212 research outputs found

    Heterogeneous thin films: Combining homogenization and dimension reduction with directors

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    We analyze the asymptotic behavior of a multiscale problem given by a sequence of integral functionals subject to differential constraints conveyed by a constant-rank operator with two characteristic length scales, namely the film thickness and the period of oscillating microstructures, by means of Γ\Gamma-convergence. On a technical level, this requires a subtile merging of homogenization tools, such as multiscale convergence methods, with dimension reduction techniques for functionals subject to differential constraints. One observes that the results depend critically on the relative magnitude between the two scales. Interestingly, this even regards the fundamental question of locality of the limit model, and, in particular, leads to new findings also in the gradient case.Comment: 28 page

    A comparative review of peridynamics and phase-field models for engineering fracture mechanics

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    Computational modeling of the initiation and propagation of complex fracture is central to the discipline of engineering fracture mechanics. This review focuses on two promising approaches: phase-field (PF) and peridynamic (PD) models applied to this class of problems. The basic concepts consisting of constitutive models, failure criteria, discretization schemes, and numerical analysis are briefly summarized for both models. Validation against experimental data is essential for all computational methods to demonstrate predictive accuracy. To that end, the Sandia Fracture Challenge and similar experimental data sets where both models could be benchmarked against are showcased. Emphasis is made to converge on common metrics for the evaluation of these two fracture modeling approaches. Both PD and PF models are assessed in terms of their computational effort and predictive capabilities, with their relative advantages and challenges are summarized. © 2022, The Author(s)

    A comparative review of peridynamics and phase-field models for engineering fracture mechanics

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    Computational modeling of the initiation and propagation of complex fracture is central to the discipline of engineering fracture mechanics. This review focuses on two promising approaches: phase-field (PF) and peridynamic (PD) models applied to this class of problems. The basic concepts consisting of constitutive models, failure criteria, discretization schemes, and numerical analysis are briefly summarized for both models. Validation against experimental data is essential for all computational methods to demonstrate predictive accuracy. To that end, the Sandia Fracture Challenge and similar experimental data sets where both models could be benchmarked against are showcased. Emphasis is made to converge on common metrics for the evaluation of these two fracture modeling approaches. Both PD and PF models are assessed in terms of their computational effort and predictive capabilities, with their relative advantages and challenges are summarized

    Mechanics of Materials: Towards Predictive Methods for Kinetics in Plasticity, Fracture, and Damage

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    The workshop dealt with current advances of computational methods, mathematics and continuum mechanics directed at thermodynamically consistent forms of constitutive equations for complex evolutionary phenomena in modern materials such as plasticity, fracture and damage. The main aspects addressed in presentations and discussions were multiphysical description of new materials, (visco)plasticity, fracture, damage, structural mechanics, mechanics of materials and dislocation dynamics

    Real-Space Mesh Techniques in Density Functional Theory

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    This review discusses progress in efficient solvers which have as their foundation a representation in real space, either through finite-difference or finite-element formulations. The relationship of real-space approaches to linear-scaling electrostatics and electronic structure methods is first discussed. Then the basic aspects of real-space representations are presented. Multigrid techniques for solving the discretized problems are covered; these numerical schemes allow for highly efficient solution of the grid-based equations. Applications to problems in electrostatics are discussed, in particular numerical solutions of Poisson and Poisson-Boltzmann equations. Next, methods for solving self-consistent eigenvalue problems in real space are presented; these techniques have been extensively applied to solutions of the Hartree-Fock and Kohn-Sham equations of electronic structure, and to eigenvalue problems arising in semiconductor and polymer physics. Finally, real-space methods have found recent application in computations of optical response and excited states in time-dependent density functional theory, and these computational developments are summarized. Multiscale solvers are competitive with the most efficient available plane-wave techniques in terms of the number of self-consistency steps required to reach the ground state, and they require less work in each self-consistency update on a uniform grid. Besides excellent efficiencies, the decided advantages of the real-space multiscale approach are 1) the near-locality of each function update, 2) the ability to handle global eigenfunction constraints and potential updates on coarse levels, and 3) the ability to incorporate adaptive local mesh refinements without loss of optimal multigrid efficiencies.Comment: 70 pages, 11 figures. To be published in Reviews of Modern Physic

    Advanced Mechanical Modeling of Nanomaterials and Nanostructures

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    This reprint presents a collection of contributions on the application of high-performing computational strategies and enhanced theoretical formulations to solve a wide variety of linear or nonlinear problems in a multiphysical sense, together with different experimental studies

    Beyond classical electrodynamics: mesoscale electron dynamics and nonlinear effects in hybrid nanostructured systems

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    This work investigates the optial properties of hybrid metal-dielectric and ionic-solid largely regular nanostructures in the presence of nanosized features such as gaps and thin walls in tubular structures. The fundamental optical response of plasmonic, ionic and dielectric systems is considered from a classical electromagnetic perspective, including properties of amorphous materials, rough interfaces, nonlinear and semi-classical charge interactions. We focus hereby on two aspects: (i) nonclassical effects stemming from the quantum nature of freely moving charges and (ii) nonlinear optical response. The overall aim is to realistically describe complex nanoparticle distributions and ultrathin multilayers with reliable and rapid methods of computational nanophotonics while extending its scope towards multiphysics aspects beyond classical electrodynamics. The analytical and numerical models developed over the past years are presented in this work in detail with standard, but necessary technical details available in the appendices. We often assume a multilayered system where one layer is a nanostructure with either one- or two-dimensional symmetry, i.e., a grating or laminar structure in the first and an array of nanoparticles (disks, holes, pillars, etc.) in the latter case. Given the symmetries and overall composition of the structure, our method of choice is the Fourier Modal Method (FMM) together with the scattering matrix approach to connect the different layers. The standard FMM formulation is extended to include spatial dispersion effects of conduction band electrons in metals introducing not only an additional boundary condition, but an overall third longitudinal solution to the standard transversal solutions of the electromagnetic wave equation. Furthermore, we explore the impact of higher harmonic waves, in particular second and third harmonic generation, from the local fields around the nanostructures studied
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