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discussed The new kernel is longer ranged and physically meaningfull improving therefore upon the existing Gaussian like non locality kernels As in the original Peierls Nabarro model lattice trapping cannot be captured in the purely continuum non local formulation and therefore a semi discrete framework is used The constitutive law of the elastic continuum and that of the glide plane are considered both local and non local in separate models

Original URL path: http://www.scorec.rpi.edu/reports/view_report.php?id=46 (2015-07-15)

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interatomic interactions are represented by pair as well as embedded atom type potentials are considered The derived kernels have a range which extends up to the cut off radius of the interatomic potential are positive in the origin and become negative approximately one atomic distance away thus departing from the commonly assumed Gaussian functional form The fuctional form of the potential and the radial distribution fuction of interacting neighbors about

Original URL path: http://www.scorec.rpi.edu/reports/view_report.php?id=47 (2015-07-15)

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relaxation corresponds to the return to isotropy of the atomic distribution in the neighborhood of a representative atom and encompasses a quasi elastic mode B1 and a slower mode B2 A diffusion like process governs the B2 mode The B1 mode is non exponential and accounts for roughly 50 of the total atomic scale stress drop during relaxation The B2 mode is exponential leads to a smaller stress drop but

Original URL path: http://www.scorec.rpi.edu/reports/view_report.php?id=48 (2015-07-15)

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In this paper we present a new point of view for efficiently managing general mesh representations After reviewing some mesh representation basics we introduce the new Algorithm Oriented Mesh Database AOMD Some hypothesis are taken in order to be able to manage any set of adjacencies Then we present the design of the AOMD in terms of classes and algorithms The Standard Template Library STL is used for managing the

Original URL path: http://www.scorec.rpi.edu/reports/view_report.php?id=50 (2015-07-15)

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evolution in brittle composites A nonlocal damage theory for obtaining numerical approximation to a boundary value problem describing damage phenomena in brittle composites is developed The damage evolution is defined on the smallest scale of interest and described within the context of Continuum Damage Mechanics Nonlocal damage theory is developed by introducing the concept of nonlocal phase fields The mathematical homogenization method based on the asymptotic expansion is generalized to account for damage effects in heterogeneous media A two scale nonlocal damage mechanics model is developed first and then extended to the case of three scales for the composites with heterogeneous microphases Fatigue in brittle composites By extending the damage cumulative law defined for the monotonic loading to the case of cyclic loading the homogenization framework of the two scale nonlocal damage theory is applied to the fatigue damage in brittle composites A novel accelerating technique to alleviate the computational inefficiency due to the coupling between damage evolution and the mechanical response is developed for the integration of the fatigue damage cumulative law Multiple temporal scale analysis for the rate dependent solids under locally periodic loading For the rate dependent solids under locally periodic loading the multiple temporal scales are

Original URL path: http://www.scorec.rpi.edu/reports/view_report.php?id=53 (2015-07-15)

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steady two dimensional hyperbolic conservation laws on unstructured meshes We shoe that the leading term of the error on each element is a linear combination of orthogonal polynominals of degrees p and p 1 We further show that there is a strong superconvergence property at the outflow edge s of each element where the average discretization error converges as o h exp 2p 1 compared to a global rate of

Original URL path: http://www.scorec.rpi.edu/reports/view_report.php?id=54 (2015-07-15)

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molecular dynamics The atomic level stress is defined in intrinsic coordinates a mobile frame tied to the generic bond The global stress sigma is obtained in the global coordinate system by summing up the contribution due to the intrinsic stress corresponding to each atom in the population The atom based global stress is proportional to an average measure of bond orientation P2 with the proportionality constant sigma P2 being related to the macroscopic stress optical coefficient SOC The proportionality constant may be expressed in terms of intrinsic quantities which in turn are computable from equilibrium simulations The model reproduces most experimentally observed properties of the SOC The ratio sigma P2 is chain length and deformation rate independent in the melt and becomes rate dependent in the glassy state The dependence of the global stress on temperature at imposed average bond orientation is therefore determined by the variation of the intrinsic stresses with temperature The stress is purely entropic in the melt for all chain lengths However neither one of its components that due to bonded and that due to non bonded interactions is purely entropic The global stress sigma acquires an energetic component at high temperatures and at large deformations

Original URL path: http://www.scorec.rpi.edu/reports/view_report.php?id=336 (2015-07-15)

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Journal MED Volume 11 Pages 761 767 Editor R J Forness Abstract A stabilized mixed finite element method for viscoplastic flow analysis is presented Preliminary results show promise for modeling steady state bulk forming processes In this work the Ladyzenskaya Babuska Brezzi LBB condition is circumvented by adding mesh dependent terms stabilization terms which are functions of the residual of the Euler Lagrange equations to the usual Galerkin method The

Original URL path: http://www.scorec.rpi.edu/reports/view_report.php?id=1 (2015-07-15)

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