Percolation in Isotropic Elastic Media

García-Molina, Rafael; Guinea, F.; Louis, E.

doi:10.1103/physrevlett.60.124

Cited by 25 publications

(3 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Another drawback inherent to some percolation studies resides in the preservation of isotropy during the percolation process that proceeds by random either suppression/strengthening of links (e.g. Garcia-Molina et al 1988), which makes them ill posed to study damage induced anisotropy that immediately arise in quasi-brittle (vectorial) systems (Rinaldi 2009). A critical review by Guyon et al (1990) represents a relevant and insightful reading on the subject.…”

Section: /31mentioning

confidence: 99%

The Krajcinovic approach to model size dependent fracture in quasi-brittle solids

Rinaldi

Mastilović

2014

Mechanics of Materials

View full text Add to dashboard Cite

Section: /31mentioning

confidence: 99%

The Krajcinovic approach to model size dependent fracture in quasi-brittle solids

Rinaldi

Mastilović

2014

Mechanics of Materials

View full text Add to dashboard Cite

“…In practice, we compute the Laplace transform in time 0(s) of the signal 4>( t). If we expand in powers of s, we obtain using equations (6) and (7) :…”

Section: Methodmentioning

confidence: 99%

Anomalous viscous retardation of a mechanical wave at percolation threshold

Roux¹,

Hansen

1988

J. Phys. France

View full text Add to dashboard Cite

We study the mean transit time needed for a mechanical shock to propagate through a random depleted lattice of freely-rotating elastic springs in a viscous medium at the central-force percolation threshold. This problem is the exact mechanical counterpart of anomalous diffusion. We show that the mean transit time for a pulse to cross a lattice of size L, scales as ∝ L2+θ' through a transfer-matrix analysis

show abstract

“…The increasing availability of experimental data at a detailed level raises the non-trivial problem of transferring the random properties of the microstructure to a lattice model. The procedures proposed by Monette and Anderson (1994), He and Thorpe (1985) and Garcia-Molina et al (1988) are either based on mean-field theory or limited to isotropic materials, which are not easily applicable to disordered polycrystalline materials. Without a general discretization procedure to assign the lattice parameters, the wealth of high-quality experimental data is just a sterile prerequisite for the leap of lattice models from abstract mathematical schemes to practical engineering tool, capable of quantitative estimates.…”

Section: Introductionmentioning

confidence: 99%

Lattice models of polycrystalline microstructures: A quantitative approach

Rinaldi

Krajčinović

Peralta

et al. 2008

Mechanics of Materials

View full text Add to dashboard Cite

This paper addresses the issue of creating a lattice model suitable for design purposes and capable of quantitative estimates of the mechanical properties of a disordered microstructure. The lack of resemblance between idealized lattice models and real materials has limited these models to the realm of qualitative analysis. Two procedures based on the same methodology are presented in the two-dimensional case to achieve the rigorous mapping of the geometrical and the elastic properties of a disordered polycrystalline microstructure into a spring lattice. The theory is validated against finite elements models and literature data of NiAl. The statistical analysis of 900 models provided the effective Young's modulus and Poisson ratio as function of the lattice size. The lattice models that were created have in average the same Young's modulus of the real microstructure. However, the Poisson's ratio could not be matched in the two-dimensional case. The spring constants of the lattices from this technique follow a Gaussian distribution, which intrinsically reflects the mechanical and geometrical disorder of the microscale. The detailed knowledge of the microstructure and the Voronoi tessellation necessary to implement this technique are supplied by modern laboratory equipments and software. As an illustrative example of lattice application, damage simulations of several biaxial loading schemes are briefly reported to show the effectiveness of discrete models towards elastic anisotropy induced by damage and damage localization.

show abstract

Percolation in Isotropic Elastic Media

Cited by 25 publications

References 11 publications

The Krajcinovic approach to model size dependent fracture in quasi-brittle solids

The Krajcinovic approach to model size dependent fracture in quasi-brittle solids

Anomalous viscous retardation of a mechanical wave at percolation threshold

Lattice models of polycrystalline microstructures: A quantitative approach

Contact Info

Product

Resources

About