English
Related papers

Related papers: Interfacial crack integral identities incorporatin…

200 papers

Given any elliptic system with $t$-independent coefficients in the upper-half space, we obtain representation and trace for the conormal gradient of solutions in the natural classes for the boundary value problems of Dirichlet and Neumann…

Classical Analysis and ODEs · Mathematics 2015-11-06 Pascal Auscher , Mihalis Mourgoglou

This paper presents an integral formulation for Helmholtz problems with mixed boundary conditions. Unlike most integral equation techniques for mixed boundary value problems, the proposed method uses a global boundary charge density. As a…

Numerical Analysis · Mathematics 2016-01-12 Adrianna Gillman

The dynamics of a crack propagating in an elastic inhomogeneous material is investigated. The variations of the average crack velocity with the external loading are measured for a brittle rock and are shown to display two distinct regimes:…

Statistical Mechanics · Physics 2008-12-18 Laurent Ponson

We propose a one-dimensional, nonconvex elastic constitutive model with higher gradients that can predict spontaneous fracture at a critical load via a bifurcation analysis. It overcomes the problem of discontinuous deformations without…

Analysis of PDEs · Mathematics 2021-03-17 Phoebus Rosakis , Timothy J. Healey , Ugur Alyanak

We investigate the interaction between two cracks propagating in a thin sheet. Two different experimental geometries allow us to tear sheets by imposing an out-of-plane shear loading. We find that two tears converge along self-similar paths…

Materials Science · Physics 2015-05-27 E. Bayart , A. Boudaoud , M. Adda-Bedia

We present algorithms for computing strongly singular and near-singular surface integrals over curved triangular patches, based on singularity subtraction, the continuation approach, and transplanted Gauss quadrature. We demonstrate the…

Numerical Analysis · Mathematics 2024-06-24 Hadrien Montanelli , Francis Collino , Houssem Haddar

Fractures are ubiquitous in the subsurface. The flow and mechanical properties of these fractures are controlled by its compliance or stiffness. Characterizing fracture compliance is crucial in applications such as fault zone studies,…

Geophysics · Physics 2017-11-17 HanYi Wang , Mukul. M. Sharma

Material failure is mediated by the propagation of cracks, which in realistic 3D materials typically involve multiple coexisting fracture planes. Multiple fracture-plane interactions create poorly understood out-of-plane crack structures,…

Materials Science · Physics 2024-11-27 Meng Wang , Eran Bouchbinder , Jay Fineberg

The chapter contains a detailed presentation of the surface integral theory for modelling light diffraction by surface-relief diffraction gratings having a one-dimensional periodicity. Several different approaches are presented, leading…

Optics · Physics 2014-06-03 Daniel Maystre , Evgeny Popov

Two model problems of an elastic wedge with an internal and edge crack are analyzed. The problem of an internal crack reduces to an order-4 vector Riemann-Hilbert problem whose matrix kernel entries are meromorphic functions and have…

Analysis of PDEs · Mathematics 2025-02-19 Y. A. Antipov

Heterogeneous interfaces are central to many energy-related applications in the nanoscale. From the first-principles electronic structure perspective, one of the outstanding problems is accurately and efficiently calculating how the…

Materials Science · Physics 2023-08-29 Zhen-Fei Liu

A formulation of the boundary integral method for solving partial differential equations has been developed whereby the usual weakly singular integral and the Cauchy principal value integral can be removed analytically. The broad…

Computational Physics · Physics 2019-10-02 E. Klaseboer , Q. Sun , D. Y. C. Chan

A spectral formulation of the plane-strain boundary integral equations for an interface between dissimilar elastic solids is presented. The boundary integral equations can be written in two equivalent forms: (a) The tractions can be written…

Materials Science · Physics 2015-04-08 K. Ranjith

This paper shows that the plane wave expansion can be a useful tool in obtaining analytical solutions to infinite integrals over spherical Bessel functions and the derivation of identites for these functions. The integrals are often used in…

Mathematical Physics · Physics 2011-08-29 Rami Mehrem

This research investigates the simultaneous effect of in-plane and transverse loads in reinforced concrete shells. The infinitesimal shell element is divided into layers (with triaxial behavior) that are analyzed according to the smeared…

Classical Physics · Physics 2013-08-13 Mauro Schulz , Maria Paola Santisi D'Avila

We give an elegant formulation of the structure equations (of Cartan) and the Bianchi identities in terms of exterior calculus without reference to a particular basis and without the exterior covariant derivative. This approach allows both…

Differential Geometry · Mathematics 2023-07-26 Thoan Do , Geoff Prince

In this paper, the effect of local defects, viz., cracks and cutouts on the buckling behaviour of functionally graded material plates subjected to mechanical and thermal load is numerically studied. The internal discontinuities, viz.,…

Numerical Analysis · Mathematics 2013-11-14 S Natarajan , S Chakraborty , M Ganapathi , M Subramaniam

This paper deals with the solution of an inverse problem for the heat equation aimed at nondestructive evaluation of fractures. A fundamental step in any typical iterative inversion method, is the numerical solution of the underlying direct…

Applied Physics · Physics 2019-05-27 G. Inglese , R. Olmi , A. Scalbi

The paper is concerned with comparative analysis of differential and integral formulations for boundary value problems in nonlocal elasticity. For the sake of simplicity, the focus is on an antiplane problem for a half-space for an…

Analysis of PDEs · Mathematics 2021-07-22 Julius Kaplunov , Danila A Prikazchikov , Ludmila Prikazchikova

Rock formations are very often characterized by the presence of fractures that have grown subcritically over geological time scales and under evolving stress fields. In mechanically layered systems, such fractures can either become…

Geophysics · Physics 2026-01-01 Juan Michael Sargado , Michael Welch , Michael Lüthje