Redes de fusíveis livres de escala para simulação de fratura em materiais compósitos

AUTOR(ES)
DATA DE PUBLICAÇÃO

2007

RESUMO

The study of fracture of composite materials has a distinguished relevance due the broad and ever increasing use of multiphase materials to attend specific needs and/or combine cost and functionality. Theoretical approach to the issue include simplified models, yet many times mathematically unfeasible, providing information of little practical use. As an alternate approach, lattice models for non-homogeneous media give the possibility of employing computer simulation to provide predictions or qualitative answers for the mechanical behaviour of composite materials. The random fuse network has been for sure one of the most successful lattice models in the last two decades. It places resistive fuses connecting nodes in a lattice, exploring the analogy between Ohms law for conduction and Hookes law for elasticity. As an external voltage, placed between two extremities of the network, increases, fuses will burn opening flaws in the lattice. It is the analogous to cracks growing and/or coalescing in a material as it is tracted, with the advantage of dealing with a scalar electrical problem, as opposed to the tensorial mechanical problem. This model has been historically used with square, cubic or triangular lattices, but always regular lattices. Disorder, thought in a mesoscopic scale, is introduced by removing fuses a priori (dilution) or statistically giving the fuses different conductances or current thresholds. This work proposes that scale-free networks of fuses can describe the fracture process in composite materials without the use of ad hoc introduced disorder. This novel approach requires new ways of thinking the loading of a network based on its topology instead of its geometry, since node spatial localization has no clear meaning for this sort of network. Scale-free networks are characterized by the existence a highly connected node (hub) and a huge amount of poorly connected nodes, resulting in a power-law distribution of connectivities among nodes. Identified the roles of central (most connected) and peripheral (least connected) nodes, three load modes are proposed and tested, providing responses similar to classical cases of composite materials fiber reinforced and highly porous. Further investigating the proprieties of these networks, simulations were also performed with other complex networks: apolonian networks (which are also scale-free) and random networks. Several conductance distribution were also tested, which revealed the distinction of universality classes defined only by the load modes.

ASSUNTO(S)

1. materiais compostos teses. 2. mecânica da fratura teses. 3. simulação (computadores) teses. i. universidade federal de ouro preto. ii. título. engenharia de materiais e metalurgica

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