Issue 39

J. Eliáš, Frattura ed Integrità Strutturale, 39 (2017) 1-6; DOI: 10.3221/IGF-ESIS.39.01 1 Focussed on Modelling in Mechanics On adaptive refinements in discrete probabilistic fracture models J. Eliáš Brno University of Technology, Faculty of Civil Engineering, Veveří 331/95, Brno, 60200, Czech Republic elias.j@fce.vutbr.cz A BSTRACT . The possibility to adaptively change discretization density is a well acknowledged and used feature of many continuum models. It is employed to save computational time and increase solution accuracy. Recently, adaptivity has been introduced also for discrete particle models. This contribution applies adaptive technique in probabilistic discrete modelling where material properties are varying in space according to a random field. The random field discretization is adaptively refined hand in hand with the model geometry. K EYWORDS . Adaptivity; Discrete model; Probability; Random field. Citation: Eliáš, J., On adaptive refinements in discrete probabilistic fracture models, Frattura ed Integrità Strutturale, 39 (2017) 1-6. Received: 11.07.2016 Accepted: 12.09.2016 Published: 01.01.2017 Copyright: © 2017 This is an open access article under the terms of the CC-BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. I NTRODUCTION he adaptivity of model geometry has been originally developed for elastic problems [1,2] and later applied also in inelastic problems with localization [3,4]. The classical rigorous approach involves an error estimation, remeshing criterion, mesh re-generation and transfer of variables onto the new mesh. Recently, the adaptive concept was applied also in discrete modelling [5]. The goal of this work is to extend it for probabilistic discrete models. Discrete models represent the material via collection of interconnected rigid bodies organized into a net structure. There are several versions of discrete models developed and used for many purposes. In case of simulating fracture in concrete, the lattice models are often employed [6-8]. These models represent the concrete meso-structure by projecting it onto the independently generated lattice. They are excellent in describing fracture phenomena, but applicable only for small laboratory specimens due to their extreme computational demands. Another group of discrete meso-level modelling approaches, sometimes called particle models, generates the network geometry directly according to the meso-structure of concrete [9,10]; typically one node for each mineral aggregate. We focus here on the latter group with geometry generated via Voronoi tessellation [11-14]. Though some reduction of computational cost in particle models is achieved when compared to the lattice models, further reduction would be desirable. It can be done by adaptive construction of the discrete geometry as described in [5]. Availability of adaptive refinement allows starting simulation with coarse discretization and refining it adaptively during the simulation run only in areas where needed. T