A scalable parallel finite element framework for growing geometries. Application to metal additive manufacturing

This work introduces an innovative parallel, fully-distributed finite element framework for growing geometries and its application to metal additive manufacturing. It is well-known that virtual part design and qualification in additive manufacturing requires highly-accurate multiscale and multiphysics analyses. Only high performance computing tools are able to handle such complexity in time frames compatible with time-to-market. However, efficiency, without loss of accuracy, has rarely held the centre stage in the numerical community. Here, in contrast, the framework is designed to adequately exploit the resources of high-end distributed-memory machines. It is grounded on three building blocks: (1) Hierarchical adaptive mesh refinement with octree-based meshes; (2) a parallel strategy to model the growth of the geometry; (3) state-of-the-art parallel iterative linear solvers. Computational experiments consider the heat transfer analysis at the part scale of the printing process by powder-bed technologies. After verification against a 3D benchmark, a strong-scaling analysis assesses performance and identifies major sources of parallel overhead. A third numerical example examines the efficiency and robustness of (2) in a curved 3D shape. Unprecedented parallelism and scalability were achieved in this work. Hence, this framework contributes to take on higher complexity and/or accuracy, not only of part-scale simulations of metal or polymer additive manufacturing, but also in welding, sedimentation, atherosclerosis, or any other physical problem where the physical domain of interest grows in time

Effects of material properties of femoral hip components on bone remodeling

Bone loss around femoral hip stems is one of the problems threatening the long-term fixation of uncemented stems. Many believe that this phenomenon is caused by reduced stresses in the bone (stress shielding). In the present study the mechanical consequences of different femoral stem materials were investigated using adaptive bone remodeling theory in combination with the finite element method. Bone-remodeling in the femur around the implant and interface stresses between bone and implant were investigated for fully bonded femoral stems. Cemented stems (cobalt-chrome or titanium alloy) caused less bone resorption and lower interface stresses than uncemented stems made from the same materials. The range of the bone resorption predicted in the simulation models was from 23% in the proximal medial cortex surrounding the cemented titanium alloy stem to 76% in the proximal medial cortex around the uncemented cobalt-chrome stem. Very little bone resorption was predicted around a flexible, uncemented iso-elastic stem, but the proximal interface stresses increased drastically relative to the stiffer uncemented stems composed of cobalt-chrome or titanium alloy. However, the proximal interface stress peak was reduced and shifted during the adaptive remodeling process. The latter was found particularly in the stiffer uncemented cobalt-chrome-molybdenum implant and less for the flexible isoelastic implant

Astrophysical jets: observations, numerical simulations, and laboratory experiments

This paper provides summaries of ten talks on astrophysical jets given at the HEDP/HEDLA-08 International Conference in St. Louis. The talks are topically divided into the areas of observation, numerical modeling, and laboratory experiment. One essential feature of jets, namely, their filamentary (i.e., collimated) nature, can be reproduced in both numerical models and laboratory experiments. Another essential feature of jets, their scalability, is evident from the large number of astrophysical situations where jets occur. This scalability is the reason why laboratory experiments simulating jets are possible and why the same theoretical models can be used for both observed astrophysical jets and laboratory simulations

Adaptive Mesh Refinement for Characteristic Grids

I consider techniques for Berger-Oliger adaptive mesh refinement (AMR) when numerically solving partial differential equations with wave-like solutions, using characteristic (double-null) grids. Such AMR algorithms are naturally recursive, and the best-known past Berger-Oliger characteristic AMR algorithm, that of Pretorius & Lehner (J. Comp. Phys. 198 (2004), 10), recurses on individual "diamond" characteristic grid cells. This leads to the use of fine-grained memory management, with individual grid cells kept in 2-dimensional linked lists at each refinement level. This complicates the implementation and adds overhead in both space and time. Here I describe a Berger-Oliger characteristic AMR algorithm which instead recurses on null \emph{slices}. This algorithm is very similar to the usual Cauchy Berger-Oliger algorithm, and uses relatively coarse-grained memory management, allowing entire null slices to be stored in contiguous arrays in memory. The algorithm is very efficient in both space and time. I describe discretizations yielding both 2nd and 4th order global accuracy. My code implementing the algorithm described here is included in the electronic supplementary materials accompanying this paper, and is freely available to other researchers under the terms of the GNU general public license.Comment: 37 pages, 15 figures (40 eps figure files, 8 of them color; all are viewable ok in black-and-white), 1 mpeg movie, uses Springer-Verlag svjour3 document class, includes C++ source code. Changes from v1: revised in response to referee comments: many references added, new figure added to better explain the algorithm, other small changes, C++ code updated to latest versio

IGA-based Multi-Index Stochastic Collocation for random PDEs on arbitrary domains

This paper proposes an extension of the Multi-Index Stochastic Collocation (MISC) method for forward uncertainty quantification (UQ) problems in computational domains of shape other than a square or cube, by exploiting isogeometric analysis (IGA) techniques. Introducing IGA solvers to the MISC algorithm is very natural since they are tensor-based PDE solvers, which are precisely what is required by the MISC machinery. Moreover, the combination-technique formulation of MISC allows the straight-forward reuse of existing implementations of IGA solvers. We present numerical results to showcase the effectiveness of the proposed approach.Comment: version 3, version after revisio

One-step deposition of nano-to-micron-scalable, high-quality digital image correlation patterns for high-strain in-situ multi-microscopy testing

Digital Image Correlation (DIC) is of vital importance in the field of experimental mechanics, yet, producing suitable DIC patterns for demanding in-situ mechanical tests remains challenging, especially for ultra-fine patterns, despite the large number of patterning techniques in the literature. Therefore, we propose a simple, flexible, one-step technique (only requiring a conventional deposition machine) to obtain scalable, high-quality, robust DIC patterns, suitable for a range of microscopic techniques, by deposition of a low melting temperature solder alloy in so-called 'island growth' mode, without elevating the substrate temperature. Proof of principle is shown by (near-)room-temperature deposition of InSn patterns, yielding highly dense, homogeneous DIC patterns over large areas with a feature size that can be tuned from as small as 10nm to 2um and with control over the feature shape and density by changing the deposition parameters. Pattern optimization, in terms of feature size, density, and contrast, is demonstrated for imaging with atomic force microscopy, scanning electron microscopy (SEM), optical microscopy and profilometry. Moreover, the performance of the InSn DIC patterns and their robustness to large deformations is validated in two challenging case studies of in-situ micro-mechanical testing: (i) self-adaptive isogeometric digital height correlation of optical surface height profiles of a coarse, bimodal InSn pattern providing microscopic 3D deformation fields (illustrated for delamination of aluminum interconnects on a polyimide substrate) and (ii) DIC on SEM images of a much finer InSn pattern allowing quantification of high strains near fracture locations (illustrated for rupture of a Fe foil). As such, the high controllability, performance and scalability of the DIC patterns offers a promising step towards more routine DIC-based in-situ micro-mechanical testing.Comment: Accepted for publication in Strai