Related papers: Fracture Surfaces as Multiscaling Graphs
Flow in fractured porous media is modeled frequently by discrete fracture-matrix approaches where fractures are treated as dimensionally reduced manifolds. Generalizing earlier work we focus on two-phase flow in time-dependent fracture…
Variational phase-field models of brittle fracture are powerful tools for studying Griffith-type crack propagation in complex scenarios. However, as approximations of Griffith's theory-which does not incorporate a strength criterion-these…
It is shown here that fracture after a brief plastic strain, typically of a few percents, is a necessary consequence of the polycrystalline nature of the materials. The polycrystal undergoing plastic deformation is modeled as a flowing…
A two-dimensional (2D) dislocation continuum theory is being introduced. The present theory adds elastic rotation, dislocation density, and background stress to the classical energy density of elasticity. This theory contains four material…
We study experimentally the fracture mechanisms of a model cohesive granular medium consisting of glass beads held together by solidified polymer bridges. The elastic response of this material can be controlled by changing the cross-linking…
Over the last decade, finite volume discretizations for flow in porous media have been extended to handle situations where fractures dominate the flow. These discretizations have successfully been combined with the discrete fracture-matrix…
In this paper, we investigate crossing-free 3D morphs between planar straight-line drawings. We show that, for any two (not necessarily topologically equivalent) planar straight-line drawings of an $n$-vertex planar graph, there exists a…
Rayleigh scattering has shown powerful abilities to study electron resonances of nanomaterials regardless of the specific shapes. In analogy to Rayleigh scattering, here we demonstrate that edge optical scattering from two-dimensional (2D)…
A new geometrically exact micro-structured model is constructed using a generalisation of the notion of Riemann-Cartan manifolds and fibre bundle theory of rank 3. This model is based around the concept of two different length scales: a…
Building upon [1], this study aims to introduce fractal geometry into graph theory, and to establish a potential theoretical foundation for complex networks. Specifically, we employ the method of substitution to create and explore…
A fiber bundle model in $(1+1)$-dimensions for the breaking of fibrous composite matrix is introduced. The model consists of $N$ parallel fibers fixed in two plates. When one of the plates is pulled in the direction parallel to the fibers,…
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…
We review microstructural fracture growth models suitable for the study of hydraulic fracture processes in disordered porous materials and present some basic results. It is shown that microstructural models exhibit certain similarities to…
Two-dimensional random surfaces are studied numerically by the dynamical triangulation method. In order to generate various kinds of random surfaces, two higher derivative terms are added to the action. The phases of surfaces in the…
We study propagating mode-I fracture in two dimensional amorphous materials using atomistic simulations. We used the continuous random network (CRN) model of an amorphous material, creating samples using a two dimensional analogue of the…
Graphene-based papers attract particular interests recently owing to their outstanding properties, the key of which is their layer-by-layer hierarchical structures similar to the biomaterials such as bone, teeth and nacre, combining…
We consider numerical solution of elliptic problems with heterogeneous diffusion coefficients containing thin highly conductive structures. Such problems arise e.g. in fractured porous media, reinforced materials, and electric circuits. The…
The interstellar medium is structured as a hierachy of gas clouds, that looks self-similar over 6 orders of magnitude in scales and 9 in masses. This is one of the more extended fractal in the Universe. At even larger scales, the ensemble…
A two-dimensional (2D) topological semimetal is characterized by the nodal points in its low-energy band structure. While the linear nodal points have been extensively studied, especially in the context of graphene, the realm beyond linear…
Graphene and some graphene like two dimensional materials; hexagonal boron nitride (hBN) and silicene have unique mechanical properties which severely limit the suitability of conventional theories used for common brittle and ductile…