The Simulation and Modelling of the Crack Path of Biomaterials

2011 ◽  
Vol 465 ◽  
pp. 141-144
Author(s):  
Sebastian Stach
Keyword(s):  
Fracture Surface ◽  
Spanning Tree ◽  
Crack Path ◽  
Quantitative Description ◽  
Three Dimensional ◽  
Minimal Spanning Tree ◽  
Simulation And Modelling ◽  
Metallic Biomaterial ◽  
Cracking Process

Analysis of issues related to the cracking process of materials requires a quantitative description of the problem which frequently, due to its complexity, is difficult or impossible to solve. In a number of cases, the deficiencies of a quantitative description made using classical methods are compensated for by such unconventional tools as percolation, which requires creating an appropriate model. The aim of the study was to use a three-dimensional minimal spanning tree (3DMST) to create a model of the crack path, based on an example of a metallic biomaterial. For this purpose, a stereometric file, obtained as a result of measuring its fracture surface, was applied.

FSAT - An Open-Source Fracture Surface Analysis Toolbox

2021 ◽  
Author(s):  
Thomas Heinze ◽  
Sascha Frank ◽  
Stefan Wohnlich
Keyword(s):  
Fracture Surface ◽  
Open Source ◽  
Quantitative Description ◽  
Three Dimensional ◽  
Fracture Morphology ◽  
Roughness Parameters ◽  
Statistical Parameters ◽  
Rock Samples ◽  
Fracture Surfaces ◽  
Custom Made

<p>Fracture morphology influences various physical processes within a fracture, such as fluid flow, contaminant, and heat transport as well as mechanical shearing. Through the increasing availability of affordable high-precision scanning technology of open surfaces, drill cores, and broken rock samples, digital rock surfaces are easy to obtain and become a common tool to study hydraulic and mechanical processes inside fractures. Through statistical fracture generation and 3D printing technology, even custom-made fracture surfaces have been applied in numerous studies.</p><p>However, the complexity to describe and quantify fracture surface morphology is a major obstacle in evaluating and comparing results from laboratory and numerical experiments across studies and rock samples. While many so-called roughness parameters exist, there is no single parameter representing all features of a fracture surface. Only through a combination of parameters, which often is problem depending, a fracture surface can be suitably characterized to enable reproducibility of experiments and analysis across samples and studies. The effort of calculating various parameters is impeding scientists to sufficiently and quantitatively describe fracture surfaces.</p><p>We introduce an open-source MATLAB toolbox that allows the determination of over 25 different roughness parameters for height profiles as well as full 3D fracture surfaces. The selection of parameters includes statistical parameters, amplitude and spatial metrics, joint roughness coefficients, and fractal parameters. Variation of those parameters across as fracture surface as well as anisotropy is also calculated. For three-dimensional profiles, also surface measures are determined. If the top and bottom surfaces of a fracture are provided, even an estimated aperture distribution can be obtained, which is analyzed as well as provided for subsequent calculations, e.g., regarding the flow field. Further, the toolbox includes pre-processing routines for digital fracture surfaces of different sizes, shapes, and orientations. The toolbox is validated with standard profiles and synthetically generated fractures with known characteristics.</p><p>The toolbox massively simplifies the quantitative description of fracture surfaces, unifies the methodology of determining roughness parameters, and allows an easy generation of digital fractures with known characteristics. On the other hand, the toolbox enables easy customization for advanced users with specific demands. The toolbox consists of well-documented MATLAB scripts and functions that require a minimum of user-defined metadata. Extensive examples are also provided. The source code is freely available for download at https://gitlab.com/thomhGeoCode/fsat</p>

DEVELOPING PROXIMITY GRAPHS BY PHYSARUM POLYCEPHALUM: DOES THE PLASMODIUM FOLLOW THE TOUSSAINT HIERARCHY?

2009 ◽  
Vol 19 (01) ◽  
pp. 105-127 ◽  
Author(s):  
ANDREW ADAMATZKY
Keyword(s):  
Foraging Behavior ◽  
Delaunay Triangulation ◽  
Spanning Tree ◽  
Physarum Polycephalum ◽  
Minimum Spanning Tree ◽  
Nearest Neighbour ◽  
Minimal Spanning Tree ◽  
Proximity Graphs ◽  
Relative Neighborhood Graph ◽  
Plasmodium Of Physarum Polycephalum

Plasmodium of Physarum polycephalum spans sources of nutrients and constructs varieties of protoplasmic networks during its foraging behavior. When the plasmodium is placed on a substrate populated with sources of nutrients, it spans the sources with protoplasmic network. The plasmodium optimizes the network to deliver efficiently the nutrients to all parts of its body. How exactly does the protoplasmic network unfold during the plasmodium's foraging behavior? What types of proximity graphs are approximated by the network? Does the plasmodium construct a minimal spanning tree first and then add additional protoplasmic veins to increase reliability and through-capacity of the network? We analyze a possibility that the plasmodium constructs a series of proximity graphs: nearest-neighbour graph (NNG), minimum spanning tree (MST), relative neighborhood graph (RNG), Gabriel graph (GG) and Delaunay triangulation (DT). The graphs can be arranged in the inclusion hierarchy (Toussaint hierarchy): NNG ⊆ MST ⊆ RNG ⊆ GG ⊆ DT . We aim to verify if graphs, where nodes are sources of nutrients and edges are protoplasmic tubes, appear in the development of the plasmodium in the order NNG → MST → RNG → GG → DT , corresponding to inclusion of the proximity graphs.

A Constrained Delaunay Triangulation Algorithm Based on Incremental Points

2011 ◽  
Vol 90-93 ◽  
pp. 3277-3282 ◽  
Author(s):  
Bai Chao Wu ◽  
Ai Ping Tang ◽  
Lian Fa Wang
Keyword(s):  
Information System ◽  
Data Structures ◽  
Delaunay Triangulation ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Three Dimensional ◽  
Geographical Information ◽  
Two Dimensional ◽  
Data Set ◽  
Constrained Delaunay Triangulation

The foundation ofdelaunay triangulationandconstrained delaunay triangulationis the basis of three dimensional geographical information system which is one of hot issues of the contemporary era; moreover it is widely applied in finite element methods, terrain modeling and object reconstruction, euclidean minimum spanning tree and other applications. An algorithm for generatingconstrained delaunay triangulationin two dimensional planes is presented. The algorithm permits constrained edges and polygons (possibly with holes) to be specified in the triangulations, and describes some data structures related to constrained edges and polygons. In order to maintain the delaunay criterion largely，some new incremental points are added onto the constrained ones. After the data set is preprocessed, the foundation ofconstrained delaunay triangulationis showed as follows: firstly, the constrained edges and polygons generate initial triangulations，then the remained points completes the triangulation . Some pseudo-codes involved in the algorithm are provided. Finally, some conclusions and further studies are given.

Minimal spanning tree subject to a side constraint

1982 ◽  
Vol 9 (4) ◽  
pp. 287-296 ◽  
Author(s):  
V. Aggarwal ◽  
Y.P. Aneja ◽  
K.P.K. Nair
Keyword(s):  
Spanning Tree ◽  
Minimal Spanning Tree ◽  
Side Constraint
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