Progressive damage in discrete models and consequences on continuum modelling

Delaplace, Arnaud; Pijaudier‐Cabot, Gilles; Roux, Stéphane

doi:10.1016/0022-5096(95)00062-3

Cited by 94 publications

(73 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Although discrete lattice models do not describe the specific behavior of any real material, they incorporate the essential ingredients of a breakdown process, namely, the initial material disorder and the redistribution of forces due to damage evolution. In this respect, any realistic progressive damage evolution model that describes the behavior of real materials should be capable of reproducing the behavior of these idealized discrete lattice models [34].…”

Section: Fracture Strength Of a Discrete Lattice Systemmentioning

confidence: 99%

See 1 more Smart Citation

Scaling of fracture strength in disordered quasi-brittle materials

Nukala

Šimunović

2003

The European Physical Journal B - Condensed Matter

View full text Add to dashboard Cite

This paper presents two main results. The first result indicates that in materials with broadly distributed microscopic heterogeneities, the fracture strength distribution corresponding to the peak load of the material response does not follow the commonly used Weibull and (modified) Gumbel distributions. Instead, a lognormal distribution describes more adequately the fracture strengths corresponding to the peak load of the response. Lognormal distribution arises naturally as a consequence of multiplicative nature of large number of random distributions representing the stress scale factors necessary to break the subsequent "primary" bond (by definition, an increase in applied stress is required to break a "primary" bond) leading up to the peak load. Numerical simulations based on two-dimensional triangular and diamond lattice topologies with increasing system sizes substantiate that a lognormal distribution represents an excellent fit for the fracture strength distribution at the peak load. The second significant result of the present study is that, in materials with broadly distributed microscopic heterogeneities, the mean fracture strength of the lattice system behaves as µ f = µ ⋆ f (LogL) ψ + c L , and scales as µ f ≈ 1 (LogL) ψ as the lattice system size, L, approaches infinity.

show abstract

Section: Fracture Strength Of a Discrete Lattice Systemmentioning

confidence: 99%

“…In this study, we pursue an electrical equivalence to the mechanical problem [34,35,36]. We assume equivalence between electrical current, voltage, and conductance in the electrical system and the mechanical stress, strain, and Young's modulus in the mechanical system, respectively.…”

Section: Numerical Simulationsmentioning

confidence: 99%

Scaling of fracture strength in disordered quasi-brittle materials

Nukala

Šimunović

2003

The European Physical Journal B - Condensed Matter

View full text Add to dashboard Cite

show abstract

“…The condition of spatially uniform shear traction across the zone implies that the perturbed state variable is In principle, the length scale for a continuum can be obtained from percolation theory [Delaplace et al, 1996]. However, I do have not a practical way of doing this for fault zones.…”

Section: Oxx Ot Exp [1 ---•-Tl (28) E App = Oexx = Oe---•-mentioning

confidence: 99%

Application of a unified rate and state friction theory to the mechanics of fault zones with strain localization

Sleep¹

1997

J. Geophys. Res.

151

177

View full text Add to dashboard Cite

is •n Cn(O)/AP•Cn(AT). The theoryis complete in the sense that the complete earthquake cycle is represented and that there are no unmeasurable state parameters. The theory was applied to investigate earthquake quenching by fluid pressure decreases associated with frictional dilatancy and the related topic of strain localization and delocalization within fault zones. It was found that strain localization will occur when b > a. Such strain localization tends to destabilize sliding within drained faults by reducing the effective value of the critical displacement. Fault zones that are hydraulically sealed from the country rock but internally hydraulically connected are also destabilized because strain localization reduces the fluid pressure decrease from frictional dilatancy. Two mechanisms that delocalize strain once sliding is well underway were investigated. Strain rate strengthening at high-strain rates leads to a high strain zone that gradually broadens throughout an earthquake. An increase in the coefficient of friction with temperature leads to a high strain rate zone that moves through the fault zone from hot regions created by frictional heating to cold regions.

show abstract

“…LEM has been extensively used for the statistical mechanics of fracture in disordered media [7], and applied to study the fracture properties of concrete [8], ceramics [9] and biomaterials like wheat endosperm [5,6]. The space is discretized as a grid of points (nodes) interconnected by one-dimensional elements (bonds).…”

Section: Sub-particle Stress Transmission In Granular Solidsmentioning

confidence: 99%