We derive a new class of particle methods for conservation laws, which are based on numerical flux functions to model the interactions between moving particles. The derivation is similar to that of classical finite-volume methods; except that the fixed spatial mesh in a finite-volume method is substituted by so-called mass packets of particles. We give some numerical results on a shock wave solution for Burgers equation as well as the well-known one-dimensional shock tube problem. *

The finite volume particle method is a meshless discretization technique, which generalizes the classical finite volume method by using smooth, overlapping and moving test functions applied in the weak formulation of the conservation law. The method was originally developed for hyperbolic conservation laws so that the compressible Euler equations particularly apply.In the present work we analyze the discretization error and enforce consistency by a new set of geometrical quantities. Furthermore, we introduce a discrete Laplace operator for the scheme in order to extend the method to second order partial differential equations. Finally, we transfer Chorin's projection technique to the finite volume particle method in order to obtain a meshless scheme for incompressible flow.

No abstract

No abstract

Fiber networks with out-of-plane auxetic behavior have been sporadically investigated. One of the major challenges is to design such materials with giant negative Poissons ratio over large deformations. Here in, we report a systematic investigation to create three-dimensional (3D) fiber networks in the form of needle punched nonwoven materials with out-of-plane auxetic behavior over large deformations via theoretical modeling and extensive set of experiments. The experimental matrix has encapsulated the key parameters of the needlepunching nonwoven process. Under uniaxial tensile loading, the anisotropy coupled with local fiber densification in networks has yielded large negative Poissons ratio (up to −5.7) specifically in the preferential direction. The in-plane and out-of-plane Poissons ratios of fiber networks have been predicted and, subsequently, compared with the experimental results. Fiber orientation was found to be a core parameter that modulated the in-plane Poissons ratio of fiber networks. A parametric analysis has revealed the interplay between the anisotropy of the fiber network and the out-of-plane Poissons ratio based upon constant volume consideration