Exact transient results for pure and grazing indentation with friction
type: Item
instance of: scholarly article
title: Exact transient results for pure and grazing indentation with friction
zbMATH Open document ID: 0816.73053
DOI: 10.1007/BF00705802
published in: Journal of Elasticity
publication date: 1995-07-16T00:00:00Z
review text: Let us consider the elastic half-plane \(y \leq 0\) and suppose that, at the instant \(t=0\), a rigid wedge, of half-angle \(\Theta\) and symmetric with respect to the \(y\)-axis, is applied with its vertex at the origin while the remaining part of the wedge is placed in the half-plane \(y>0\). Then the wedge is pushed with a constant vertical velocity \(V\) into the lower half-plane, but assuming, as opposed to what had been done in the previous literature, that friction arises between punch and half-plane along the region of contact. The problem is solved by using the Laplace transforms of the unknown fields with respect to the time and their Fourier transforms with respect to the \(x\)-variable. The explicit forms of the solutions can be obtained after inversions of the results. In the same way it is possible to study the case in which the die, besides penetrating into the half-plane, moves simultaneously in the direction of the \(x\)-axis. With the same technique, it is possible to write the formal solutions of the problem in which the moving punch is not a wedge but a rigid circle. In all there cases, the most difficult step is that of finding the inverse transforms of the solutions. This proves, once more, that the method of integral transforms is not efficient, exept for simple cases.
Mathematics Subject Classification ID: 74A55
Mathematics Subject Classification ID: 74M15
zbMATH DE Number: 549822
zbMATH Keywords: rigid wedge
zbMATH Keywords: Laplace transforms
zbMATH Keywords: Fourier transforms
zbMATH Keywords: moving punch
zbMATH Keywords: rigid circle
zbMATH Keywords: inverse transforms
author: L. M. Brock
reviewed by: Piero Villaggio
MaRDI profile type: Publication
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cites work: Dynamic analysis of non-symmetric problems for frictionless indentation and plane crack extension
full work available at URL: https://doi.org/10.1007/bf00705802
OpenAlex ID: W1998032558
description: scientific article; zbMATH DE number 549822