Three-points interfacial quadrature for geometrical source terms on nonuniform grids

International audienceThis paper deals with numerical (finite volume) approximations, on nonuniform meshes, for ordinary differential equations with parameter-dependent fields. Appropriate discretizations are constructed over the space of parameters, in order to guarantee the consistency in presence of variable cells' size, for which $L^p$-error estimates, $1\le p < +\infty$, are proven. Besides, a suitable notion of (weak) regularity for nonuniform meshes is introduced in the most general case, to compensate possibly reduced consistency conditions, and the optimality of the convergence rates with respect to the regularity assumptions on the problem's data is precisely discussed. This analysis attempts to provide a basic theoretical framework for the numerical simulation on unstructured grids (also generated by adaptive algorithms) of a wide class of mathematical models for real systems (geophysical flows, biological and chemical processes, population dynamics)

Scaling of the size and temporal occurrence of burst sequences in creep rupture of fiber bundles

We present a detailed statistical analysis of the size and temporal occurrence of burst sequences in the creep rupture of a proposed linear viscoelastic fiber bundle model. According to the model, the burst sequences of fiber breaks display a power law asymptotic behavior analogous to that of the static-fracture [Kloster et al., Phys. Rev. E 56, 2615, (1997)]. Moreover, power law asymptotics apply to inter-arrival times between successive bursts with a universal exponent close to unity

Burst avalanches and inter-occurrence times in creep rupture

The statistics of fracture precursors in the creep-damage process are studied on the basis of a proposed dry, non-linear viscoelastic fiber bundle model. This model permits the occurrence of damage avalanches consisting of simultaneous rupture of several fibers. The avalanche size distribution for the global-load sharing rule follows a power law asymptotic behavior analogous to that of static fracture (Kloste

Scaling of the size and temporal occurrence of burst sequences in creep rupture of fiber bundles

We present a detailed statistical analysis of the size and temporal occurrence of burst sequences in the creep rupture of a proposed linear viscoelastic fiber bundle model. According to the model, the burst sequences of fiber breaks display a power law asymptotic behavior analogous to that of the static-fracture [Kloster et al., Phys. Rev. E 56, 2615, (1997)]. Moreover, power law asymptotics apply to inter-arrival times between successive bursts with a universal exponent close to unity. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 200846.35.+z Viscoelasticity, plasticity, viscoplasticity, 46.50.+a Fracture mechanics, fatigue and cracks , 62.20.Mk Fatigue, brittleness, fracture, and cracks,