A half-plane crack propagates dynamically, nominally in the x direction, along the plane y = 0 in an unbounded solid subjected to remote loading equivalent to a static stress intensity factor K∗. The crack front at time t lies along the arc x = v0t + ϵƒ(z, t) where ƒv 0 is a constant velocity, (z, t) is an arbitrary function, and ϵ is a small parameter. The crack front speed thus varies along the z axis and its shape deviates from straightness. We address this problem within a model 3D elastodynamic theory involving a single displacement variable u, satisfying a scalar wave equation, and representing tensile opening or shear slippage, with associated tensile or shear stress σ = M δu δy across planes parallel to the crack, where M is an elastic modulus. The problem is then one of finding a solution to the scalar wave equation satisfying σ = 0 on y = 0 within the rupture. When ϵ = 0 the solutions for u, σ, dynamic stress intensity factor K and energy release rate G are familiar 2D results. We develop corresponding 3D solutions to first order in σ, for arbitrary ƒ(z, t). The solutions are used to address in some elementary cases how a crack front moves unsteadily through regions of locally variable fracture resistance. When a straight crack front approaches a slightly heterogeneous strip, lying parallel to the crack tip along an otherwise homogeneous fracture plane, it may be blocked by asperities after some advancement into the heterogeneous region if it has a relatively small incoming velocity. If, however, the incoming crack velocity is relatively high, the asperities give way and the, now curved, crack front propagates into the bordering homogeneous region. There, the moving crack front recovers a straight configuration through slowly damped space-time oscillations. The oscillatory crack tip motion results from constructive-destructive interferences of stress intensity waves, initiated by encounters of the crack front with asperities, and then propagating along the front. Oscillations in response to a heterogeneity that is spatially periodic in the direction along the crack front decay as tt- 1 2 at large t. The slowness of the decay suggests that the straight crack front configuration may be sensitive to small sustained heterogeneity of the fracture resistance. This is consistent with results of a related analysis (Perrin and Rice, 1994, in press, J. Mech. Phys. Solids) based upon a strictly linearized form of our equations. The persistence of unsteady crack tip motion beyond the immediate region of heterogeneities provides an explanation for high frequency seismic radiation, using a lesser amount of heterogeneity than what might be naively assumed by strict correspondence of all curved and variable velocity portions of a propagating rupture front to asperities. Also, oscillations of crack tip velocity in the presence of sustained small heterogeneities, suggested by features of our 3D results for the model theory, may provide a mechanism for the generation of rough tensile fracture surfaces when the average (macroscopic) propagation speed of the crack is relatively small.
An Eulerian finite element formulation is presented for problems of large elastic-plastic flow. The method is based on Hill's variational principle for incremental deformations, and is ideally suited to isotropically hardening Prandtl-Reuss materials. Further, the formulation is given in a manner which allows any conventional finite element program, for “small strain” elastic-plastic analysis, to be simply and rigorously adapted to problems involving arbitrary amounts of deformation and arbitrary levels of stress in comparison to plastic deformation moduli. The method is applied to a necking bifurcation analysis of a bar in plane-strain tension. The paper closes with a unified general formulation of finite element equations, both Lagrangian and Eulerian, for large deformations, with arbitrary choice of the conjugate stress and strain measures. Further, a discussion is given of other proposed formulations for elastic-plastic finite element analysis at large strain, and the inadequacies of some of these are commented upon.
Nanometer scale structures represent an intellectually challenging and rapidly expanding area of research that crosses the borders between many areas of the physical sciences and engineering. In this review, results, drawn primarily from the author's laboratory, and addressing the rational growth, physical properties and applications of 1D nanostructures will be discussed. In addition, present and future challenges in this broad area of research are outlined.
Finite element calculations of dynamic fracture based on embedding cohesive surfaces in a continuum indicate that the predictions are sensitive to the cohesive law used. Simulations were performed on a square block in plane strain with an initial edge crack loaded at a constant rate of strain. Cohesive laws that have an initial elastic response were observed to produce spontaneous branching at high velocity, but to modify the linear elastic properties of the body. As a consequence the cohesive surface spacing cannot be refined arbitrarily and becomes an important length scale in the simulations. Cohesive laws that are initially rigid do not alter the linear elastic response of the body. However, crack branching behavior was not observed when such a cohesive relation was implemented using a regular finite element mesh.
This paper is concerned with the statistics of the height of rise and full for continuous random processes. In particular, approximate methods are given for determining the probability density of the increment in a random continuous function as the function passes from one extremum to the next. Application of the general result is made to the case of processes with a Gaussian distribution. Numerical results are given for four special cases of stationary Gaussian processes. Computed results are found to agree well with available experimental data. The knowledge of such statistical information is of use in studies dealing with fatigue under random loadings.
article Free AccessArtifacts AvailableArtifacts Evaluated & Reusable Share on Algorithm 637: GENCOL: collocation of general domains with bicubic hermite polynomials Authors: E. N. Houstis Purdue Univ. and Univ. of Thessaloniki Purdue Univ. and Univ. of ThessalonikiView Profile , W. F. Mitchell Purdue Univ. Purdue Univ.View Profile , J. R. Rice Purdue Univ. Purdue Univ.View Profile Authors Info & Claims ACM Transactions on Mathematical SoftwareVolume 11Issue 4Dec. 1985 pp 413–415https://doi.org/10.1145/6187.6194Published:01 December 1985Publication History 13citation376DownloadsMetricsTotal Citations13Total Downloads376Last 12 Months8Last 6 weeks1 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my Alerts New Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF
A thin-walled tube, e.g., a drinking straw, manifests an instability when bent by localizing the curvature change in a small region. This instability has been extensively studied since the seminal work of Brazier nearly a century ago. However, the scenario of pressurized tubes has received much less attention. Motivated by rod-shaped bacteria such as E. coli, whose cell walls are much thinner than their radius and are subject to a substantial internal pressure, we study, theoretically, how this instability is affected by this internal pressure. In the parameter range relevant to the bacteria, we find that the internal pressure significantly postpones the onset of the instability, while the bending stiffness of the cell wall has almost no influence. This study suggests a new method to infer turgor pressure in rod-shaped bacteria from bending experiments.
Semiconductor nanowires were initially discovered in late 90's and since then there has been an explosion in the research of their synthesis and understanding of their structures, growth mechanisms and properties. The realisation of their unique electrical, optical and mechanical properties has led to a great interest for their use in electronics, energy generation and storage. This book provides a timely reference on semiconductor nanowires including an introduction to their synthesis and properties and specific chapters focusing on the different applications including photovoltaics, nanogenerators, transistors, biosensors and photonics. This is the first book dedicated to Semiconductor Nanowires and provides an invaluable resource for researchers already working in the area as well as those new to the field. Edited by leading experts in the field and with contributions from well-known scientists, the book will appeal to both those working on fundamental nanomaterial research and those commercially interested in their applications.
