arXiv subjects

Martin Dutko

Publications and source records attributed to Martin Dutko.

4 recordsLinked to original sources

arXiv2023

Asymptotic analysis a perturbed Robin problem in a planar domain

We consider a perforated domain $\Omega(\epsilon)$ of $\mathbb{R}^2$ with a small hole of size $\epsilon$ and we study the behavior of the solution of a mixed Neumann-Robin problem in $\Omega(\epsilon)$ as the size $\epsilon$ of the small hole tends to $0$. In addition to the geometric degeneracy of the problem, the $\epsilon$-dependent Robin condition may degenerate into a Neumann condition for $\epsilon=0$ and the Robin datum may diverge to infinity. Our goal is to analyze the asymptotic behavior of the solutions to the problem as $\epsilon$ tends to $0$ and understand how the boundary condition affects the behavior of the solutions when $\epsilon$ is close to $0$.

math.AP↗

arXiv2022

Averaging-based approach to toughness homogenisation for radial hydraulic fracture

The homogenisation of the fracture toughness is considered in the context of a propagating hydraulic fracture. The radial (penny-shape) model is utilized, in order to incorporate the impact of the viscosity-toughness regime transition over time. A homogenisation strategy based upon temporal-averaging is investigated. This approach incorporates the instantaneous fracture velocity, meaning that it should remain effective in the case of step-wise crack advancement. The effectiveness of the approach is demonstrated for periodic toughness distributions, including those which are unbalanced, utilizing a highly accurate solver.

physics.geo-ph↗

arXiv2022

A temporal-averaging based approach to toughness homogenisation in heterogeneous material

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 new technique is investigated in the context of hydraulic fracture through heterogeneous rock with a periodic material toughness. The plane strain model is considered without fluid leak-off, to more easily investigate different regimes (toughness/viscosity). Numerical simulations are used to examine the effectiveness of the new homogenisation strategy, with comparison against the recently-proposed maximum toughness strategy. Simulations are conducted using an extremely effective (in house-built) time-space adaptive solver. The regimes in which each strategy is effective are determined.

physics.geo-ph↗

arXiv2022

On the pressure decline analysis for hydraulic fractures in elasto-plastic materials

In this paper the problem of a plane strain hydraulic fracture in elasto-plastic material is analyzed. The analysis is based on Finite Element Method computations of crack propagation and closure to simulate the Mini-Frac calibration test. The basic trends of fracture evolution are identified for both, the propagation and the closure stage in elasto-plastic materials and compared with the results obtained for purely elastic deformation of rock. Pressure decline analysis is conducted to identify the closure stress and leak-off coefficient. The results show that the standard techniques of pressure decline analysis can be adopted also for the case where the fractured material deforms inelastically.

cond-mat.mtrl-sci↗