Related papers: Time dependence of breakdown in a global fiber-bun…
A standard approach to analyzing tunneling processes in various physical contexts is to use instanton or imaginary time path techniques. For systems in which the tunneling takes place in a time dependent setting, the standard methods are…
We address classical and quantum mechanics in a general setting of arbitrary time-dependent transformations. Classical non-relativistic mechanics is formulated as a particular field theory on smooth fibre bundles over a time axis.…
Of primary interest in this paper is the numerical approximation of a time dependent fractional, in space, diffusion equation where the domain is assumed to be nonhomogeneous, having different axial diffusion coefficients. This work is…
The time-dependent Bragg diffraction by multilayer gratings working by reflection or by transmission is investigated. The study is performed by generalizing the time-dependent coupled-wave theory previously developed for one-dimensional…
This paper introduces a linear state-space model with time-varying dynamics. The time dependency is obtained by forming the state dynamics matrix as a time-varying linear combination of a set of matrices. The time dependency of the weights…
Using the global fiber bundle model as a tractable scheme of progressive fracture in heterogeneous materials, we define the branching ratio in avalanches as a suitable order parameter to clarify the order of the phase transition occurring…
The diffusion equation and its time-fractional counterpart can be obtained via the diffusion limit of continuous-time random walks with exponential and heavy-tailed waiting time distributions. The space dependent variable-order…
We review statistical theories and numerical methods employed to consider the sample size dependence of the failure strength distribution of disordered materials. We first overview the analytical predictions of extreme value statistics and…
We show that the failure time $\tau_f$ in fiber bundle model, taken as a prototype of heterogeneous materials, depends crucially on the strength of the disorder $\delta$ and the stress release range $R$ in the system. For $R$ beyond a…
We examine an infinite, linear system of ordinary differential equations that models the evolution of fragmenting clusters, where each cluster is assumed to be composed of identical units. In contrast to previous investigations into such…
A damage-plasticity constitutive model for the description of fracture in plain concrete is presented. Two approaches, the local model comprising the adjustment of the softening modulus and the nonlocal model based on spatial averaging of…
A recent theory that determines the properties of disordered solids as the solid accumulates damage is applied to the special case of fiber bundles with global load sharing and is shown to be exact in this case. The theory postulates that…
We study the creep rupture of bundles of viscoelastic fibers occurring under uniaxial constant tensile loading. A novel fiber bundle model is introduced which combines the viscoelastic constitutive behaviour and the strain controlled…
Generalized impedance boundary conditions are effective, approximate boundary conditions that describe scattering of waves in situations where the wave interaction with the material involves multiple scales. In particular, this includes…
An equal load sharing fiber bundle model for thermally activated breakdown is developed using transition state theory to describe the rate of elementary failures. The lifetime distribution, average, variance and their asymptotic limits for…
We propose a generic model to describe the mechanical response and failure of systems which undergo a series of stick-slip events when subjected to an external load. We model the system as a bundle of fibers, where single fibers can…
In this paper we prove existence of global in time weak solutions for a highly nonlinear PDE system arising in the context of damage phenomena in thermoviscoelastic materials. The main novelty of the present contribution with respect to the…
A mathematical model for the discrete nonlinear fragmentation (collision-induced breakage) equation with diffusion is studied. The existence of global weak solutions is established in arbitrary spatial dimensions without assuming a strictly…
Breakability rate of fragile item depends on the accumulated stress of heaped stock level. So breakablility rate can be considered as dependent parameter of stock variable. The unit production cost is a function of production rate and also…
Various kinds of heterogeneity in solids including atomistic discreteness affect the fracture strength as well as the failure dynamics remarkably. Here we study the effects of an initial crack in a discrete model for fracture in…