1,153 research outputs found
Parallel three-dimensional simulations of quasi-static elastoplastic solids
Hypo-elastoplasticity is a flexible framework for modeling the mechanics of
many hard materials under small elastic deformation and large plastic
deformation. Under typical loading rates, most laboratory tests of these
materials happen in the quasi-static limit, but there are few existing
numerical methods tailor-made for this physical regime. In this work, we extend
to three dimensions a recent projection method for simulating quasi-static
hypo-elastoplastic materials. The method is based on a mathematical
correspondence to the incompressible Navier-Stokes equations, where the
projection method of Chorin (1968) is an established numerical technique. We
develop and utilize a three-dimensional parallel geometric multigrid solver
employed to solve a linear system for the quasi-static projection. Our method
is tested through simulation of three-dimensional shear band nucleation and
growth, a precursor to failure in many materials. As an example system, we
employ a physical model of a bulk metallic glass based on the shear
transformation zone theory, but the method can be applied to any
elastoplasticity model. We consider several examples of three-dimensional shear
banding, and examine shear band formation in physically realistic materials
with heterogeneous initial conditions under both simple shear deformation and
boundary conditions inspired by friction welding.Comment: Final version. Accepted for publication in Computer Physics
Communication
A robust adaptive algebraic multigrid linear solver for structural mechanics
The numerical simulation of structural mechanics applications via finite
elements usually requires the solution of large-size and ill-conditioned linear
systems, especially when accurate results are sought for derived variables
interpolated with lower order functions, like stress or deformation fields.
Such task represents the most time-consuming kernel in commercial simulators;
thus, it is of significant interest the development of robust and efficient
linear solvers for such applications. In this context, direct solvers, which
are based on LU factorization techniques, are often used due to their
robustness and easy setup; however, they can reach only superlinear complexity,
in the best case, thus, have limited applicability depending on the problem
size. On the other hand, iterative solvers based on algebraic multigrid (AMG)
preconditioners can reach up to linear complexity for sufficiently regular
problems but do not always converge and require more knowledge from the user
for an efficient setup. In this work, we present an adaptive AMG method
specifically designed to improve its usability and efficiency in the solution
of structural problems. We show numerical results for several practical
applications with millions of unknowns and compare our method with two
state-of-the-art linear solvers proving its efficiency and robustness.Comment: 50 pages, 16 figures, submitted to CMAM
Computational multiscale solvers for continuum approaches
Computational multiscale analyses are currently ubiquitous in science and technology. Different problems of interest-e.g., mechanical, fluid, thermal, or electromagnetic-involving a domain with two or more clearly distinguished spatial or temporal scales, are candidates to be solved by using this technique. Moreover, the predictable capability and potential of multiscale analysis may result in an interesting tool for the development of new concept materials, with desired macroscopic or apparent properties through the design of their microstructure, which is now even more possible with the combination of nanotechnology and additive manufacturing. Indeed, the information in terms of field variables at a finer scale is available by solving its associated localization problem. In this work, a review on the algorithmic treatment of multiscale analyses of several problems with a technological interest is presented. The paper collects both classical and modern techniques of multiscale simulation such as those based on the proper generalized decomposition (PGD) approach. Moreover, an overview of available software for the implementation of such numerical schemes is also carried out. The availability and usefulness of this technique in the design of complex microstructural systems are highlighted along the text. In this review, the fine, and hence the coarse scale, are associated with continuum variables so atomistic approaches and coarse-graining transfer techniques are out of the scope of this paper
Data-driven finite elements for geometry and material design
Crafting the behavior of a deformable object is difficult---whether it is a biomechanically accurate character model or a new multimaterial 3D printable design. Getting it right requires constant iteration, performed either manually or driven by an automated system. Unfortunately, Previous algorithms for accelerating three-dimensional finite element analysis of elastic objects suffer from expensive precomputation stages that rely on a priori knowledge of the object's geometry and material composition. In this paper we introduce Data-Driven Finite Elements as a solution to this problem. Given a material palette, our method constructs a metamaterial library which is reusable for subsequent simulations, regardless of object geometry and/or material composition. At runtime, we perform fast coarsening of a simulation mesh using a simple table lookup to select the appropriate metamaterial model for the coarsened elements. When the object's material distribution or geometry changes, we do not need to update the metamaterial library---we simply need to update the metamaterial assignments to the coarsened elements. An important advantage of our approach is that it is applicable to non-linear material models. This is important for designing objects that undergo finite deformation (such as those produced by multimaterial 3D printing). Our method yields speed gains of up to two orders of magnitude while maintaining good accuracy. We demonstrate the effectiveness of the method on both virtual and 3D printed examples in order to show its utility as a tool for deformable object design.National Science Foundation (U.S.) (Grant CCF-1138967)United States. Defense Advanced Research Projects Agency (N66001-12-1-4242
An Optimized, Easy-to-use, Open-source GPU Solver for Large-scale Inverse Homogenization Problems
