Abstract:In this paper, a finite element model including both material heterogeneity and size effects is presented. The concrete is considered as a statistical combination of constituent phase with different properties (aggregate, mortar and interface material). The material point response is based on a combination of the random occurrence of the solid phases in the structural volume as well as on the differences of structural response due to the size effect. Such combination allows for higher or lower heterogeneity co… Show more
“…Although lacking of predictability, the authors concluded that the model is suitable for rock mechanics. A statistical approach for modelling heterogeneous concrete, where the different phases were represented by a statistical distribution of constituent phases, has previously been developed within the framework of FEM [36]. For heterogeneous material a combined FEM and a nonlinear cohesive model to simulate compacted metal powder was presented and validated in [21].…”
By utilizing numerical models and simulation, insights about the fracture process of brittle heterogeneous materials can be gained without the need for expensive, difficult, or even impossible, experiments. Brittle and heterogeneous materials like rocks usually exhibit a large spread of experimental data and there is a need for a stochastic model that can mimic this behaviour. In this work, a new numerical approach, based on the Bonded Discrete Element Method, for modelling of heterogeneous brittle materials is proposed and evaluated. The material properties are introduced into the model via two main inputs. Firstly, the grains are constructed as ellipsoidal subsets of spherical discrete elements. The sizes and shapes of these ellipsoidal subsets are randomized, which introduces a grain shape heterogeneity Secondly, the micromechanical parameters of the constituent particles of the grains are given by the Weibull distribution. The model was applied to the Brazilian Disc Test, where the crack initiation, propagation, coalescence and branching could be investigated for different sets of grain cement strengths and sample heterogeneities. The crack initiation and propagation was found to be highly dependent on the level of heterogeneity and cement strength. Specifically, the amount of cracks initiating from the loading contact was found to be more prevalent for cases with higher cement strength and lower heterogeneity, while a more severe zigzag shaped crack pattern was found for the cases with lower cement strength and higher heterogeneity. Generally, the proposed model was found to be able to capture typical phenomena associated with brittle heterogeneous materials, e.g. the unpredictability of the strength in tension and crack properties.
“…Although lacking of predictability, the authors concluded that the model is suitable for rock mechanics. A statistical approach for modelling heterogeneous concrete, where the different phases were represented by a statistical distribution of constituent phases, has previously been developed within the framework of FEM [36]. For heterogeneous material a combined FEM and a nonlinear cohesive model to simulate compacted metal powder was presented and validated in [21].…”
By utilizing numerical models and simulation, insights about the fracture process of brittle heterogeneous materials can be gained without the need for expensive, difficult, or even impossible, experiments. Brittle and heterogeneous materials like rocks usually exhibit a large spread of experimental data and there is a need for a stochastic model that can mimic this behaviour. In this work, a new numerical approach, based on the Bonded Discrete Element Method, for modelling of heterogeneous brittle materials is proposed and evaluated. The material properties are introduced into the model via two main inputs. Firstly, the grains are constructed as ellipsoidal subsets of spherical discrete elements. The sizes and shapes of these ellipsoidal subsets are randomized, which introduces a grain shape heterogeneity Secondly, the micromechanical parameters of the constituent particles of the grains are given by the Weibull distribution. The model was applied to the Brazilian Disc Test, where the crack initiation, propagation, coalescence and branching could be investigated for different sets of grain cement strengths and sample heterogeneities. The crack initiation and propagation was found to be highly dependent on the level of heterogeneity and cement strength. Specifically, the amount of cracks initiating from the loading contact was found to be more prevalent for cases with higher cement strength and lower heterogeneity, while a more severe zigzag shaped crack pattern was found for the cases with lower cement strength and higher heterogeneity. Generally, the proposed model was found to be able to capture typical phenomena associated with brittle heterogeneous materials, e.g. the unpredictability of the strength in tension and crack properties.
“…Composite structures have a peculiar behavior, justified by their heterogeneity 2 . In this context, reinforced concrete structures, when subjected to any thermal variations, might have their performance altered mainly due to the concrete components 3,4 , which includes the loss of bearing capacity and/or structural performance.…”
The micro and meso-structural characteristics of materials present an inherent variability because of the intrinsic scatter in raw material and manufacturing processes. This problem is exacerbated in highly heterogeneous materials, which shows significant uncertainties in the macroscale material properties. Therefore, providing optimal designs and reliable structural analyses strongly depend on the selection of the underlying material property models. This paper is intended to provide insight into such a dependence by means of a stochastic inverse model based on an iterative optimization process depending only of one parameter, thus avoiding complex parametrizations. It relies on non-linear combinations of material property realizations with a defined spatial structure for constraining stochastic simulations to data within the framework of a Finite Element approach. In this way, the procedure gradually deforms unconditional material property realizations to approximate the reproduction of information including mechanical parameters (such as Young's modulus and Poisson's ratio fields) and variables (e.g., stress and strain fields). It allows dealing with non-multiGaussian structures for the spatial structure of the material property realizations, thus allowing to reproduce the coalescence and connectivity among phases and existing crack patterns that often take place in composite materials, being these features crucial in order to obtain more reliable safety factors and fatigue life predictions. The methodology has been successfully applied for the characterization of a complex case study, where an uncertainty assessment has been carried out by means of multiple equally likely realizations.
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