Damage and Fracture of Disordered Materials by Dusan Krajcinovic, Jan van Mier

By Dusan Krajcinovic, Jan van Mier

The imperative goal of this ebook is to narrate the random distributions of defects and fabric power at the microscopic scale with the deformation and residual power of fabrics at the macroscopic scale. to arrive this target the authors thought of experimental, analytical and computational types on atomic, microscopic and macroscopic scales.

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The volume of the earth in liters is also about 10 24 • This gives a feeling for the size of this A. Hansen and S. Roux 44 r Stress Field ' change ~ Fractures changes ~ Figure 11. The stress field changes as a result of the creation and growth of cracks and the cracks are created and grow as a result of the changing stress field. The standard approach in fracture and damage mechanics calculations is to use finite element methods (FEM) (Carroll (1999)). However, network models- which represent a very different philosophy - are as versatile as the FEM approach.

With a probability p~, it consists in four percolating sublattices of generation n, in which half the current will flow, whereas with a probability 1 - p~, it consists of only two such sublattices in series which will support the entire current. Therefure, we have the following recursion for the moments: (63) Using the fact that the system size is simply 2n, we can compute the scaling exponents x(p) as x(q) = log (2(1 - p~) + p~2 2 -q) log(2) (64) as shown in Figure 6. Applying the Legendre Transformation Eqs.

This ratio determines the convergence rate, the closer the number is to unity the faster the convergence. Figure 15. Possible deformation of a small beam lattice. So far, we have only discussed an electrical analog of elastic materials. However, it is straight forward to construct network models based on elastic equations. There are two variants that so far have been studied extensively in the physics literature: (l) The beam network (Roux and Guyon (1986)) and (2) the central-force network (Feng and Sen (1984)).

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