Related papers: On modeling hydraulic fracture in proper variables…
A new approach to defining the effective fracture toughness for heterogeneous materials is proposed. This temporal averaging approach is process-dependent, incorporating the crack velocity and material toughness. The effectiveness of the…
A novel regularized fracture model for crack propagation in porous media is proposed. Our model is obtained through homogenization theory and formal asymptotic expansions. We start with a regularized quasi-static fracture model posed in a…
Over the last decade, finite volume discretizations for flow in porous media have been extended to handle situations where fractures dominate the flow. These discretizations have successfully been combined with the discrete fracture-matrix…
In this work, we leverage the Hamiltonian kind structure for accurate uncertainty propagation through a nonlinear dynamical system. The developed approach utilizes the fact that the stationary probability density function is purely a…
Computational fluctuating hydrodynamics aims at understanding the impact of thermal fluctuations on fluid motions at small scales through numerical exploration. These fluctuations are modeled as stochastic flux terms and incorporated into…
Semi-Lagrangian methods have traditionally been developed in the framework of hyperbolic equations, but several extensions of the Semi-Lagrangian approach to diffusion and advection--diffusion problems have been proposed recently. These…
In this paper we derive a new two-dimensional brittle fracture model for thin shells via dimension reduction, where the admissible displacements are only normal to the shell surface. The main steps include to endow the shell with a small…
Fractional calculus, in allowing integrals and derivatives of any positive order (the term "fractional" kept only for historical reasons), can be considered a branch of mathematical physics which mainly deals with integro-differential…
We review microstructural fracture growth models suitable for the study of hydraulic fracture processes in disordered porous materials and present some basic results. It is shown that microstructural models exhibit certain similarities to…
Crack propagation is studied numerically using a continuum phase-field approach to mode III brittle fracture. The results shed light on the physics that controls the speed of accelerating cracks and the characteristic branching instability…
In this contribution, a variational diffuse modeling framework for cracks in heterogeneous media is presented. A static order parameter smoothly bridges the discontinuity at material interfaces, while an evolving phase-field captures the…
Premixed flames are susceptible to hydrodynamic and thermodiffusive instabilities that wrinkle the flame front and lead to complex multiscale patterns. They strongly impact the flame propagation and dynamics, increasing the speed of a…
The phase field approach to modeling fracture uses a diffuse damage field to represent a crack. This addresses the singularities that arise at the crack tip in computations with sharp interface models, mollifying some of the difficulties…
We address analytically and numerically the problem of crack path prediction in the model system of a crack propagating under thermal loading. We show that one can explain the instability from a straight to a wavy crack propagation by using…
We show that the intermittent and self-similar fluctuations displayed by a slow crack during the propagation in a heterogeneous medium can be quantitatively described by an extension of a classical statistical model for fracture. The model…
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…
This paper presents the coupled model of a hydraulic fracturing and proppant transport. The former is described in terms of enhanced pseudo-3D model that considers height growth across two symmetric stress barriers, while the latter is…
We propose inverse problems of crack propagation using the phase-field models. First, we study the crack propagation in an inhomogeneous media in which fracture toughness varies in space. Using the two phase-field models based on different…
An accurate modeling of reactive flows in fractured porous media is a key ingredient to obtain reliable numerical simulations of several industrial and environmental applications. For some values of the physical parameters we can observe…
Hydro-mechanical processes in rough fractures are highly non-linear and govern productivity and associated risks in a wide range of reservoir engineering problems. To enable high-resolution simulations of hydro-mechanical processes in…