To better simulate multi-phase interactions involving failure evolution, the material point method （MPM） has evolved for almost twenty years. Recently, a particle-based multiscale simulation procedure is being developed, within the framework of the MPM, to describe the detonation process of energetic nano-composites from molecular to continuum level so that a multiscale equation of state could be formulated. In this letter, a multiscale MPM is proposed via both hierarchical and concurrent schemes to simulate the impact response between two microrods with different nanostructures. Preliminary results are presented to illustrate that a transition region is not required between different spatial scales with the proposed approach.
Zhen ChenYilong HanShan JiangYong GanThomas D. Sewell
Biomaterials such as bone,teeth,nacre and silk are known to have superior mechanical properties due to their specific nanocomposite structures.Here we report that the woodpecker's tongue exhibits a novel strength and flexibility due to its special composite micro/nanostructure.The tongue consists of a flexible cartilage-and-bone skeleton covered with a thin layer tissue of high strength and elasticity.At the interface between the cartilage-and-bone skeleton and the tissue layer,there is a hierarchical fiber-typed connection.It is this special design of the tongue that makes the woodpeckers efficient in catching the insects inside trees.The special micro/nanostructures of the woodpecker's tongue show us a potential method to enhance the interfacial connection between soft and hard material layers for bio-inspired composite system designs.
An extended multiscale finite element method （EMsFEM） is developed for solving the mechanical problems of heterogeneous materials in elasticity.The underlying idea of the method is to construct numerically the multiscale base functions to capture the small-scale features of the coarse elements in the multiscale finite element analysis.On the basis of our existing work for periodic truss materials, the construction methods of the base functions for continuum heterogeneous materials are systematically introduced. Numerical experiments show that the choice of boundary conditions for the construction of the base functions has a big influence on the accuracy of the multiscale solutions, thus,different kinds of boundary conditions are proposed. The efficiency and accuracy of the developed method are validated and the results with different boundary conditions are verified through extensive numerical examples with both periodic and random heterogeneous micro-structures.Also, a consistency test of the method is performed numerically. The results show that the EMsFEM can effectively obtain the macro response of the heterogeneous structures as well as the response in micro-scale,especially under the periodic boundary conditions.
Hong-Wu Zhang·Jing-Kai Wu·Jun L·Zhen-Dong Fu State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology,Dalian 116024,China
By converting an optimal control problem for nonlinear systems to a Hamiltonian system,a symplecitc-preserving method is proposed.The state and costate variables are approximated by the Lagrange polynomial.The state variables at two ends of the time interval are taken as independent variables.Based on the dual variable principle,nonlinear optimal control problems are replaced with nonlinear equations.Furthermore,in the implementation of the symplectic algorithm,based on the 2N algorithm,a multilevel method is proposed.When the time grid is refined from low level to high level,the initial state and costate variables of the nonlinear equations can be obtained from the Lagrange interpolation at the low level grid to improve efficiency.Numerical simulations show the precision and the efficiency of the proposed algorithm in this paper.
An effective method to design structural Left-handed material（LHM） was proposed. A commercial finite element software HFSS and S-parameter retrieval method were used to determine the effective constitutive parameters of the metamaterials, and topology optimization technique was introduced to design the microstructure configurations of the materials with desired electromagnetic characteristics. The material considered was a periodic array of dielectric substrates attached with metal film pieces. By controlling the arrangements of the metal film pieces in the design domain, the potential microstructure with desired electromagnetic characteristics can be obtained finally. Two different LHMs were obtained with maximum bandwidth of negative refraction, and the experimental results show that negative refractive indices appear while the metamaterials have simultaneously negative permittivity and negative permeability. Topology optimization technique is found to be an effective tool for configuration design of LHMs.