We propose a high-performance GPU solver for inverse homogenization problems
to design high-resolution 3D microstructures. Central to our solver is a
favorable combination of data structures and algorithms, making full use of the
parallel computation power of today's GPUs through a software-level design
space exploration. This solver is demonstrated to optimize homogenized
stiffness tensors, such as bulk modulus, shear modulus, and Poisson's ratio,
under the constraint of bounded material volume. Practical high-resolution
examples with 512^3(134.2 million) finite elements run in less than 32 seconds
per iteration with a peak memory of 21 GB. Besides, our GPU implementation is
equipped with an easy-to-use framework with less than 20 lines of code to
support various objective functions defined by the homogenized stiffness
tensors. Our open-source high-performance implementation is publicly accessible
at https://github.com/lavenklau/homo3d
Computational Multiscale Solvers for Continuum Approaches
Computational multiscale analyses are currently ubiquitous in science and technology. Different problems of interest-e.g., mechanical, fluid, thermal, or electromagnetic-involving a domain with two or more clearly distinguished spatial or temporal scales, are candidates to be solved by using this technique. Moreover, the predictable capability and potential of multiscale analysis may result in an interesting tool for the development of new concept materials, with desired macroscopic or apparent properties through the design of their microstructure, which is now even more possible with the combination of nanotechnology and additive manufacturing. Indeed, the information in terms of field variables at a finer scale is available by solving its associated localization problem. In this work, a review on the algorithmic treatment of multiscale analyses of several problems with a technological interest is presented. The paper collects both classical and modern techniques of multiscale simulation such as those based on the proper generalized decomposition (PGD) approach. Moreover, an overview of available software for the implementation of such numerical schemes is also carried out. The availability and usefulness of this technique in the design of complex microstructural systems are highlighted along the text. In this review, the fine, and hence the coarse scale, are associated with continuum variables so atomistic approaches and coarse-graining transfer techniques are out of the scope of this paper.Abengoa Researc
Matrixfreie voxelbasierte Finite-Elemente-Methode für Materialien mit komplizierter Mikrostruktur
Modern image detection techniques such as micro computer tomography
(μCT), magnetic resonance imaging (MRI) and scanning electron microscopy (SEM) provide us with high resolution images of the microstructure of materials in a non-invasive and convenient way. They form the basis for the geometrical models of high-resolution analysis, so called image-based analysis.
However especially in 3D, discretizations of these models reach easily the size of 100 Mill. degrees of freedoms and require extensive hardware resources in terms of main memory and computing power to solve the numerical model. Consequently, the focus of this work is to combine and adapt numerical solution methods to reduce the memory demand first and then the computation time and therewith enable an execution of the image-based analysis on modern computer desktops. Hence, the numerical model is a straightforward grid discretization of the voxel-based (pixels with a third dimension) geometry which omits the boundary detection algorithms and allows reduced storage of the finite element data structure and a matrix-free solution algorithm.
This in turn reduce the effort of almost all applied grid-based solution techniques and results in memory efficient and numerically stable algorithms for the microstructural models. Two variants of the matrix-free algorithm are presented. The efficient iterative solution method of conjugate gradients is used with matrix-free applicable preconditioners such as the Jacobi and the especially suited multigrid method. The jagged material boundaries of the voxel-based mesh are smoothed through embedded boundary elements which contain different material information at the integration point and are integrated sub-cell wise though without additional boundary detection. The efficiency of the matrix-free methods can be retained.Moderne bildgebende Verfahren wie Mikro-Computertomographie (μCT), Magnetresonanztomographie (MRT) und Rasterelektronenmikroskopie (SEM) liefern nicht-invasiv hochauflösende Bilder der Mikrostruktur von Materialien. Sie bilden die Grundlage der geometrischen Modelle der hochauflösenden bildbasierten Analysis. Allerdings erreichen vor allem in 3D die Diskretisierungen dieser Modelle leicht die Größe von 100 Mill. Freiheitsgraden und erfordern umfangreiche Hardware-Ressourcen in Bezug auf Hauptspeicher und Rechenleistung, um das numerische Modell zu lösen. Der Fokus dieser Arbeit liegt daher darin, numerische Lösungsmethoden zu kombinieren und anzupassen, um den Speicherplatzbedarf und die Rechenzeit zu reduzieren und damit eine Ausführung der bildbasierten Analyse auf modernen Computer-Desktops zu ermöglichen. Daher ist als numerisches Modell eine einfache Gitterdiskretisierung der voxelbasierten (Pixel mit der Tiefe als dritten Dimension)
Geometrie gewählt, die die Oberflächenerstellung weglässt und eine reduzierte Speicherung der finiten Elementen und einen matrixfreien Lösungsalgorithmus ermöglicht. Dies wiederum verringert den Aufwand von fast allen angewandten gitterbasierten Lösungsverfahren und führt zu Speichereffizienz und numerisch stabilen Algorithmen für die Mikrostrukturmodelle. Es werden zwei Varianten der Anpassung der matrixfreien Lösung präsentiert, die Element-für-Element Methode und eine Knoten-Kanten-Variante. Die Methode der konjugierten Gradienten in Kombination mit dem Mehrgitterverfahren als sehr effizienten Vorkonditionierer wird für den matrixfreien Lösungsalgorithmus adaptiert. Der stufige Verlauf der Materialgrenzen durch die voxelbasierte Diskretisierung wird durch Elemente geglättet, die am Integrationspunkt unterschiedliche Materialinformationen enthalten und über Teilzellen integriert werden (embedded boundary elements). Die Effizienz der matrixfreien Verfahren bleibt erhalten
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