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Finite Element Convergence for State-Based Peridynamic Fracture Models

Communications on Applied Mathematics and Computation 2020年第1期2卷 93-128页

作者： Prashant K.Jha robert lipton Department of Mathematics Louisiana State UniversityBaton RougeLAUSA

We establish the a priori convergence rate for finite element approximations of a class of nonlocal nonlinear fracture *** consider state-based peridynamic models where the force at a material point is due to both the strain between two points and the change in volume inside the domain of the nonlocal *** pairwise interactions between points are mediated by a bond potential of multi-well type while multi-point interactions are associated with the volume change mediated by a hydrostatic strain *** hydrostatic potential can either be a quadratic function,delivering a linear force–strain relation,or a multi-well type that can be associated with the material degradation and *** first show the well-posedness of the peridynamic formulation and that peridynamic evolutions exist in the Sobolev space *** show that the finite element approximations converge to the H2 solutions uniformly as measured in the mean square *** linear continuous fi nite elements,the convergence rate is shown to be Ct Δt+Csh2/ε2,where𝜖is the size of the horizon,his the mesh size,and Δt is the size of the time *** constants Ct and Cs are independent of Δt and h and may depend on ε through the norm of the exact *** demonstrate the stability of the semi-discrete *** stability of the fully discrete approximation is shown for the linearized peridynamic *** present numerical simulations with the dynamic crack propagation that support the theoretical convergence rate.

关键词： Nonlocal fracture models Peridynamic State-based peridynamic Numerical analysis Finite element approximation

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A history of high-power laser research and development in the United Kingdom

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High Power Laser Science and Engineering 2021年第2期9卷 41-126页

作者： Colin N.Danson Malcolm White John R.M.Barr Thomas Bett Peter Blyth David Bowley Ceri Brenner robert J.Collins Neal Croxford A.E.Bucker Dangor Laurence Devereux Peter E.Dyer Anthony Dymoke-Bradshaw Christopher B.Edwards Paul Ewart Allister I.Ferguson John M.Girkin Denis R.Hall David C.Hanna Wayne Harris David I.Hillier Christopher J.Hooker Simon M.Hooker Nicholas Hopps Janet Hull David Hunt Dino A.Jaroszynski Mark Kempenaars Helmut Kessler Sir Peter L.Knight Steve Knight Adrian Knowles Ciaran L.S.Lewis Ken S.lipton Abby Littlechild John Littlechild Peter Maggs Graeme P.A.Malcolm OBE Stuart P.D.Mangles William Martin Paul McKenna Richard O.Moore Clive Morrison Zulfikar Najmudin David Neely Geoff H.C.New Michael J.Norman Ted Paine Anthony W.Parker Rory R.Penman Geoff J.Pert Chris Pietraszewski Andrew Randewich Nadeem H.Rizvi Nigel Seddon MBE Zheng-Ming Sheng David Slater Roland A.Smith Christopher Spindloe Roy Taylor Gary Thomas John W.G.Tisch Justin S.Wark Colin Webb S.Mark Wiggins Dave Willford Trevor Winstone AWE Aldermaston ReadingUK Oxford Centre for High Energy Density Science Department of PhysicsClarendon LaboratoryUniversity of OxfordOxfordUK Centre for Intertial Fusion Studies Blackett LaboratoryImperial College LondonLondonUK Formerly of Electrox LetchworthUK Formerly of Central Laser Facility Rutherford LaboratoryDidcotUK Formerly of Ferranti Defence Systems LincolnUK Leonardo EdinburghUK Retired AWEReadingUK Formerly of AWE ReadingUK Formerly of Laser Lines Ltd BanburyUK Formerly of Optilas Ltd Milton KeynesUK Retired Pro-Lite TechnologyCranfieldUK Specialised Imaging Ltd PitstoneUK Central Laser Facility STFC Rutherford Appleton LaboratoryDidcotUK Magna-Power Electronics Ltd ReadingUK DeBe Lasers Needham Laser TechnologiesWhitchurchUK Blackett Laboratory Imperial College LondonLondonUK SPIE Europe CardiffUK Professor Emeritus(Physics) University of HullKingston upon HullUK Kentech Instruments Ltd WallingfordUK Department of Physics Clarendon LaboratoryUniversity of OxfordOxfordUK Professor Emeritus Department of PhysicsUniversity of StrathclydeGlasgowUK Department of Physics Durham UniversityDurhamUK Professor Emeritus(Photonics) Heriot-Watt UniversityEdinburghUK Professor Emeritus University of SouthamptonSouthamptonUK Optical Surfaces Ltd KenleyUK JEH Lasers Ltd RugbyUK Scottish Universities Physics Alliance Department of PhysicsUniversity of StrathclydeGlasgowUK ITER Organization Saint-Paul-lez-DuranceFrance Manx Precision Optics Ltd BallasallaUK Laser Lines Ltd BanburyUK Elliot Scientific Ltd MetroTest Scientific GroupHarpendenUK Centre for Plasma Physics Queen’s University BelfastBelfastUK Retired Founderand former MDRofin-Sinar UK LtdHullUK Heraeus Noblelight Ltd CambridgeUK Mirli Books ChelmsfordUK M Squared Lasers Ltd GlasgowUK University of Hertfordshire HatfieldUK E&EO UK Ltd Barton-upon-HumberUK Department of Physics University of YorkYorkUK IC Optical Systems Ltd BeckenhamUK Laser Micromachining Ltd St AsaphUK MBDA UK Ltd Brist

The first demonstration of laser action in ruby was made in 1960 by *** of Hughes Research Laboratories,*** laboratories worldwide began the search for lasers using different materials,operating at different *** the UK,academia,industry and the central laboratories took up the challenge from the earliest days to develop these systems for a broad range of *** historical review looks at the contribution the UK has made to the advancement of the technology,the development of systems and components and their exploitation over the last 60 years.

关键词： high-power lasers history United Kingdom

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