Title
Taylor least squares reconstruction technique for material point methods
Author
Wobbes, E. D. (Student TU Delft)
Möller, M. (TU Delft Numerical Analysis) 
Galavi, V. (Deltares)
Vuik, Cornelis (TU Delft Numerical Analysis)
Contributor
Owen, Roger (editor)
de Borst, Rene (editor)
Reese, Jason (editor)
Pearce, Chris (editor)
Date
2020
Abstract
The material point method (MPM) is an effective computational tool for simulating problems involving large deformations. However, its direct mapping of the material-point data to the background grid frequently leads to severe inaccuracies. The standard function reconstruction techniques can considerably decrease these errors, but do not always guarantee the conservation of the total mass and linear momentum as the MPM algorithm does. In this paper, we introduce a novel technique, called Taylor Least Squares (TLS), which combines the Least Squares approximation with Taylor basis functions to reconstruct functions from scattered data. Within each element, the TLS technique approximates quantities of interest, such as stress and density, and when used with a suitable quadrature rule, it conserves the total mass and linear momentum after mapping the material-point information to the grid. The numerical and physical properties of the reconstruction technique are first illustrated on one- and two-dimensional functions. Then the TLS technique is tested as part of MPM, Dual Domain Material Point Method (DDMPM), and B-spline MPM (BSMPM) on a one-dimensional problem experiencing small and large deformations. The obtained results show that applying the TLS approximation significantly improves the accuracy of the considered versions of the material point method, while preserving the physical properties of the standard MPM.
Subject
B-spline
Dual domain
Function reconstruction
Least-squares approximation
Material Point Method
Taylor basis
To reference this document use:
http://resolver.tudelft.nl/uuid:502298af-bf32-4ec5-a5a1-c8c00e846d05
Publisher
International Centre for Numerical Methods in Engineering, CIMNE
Embargo date
2020-09-14
ISBN
9788494731167
Source
Proceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018
Event
6th ECCOMAS European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th ECCOMAS European Conference on Computational Fluid Dynamics, ECFD 2018, 2018-06-11 → 2018-06-15, Glasgow, United Kingdom
Series
Proceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018
Bibliographical note
Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.
Part of collection
Institutional Repository
Document type
conference paper
Rights
© 2020 E. D. Wobbes, M. Möller, V. Galavi, Cornelis Vuik