We present a family of convected particle domain interpolations (CPDIs) within the framework of the material point method (MPM). That includes two dimensional triangular, quadrilateral, and polygonal CPDIs and three dimensional tetrahedron and polyhedron CPDIs. Theoretical derivations as well as computer implementation aspects are provided. A new perspective of CPDIs is given to link it to the recent works on the coupling of MPM and the finite element method. Numerical examples are given to demonstrate the performance of the proposed method. © 2016 Elsevier B.V.

Sundararajan Natarajan

Department of Mechanical Engineering

Vinh Phu Nguyen

Chi Thanh Nguyen

Timon Rabczuk

geometry

interpolation

Numerical methods

COMPUTER IMPLEMENTATIONS

MATERIAL POINT METHODS

PARTICLE DOMAINS

POLYGON

POLYHEDRA

THEORETICAL DERIVATIONS

finite element method

IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

Finite Elements in Analysis and Design

We show both theoretically and numerically a connection between the smoothed finite element method (SFEM) and the virtual element method and use this approach to derive stable, cheap and optimally convergent polyhedral FEM. We show that the stiffness matrix computed with one subcell SFEM is identical to the consistency term of the virtual element method, irrespective of the topology of the element, as long as the shape functions vary linearly on the boundary. Using this connection, we propose a new stable approach to strain smoothing for polygonal/polyhedral elements where, instead of using sub-triangulations, we are able to use one single polygonal/polyhedral subcell for each element while maintaining stability. For a similar number of degrees of freedom, the proposed approach is more accurate than the conventional SFEM with triangular subcells. The time to compute the stiffness matrix scales with the O(dofs)1.1 in case of the conventional polygonal FEM, while it scales as O(dofs)0.7 in the proposed approach. The accuracy and the convergence properties of the SFEM are studied with a few benchmark problems in 2D and 3D linear elasticity. © 2015 John Wiley &amp; Sons, Ltd.

International Journal for Numerical Methods in Engineering

Virtual and smoothed finite elements: A connection and its application to polygonal/polyhedral finite element methods

Controlling the onset of numerical fracture in parallelized implementations of the material point method (MPM) with convective particle domain interpolation (CPDI) domain scaling

Applied Mechanics and Materials

A Voronoi Cell Material Point Method for Large Deformation Solid Mechanics Problems

Acta Mechanica

Continuum effective-stress approach for high-rate plastic deformation of fluid-saturated geomaterials with application to shaped-charge jet penetration

ACM Transactions on Graphics

The affine particle-in-cell method

On a family of convected particle domain interpolations in the material point method

Journal	Data powered by TypesetFinite Elements in Analysis and Design
Publisher	Data powered by TypesetElsevier B.V.
ISSN	0168874X
Open Access	No