable to near and beyond…
We introduce a model for fractures in quenched disordered media. This model has a deterministic extremal dynamics, driven by the energy function of a network of springs (Born Hamiltonian). The breakdown is the result of the cooperation…
The roughness of crack interfaces is reported in quasistatic fracture, using an elastic network of beams with random breaking thresholds. For strong disorders we obtain 0.86(3) for the roughness exponent, a result which is very different…
Predicting the mechanics of large structural networks, such as beam-based architected materials, requires a multiscale computational strategy that preserves information about the discrete structure while being applicable to large assemblies…
Fracture paths in quasi-two-dimenisonal (2D) media (e.g thin layers of materials, paper) are analyzed as self-affine graphs $h(x)$ of height $h$ as a function of length $x$. We show that these are multiscaling, in the sense that $n^{th}$…
We study the fracture surface of three dimensional samples through a model for quasi-static fractures known as Born Model. We find for the roughness exponent a value of 0.5 expected for ``small length scales'' in microfracturing…
Colloidal and other granular media experience a transition to rigidity known as jamming if the fill fraction is increased beyond a critical value. The resulting jammed structures are locally disordered, bear applied loads inhomogenously,…
This paper presents two main results. The first result indicates that in materials with broadly distributed microscopic heterogeneities, the fracture strength distribution corresponding to the peak load of the material response does not…
Disorder and long-range interactions are two of the key components that make material failure an interesting playfield for the application of statistical mechanics. The cornerstone in this respect has been lattice models of the fracture in…
We establish quantitative stability results for classical distortion minimization problems in the theory of quasiconformal mappings. We consider the mean distortion functional and prove sharp stability estimates for the minimization…
Multi-phase materials, such as composite materials, exhibit multiple competing failure mechanisms during the growth of a macroscopic defect. For the simulation of the overall fracture process in such materials, we develop a two-phase spring…
Composites with high strength and high fracture resistance are desirable for structural and protective applications. Most composites, however, suffer from poor damage tolerance and are prone to unpredictable fractures. Understanding the…
The problem of crack pattern formation due to thermal shock loading at the surface of half-space is solved numerically using two-dimensional boundary element method. The results of numerical simulations with 100-200 random simultaneously…