An adaptive space-time phase field formulation for dynamic fracture of brittle shells based on LR NURBS

We present an adaptive space-time phase field formulation for dynamic fracture of brittle shells. Their deformation is characterized by the Kirchhoff–Love thin shell theory using a curvilinear surface description. All kinematical objects are defined on the shell’s mid-plane. The evolution equation for the phase field is determined by the minimization of an energy functional based on Griffith’s theory of brittle fracture. Membrane and bending contributions to the fracture process are modeled separately and a thickness integration is established for the latter. The coupled system consists of two nonlinear fourth-order PDEs and all quantities are defined on an evolving two-dimensional manifold. Since the weak form requires C1-continuity, isogeometric shape functions are used. The mesh is adaptively refined based on the phase field using Locally Refinable (LR) NURBS. Time is discretized based on a generalized-α method using adaptive time-stepping, and the discretized coupled system is solved with a monolithic Newton–Raphson scheme. The interaction between surface deformation and crack evolution is demonstrated by several numerical examples showing dynamic crack propagation and branching

FIC/FEM formulation with matrix stabilizing terms for incompressible flows at low and high Reynolds numbers

The final publication is available at Springer via http://dx.doi.org/10.1007/s00466-006-0060-yWe present a general formulation for incompressible fluid flow analysis using the finite element method. The necessary stabilization for dealing with convective effects and the incompressibility condition are introduced via the Finite Calculus method using a matrix form of the stabilization parameters. This allows to model a wide range of fluid flow problems for low and high Reynolds numbers flows without introducing a turbulence model. Examples of application to the analysis of incompressible flows with moderate and large Reynolds numbers are presented.Peer ReviewedPostprint (author's final draft

The geochemistry and petrogenesis of the Paleoproterozoic du Chef dyke swarm, Québec, Canada

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.The du Chef dyke swarm in southern Québec, Canada is composed of numerous northeast trending, greenschist-amphibolite facies, gabbronoritic dykes that crop out either side of the Grenville Front. The age of the du Chef swarm (2408 ± 3 Ga) has led previous authors to suggest a genetic link between the du Chef dykes and coeval swarms (including the Ringvassøy, Scourie, Widgemooltha and Sebanga) preserved on other Archean cratons. These now disparate dyke swarms are proposed to have formed in response to mantle plume-induced continental breakup during the early Proterozoic. This work represents the first geochemical study of the du Chef dykes and shows that the swarm evolved through fractional crystallisation of a tholeiitic parent magma that remained largely uncontaminated during its residence in, and ascent through, the crust. We also show that the primary magma for the du Chef swarm was derived through partial melting of an enriched region of the mantle, with a similar trace element composition to the modern-day HIMU reservoir and that the magma produced was significantly hotter than the ambient mantle at the time. We contend that the du Chef dykes are the product of early Proterozoic mantle plume magmatism and may help pinpoint an ancient hotspot centre that initiated continental break up along the margin of the Superior Craton at ∼2.4 Ga. Other dyke swarms proposed to be genetically linked with the du Chef dykes record a distinctly different petrogenetic history to that of the du Chef dykes, as evidenced by their more volcanic arc-like geochemical signature. These contrasting geochemical signatures in supposedly cogenetic continental tholeiitic rocks may be evidence of early Proterozoic mantle heterogeneity sampled by the rising du Chef mantle plume.This study forms part of a Ph.D. dissertation undertaken by T.J.R.C. at the University of Cardiff, United Kingdom. A. Okrugin's assistance in the field is acknowledged. J. Strongman, J. Fletcher and J. Pett are thanked for their permission of use of the petrographic equipment at Petrolab Ltd. L. Badham, A. Oldroyd, L. Woolley and P. Fisher are thanked for their help in preparation and analysis of samples. This is publication number 38 of the Large Igneous Provinces, Supercontinent Reconstruction, Resource Exploration Project (www.supercontinent.org)

A parallel multigrid solver for multi-patch Isogeometric Analysis

Isogeometric Analysis (IgA) is a framework for setting up spline-based discretizations of partial differential equations, which has been introduced around a decade ago and has gained much attention since then. If large spline degrees are considered, one obtains the approximation power of a high-order method, but the number of degrees of freedom behaves like for a low-order method. One important ingredient to use a discretization with large spline degree, is a robust and preferably parallelizable solver. While numerical evidence shows that multigrid solvers with standard smoothers (like Gauss Seidel) does not perform well if the spline degree is increased, the multigrid solvers proposed by the authors and their co-workers proved to behave optimal both in the grid size and the spline degree. In the present paper, the authors want to show that those solvers are parallelizable and that they scale well in a parallel environment.Comment: The first author would like to thank the Austrian Science Fund (FWF) for the financial support through the DK W1214-04, while the second author was supported by the FWF grant NFN S117-0

