Non-standard bone simulation: interactive numerical analysis by computational steering

Yang, Zhengxiong; Kollmannsberger, Stefan; Düster, Alexander; Ruess, Martin; García, Eduardo Grande; Burgkart, Rainer; Rank, Ernst

doi:10.1007/s00791-012-0175-y

Cited by 47 publications

(32 citation statements)

References 29 publications

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“…The FCM has been applied to several problems like linear elasticity in 2D [13] and 3D [7], to shell problems [16] as well as to problems in biomechanics [5,26,27]. Nonlinear problems such 1 as geometrically nonlinearity [23] or elastoplasticity [1,3] have been addressed as well.…”

Section: Introductionmentioning

confidence: 99%

Theoretical and Numerical Investigation of the Finite Cell Method

2015

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We present a detailed analysis of the convergence properties of the finite cell method which is a fictitious domain approach based on high order finite elements. It is proved that exponential type of convergence can be obtained by the finite cell method for Laplace and Lamé problems in one, two as well three dimensions. Several numerical examples in one and two dimensions including a wellknown benchmark problem from linear elasticity confirm the results of the mathematical analysis of the finite cell method.

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Section: Introductionmentioning

confidence: 99%

Theoretical and Numerical Investigation of the Finite Cell Method

2015

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“…Owing to the high-order shape functions, the FCM is able to provide accurate results with an exponential rate of convergence even when there are void regions in the cells [16,23,24]. The high-order convergence can be guaranteed if the integration is performed accurately enough, provided that no singularities are introduced as a result of reentrant corners or cracks.…”

Section: Solution Characteristics Of the Fcmmentioning

confidence: 97%

“…The voxelbased geometrical representation, which is common practice in biomechanical problems, or the implicit representation of geometry can be effectively combined with the FCM with hardly any outlay for mesh generation. The FCM has successfully been applied to various types of problems such as homogenization [18], topology optimization [19], biomechanics [20][21][22][23][24], geometrically nonlinear problems [25], elastoplasticity [26] and thin-walled structures [27]. However, the convergence rate of the standard FCM deteriorates in the case of heterogeneous materials since the displacement field exhibits a loss of regularity at the material interface, introducing a weak discontinuity.…”

Section: Introductionmentioning

confidence: 99%

Local enrichment of the finite cell method for problems with material interfaces

Joulaian

Düster

2013

Comput Mech

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This paper proposes an efficient, hierarchical high-order enrichment approach for the finite cell method applied to problems of solid mechanics involving discontinuities and singularities. In contrast to the standard extended finite element method, where new degrees of freedom are introduced for all finite elements located in the enrichment zone, we define the enrichment on a so-called overlay mesh which is superimposed over the base mesh. The approximation on the base mesh is obtained by means of the finite cell method where the hp-d method is employed to introduce the hierarchical extension on the overlay mesh. We present two different strategies for defining the enrichment on the superimposed overlay mesh. In the first approach, the enrichment is based on a local h-, p-or hp-refinement utilizing the finite element method on the overlay mesh. Alternatively, the enrichment is constructed by means of the partition of unity method introducing carefully selected enrichment functions suitable for the problem at hand. Our results reveal that the proposed method improves the accuracy of the finite cell method significantly with only a minimum number of additional degrees of freedom. In this paper we will focus on examples with material interfaces although the method can also be applied to problems involving strong discontinuities and singularities. Accurate stress distribution and an exponential rate of convergence are the two striking characteristics of the proposed method. Due to the hierarchical approach it paves the way to using different approaches for the M. Joulaian (B) · A. Düster Numerical Structural Analysis with Application in Ship Technology, approximation on the base and the overlay mesh and accordingly allows multiscale problems to be addressed as well.Keywords FCM · local enrichment · PUM · multiscale method · hp-d method · high-order method · XFEM

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“…A detailled time effort analysis based on highly optimized routines and libraries is out of the scope of this contribution and is reported e.g. in [21].…”

Section: B Performance Analysismentioning

confidence: 99%

“…Computer-aided medical procedures are of increasing relevance in clinical practice and have already established in many clinical centres worldwide for minimal-invasive surgeries, surgical navigation and particularly for surgical pre-planning [21], [5], [8]. The need for patient-specific simulations controls the need for accurate, reliable, fast and parallel algorithms in this field that predict the in-vivo response of medical treatment and surgical interventions [22], [7].…”

Section: Introductionmentioning

confidence: 99%

A Parallel High-Order Fictitious Domain Approach for Biomechanical Applications

Ruess

Varduhn

Rank

et al. 2012

2012 11th International Symposium on Parallel and Distributed Computing

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Abstract-The focus of this contribution is on the parallelization of the Finite Cell Method (FCM) applied for biomechanical simulations of human femur bones. The FCM is a high-order fictitious domain method that combines the simplicity of Cartesian grids with the beneficial properties of hierarchical approximation bases of higher order for an increased accuracy and reliablility of the simulation model. A pre-computation scheme for the numerically expensive parts of the finite cell model is presented that shifts a significant part of the analysis update to a setup phase of the simulation, thus increasing the update rate of linear analyses with time-varying geometry properties to a range that even allows user interactive simulations of high quality. Paralellization of both parts, the pre-computation of the model stiffness and the update phase of the simulation is simplified due to a simple and undeformed cell structure of the computation domain. A shared memory parallelized implementation of the method is presented and its performance is tested for a biomedical application of clinical relevance to demonstrate the applicability of the presented method.

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Non-standard bone simulation: interactive numerical analysis by computational steering

Cited by 47 publications

References 29 publications

Theoretical and Numerical Investigation of the Finite Cell Method

Theoretical and Numerical Investigation of the Finite Cell Method

Local enrichment of the finite cell method for problems with material interfaces

A Parallel High-Order Fictitious Domain Approach for Biomechanical Applications

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