Feeding and dissipative waves in fracture and phase transition. I: Some 1D structures and a square-cell lattice. II: Phase-transition waves
type: Item
instance of: scholarly article
title: Feeding and dissipative waves in fracture and phase transition. I: Some 1D structures and a square-cell lattice. II: Phase-transition waves
zbMATH Open document ID: 1003.74007
author: Leonid Slepyan
published in: Journal of the Mechanics and Physics of Solids
publication date: 2001-07-05T00:00:00Z
reviewed by: Ivan A. Parinov
Mathematics Subject Classification ID: 74A45
Mathematics Subject Classification ID: 74N20
Mathematics Subject Classification ID: 74J99
zbMATH DE Number: 1590508
zbMATH Keywords: fracture
zbMATH Keywords: phase transition
zbMATH Keywords: dissipative waves
zbMATH Keywords: Fourier transform
zbMATH Keywords: Wiener-Hopf techniques
zbMATH Keywords: feeding waves
zbMATH Keywords: energy dissipation
zbMATH Keywords: square-cell lattice
zbMATH Keywords: macrolevel solution
zbMATH Keywords: microlevel solution
zbMATH Keywords: mode III crack propagation
zbMATH Keywords: higher-order derivate model
zbMATH Keywords: phase-transition wave
zbMATH Keywords: long-wave approximation
zbMATH Keywords: uniqueness
zbMATH Keywords: strain energy
zbMATH Keywords: fourth-order partial differential equation
MaRDI profile type: Publication
cites work: Q3857821
cites work: Dynamic Fracture Mechanics
cites work: Origin of crack tip instabilities
cites work: Steady-state mode I cracks in a viscoelastic triangular lattice
cites work: Q3962627
cites work: Q3668099
cites work: Q4225049
cites work: Dynamic factor in impact, phase transition and fracture
full work available at URL: s0022-5096(00)00083-1
OpenAlex ID: W2576636716
DOI: 10.1016/S0022-5096(00)00083-1
review text: These two parts are devoted to a common approach to the description of feeding and dissipative waves in fracture and phase transition, with statement of a boundary between external (macrolevel) and internal (microlevel) problems. A zero feeding wave number corresponds to a macrolevel-associated solution with the classical homogeneous-material solution as its long-wave approximation. A non-zero wavenumber corresponds to a genuine microlevel solution which has no analogue on the macrolevel. Dissipative waves appear in both macrolevel-associated and microlevel soilutions.NEWLINENEWLINENEWLINEIn the first part the author presents a complete set of steady-state solutions for mode III crack propagation in a square-cell lattice. For this, at first, three simplified one-dimensional structures (an inclined thread falling on a rigid foundation, a periodic set of oscillators, and a string on an elastic foundation under a moving load) are studied, allowing to retrace qualitatively the main phenomena in the lattice. In particular, these structures demonstrate the structure- and speed-dependent radiation and different types of feeding and dissipative waves. Then, the analytical technique for mode III crack propagaton is described in detail. The crack propagation is considered as a sequence of bond breakings caused by feeding waves carrying energy to the crack front and accompanied by dissipative waves carrying a part of this energy away from the front. The final expressions are presented for all possible feeding waves, and fast and slow decreasing dissipative waves are shown.NEWLINENEWLINENEWLINEAnalogously, in the second part the author classifies the micro- and macrolevel solutions according to the type of feeding wave delivering energy to the propagating phase transition front. Both the discrete chain consisting of particles connected by massless bonds and the higher-order-derivate (HOD) model are considered. A steady-state phase-transition wave is considered for the discrete …
description: scientific article; zbMATH DE number 1590508