A combined reduced order‐full order methodology for the solution of 3D magneto‐mechanical problems with application to magnetic resonance imaging scanners

The design of a new magnetic resonance imaging (MRI) scanner requires multiple numerical simulations of the same magneto‐mechanical problem for varying model parameters, such as frequency and electric conductivity, in order to ensure that the vibrations, noise, and heat dissipation are minimized. The high computational cost required for these repeated simulations leads to a bottleneck in the design process due to an increased design time and, thus, a higher cost. To alleviate these issues, the application of reduced order modeling techniques, which are able to find a general solution to high‐dimensional parametric problems in a very efficient manner, is considered. Building on the established proper orthogonal decomposition technique available in the literature, the main novelty of this work is an efficient implementation for the solution of 3D magneto‐mechanical problems in the context of challenging MRI configurations. This methodology provides a general solution for varying parameters of interest. The accuracy and efficiency of the method are proven by applying it to challenging MRI configurations and comparing with the full‐order solution

Applied mechanics of the Puricelli osteotomy: a linear elastic analysis with the finite element method

<p>Abstract</p> <p>Background</p> <p>Surgical orthopedic treatment of the mandible depends on the development of techniques resulting in adequate healing processes. In a new technical and conceptual alternative recently introduced by Puricelli, osteotomy is performed in a more distal region, next to the mental foramen. The method results in an increased area of bone contact, resulting in larger sliding rates among bone segments. This work aimed to investigate the mechanical stability of the Puricelli osteotomy design.</p> <p>Methods</p> <p>Laboratory tests complied with an Applied Mechanics protocol, in which results from the Control group (without osteotomy) were compared with those from Test I (Obwegeser-Dal Pont osteotomy) and Test II (Puricelli osteotomy) groups. Mandible edentulous prototypes were scanned using computerized tomography, and digitalized images were used to build voxel-based finite element models. A new code was developed for solving the voxel-based finite elements equations, using a reconditioned conjugate gradients iterative solver. The Magnitude of Displacement and von Mises equivalent stress fields were compared among the three groups.</p> <p>Results</p> <p>In Test Group I, maximum stress was seen in the region of the rigid internal fixation plate, with value greater than those of Test II and Control groups. In Test Group II, maximum stress was in the same region as in Control group, but was lower. The results of this comparative study using the Finite Element Analysis suggest that Puricelli osteotomy presents better mechanical stability than the original Obwegeser-Dal Pont technique. The increased area of the proximal segment and consequent decrease of the size of lever arm applied to the mandible in the modified technique yielded lower stress values, and consequently greater stability of the bone segments.</p> <p>Conclusion</p> <p>This work showed that Puricelli osteotomy of the mandible results in greater mechanical stability when compared to the original technique introduced by Obwegeser-Dal Pont. The increased area of the proximal segment and consequent decrease of the size of lever arm applied to the mandible in the modified technique yield lower stress values and displacements, and consequently greater stability of the bone segments.</p

A Robust Solution Procedure for Hyperelastic Solids with Large Boundary Deformation

Compressible Mooney-Rivlin theory has been used to model hyperelastic solids, such as rubber and porous polymers, and more recently for the modeling of soft tissues for biomedical tissues, undergoing large elastic deformations. We propose a solution procedure for Lagrangian finite element discretization of a static nonlinear compressible Mooney-Rivlin hyperelastic solid. We consider the case in which the boundary condition is a large prescribed deformation, so that mesh tangling becomes an obstacle for straightforward algorithms. Our solution procedure involves a largely geometric procedure to untangle the mesh: solution of a sequence of linear systems to obtain initial guesses for interior nodal positions for which no element is inverted. After the mesh is untangled, we take Newton iterations to converge to a mechanical equilibrium. The Newton iterations are safeguarded by a line search similar to one used in optimization. Our computational results indicate that the algorithm is up to 70 times faster than a straightforward Newton continuation procedure and is also more robust (i.e., able to tolerate much larger deformations). For a few extremely large deformations, the deformed mesh could only be computed through the use of an expensive Newton continuation method while using a tight convergence tolerance and taking very small steps.Comment: Revision of earlier version of paper. Submitted for publication in Engineering with Computers on 9 September 2010. Accepted for publication on 20 May 2011. Published online 11 June 2011. The final publication is available at http://www.springerlink.co