scholarly journals Effective behavior of linear viscoelastic composites: A time-integration approach

2007 ◽  
Vol 44 (2) ◽  
pp. 507-529 ◽  
Author(s):  
Noël Lahellec ◽  
Pierre Suquet
Author(s):  
Yiliu Weng ◽  
Lipeng Zheng

Engine fan blade-off (FBO) is an extreme event that could well place the flight safety at risk. When it happens, the engine will experience high-velocity impact at first, and then enter into a “high-power” stage due to huge unbalance before coming to a steady state called “windmilling”. The analytical process for FBO can be split into two phases, one for impact simulation and the other for obtaining the FBO load to pylon. Typically, explicit method with fine mesh finite elements is used in the first phase, and implicit method with coarse meshes is adopted in the second one. In most cases, the only connection between these two analyses may be the unbalance level caused by FBO. More structural responses other than the unbalance level due to fan blade impact are actually ignored in the succeeding implicit analysis. Attempts have been made by Boeing, GE and MSC to integrate these two processes by adding some features in MD Nastran. Yet the intermediate binary files created and the restricted input entries make the integration process quite inflexible. This paper introduces an explicit-implicit time integration approach for finite element analysis of engine load following an FBO event. The proposed method attempts to connect the two stages more closely, yet in a more flexible manner. In this approach, the engine structural response under FBO obtained from explicit analysis is transferred to the implicit analysis, together with the unbalance level caused by blade loss. The necessity of the approach is discussed, and sensitivity analysis is conducted to understand the factors that play significant roles in the approach. As the models for explicit and implicit analyses are different in mesh sizes and scales, the authors also develop a tool that can interpolate the load information and further, smooth it to fit calculation. Finally, the approach is tested on a full engine model to show its applicability and advantages over the traditional method for load evaluation of FBO event.


Author(s):  
Lallit Anand ◽  
Sanjay Govindjee

This chapter introduces the essential elements of linear viscoelastic material behaviour and modeling in one- and three-dimensions. Both relaxation and creep phenomena are introduced and modeled using Boltzmann’s superposition integral. Various common kernel functions are introduced, as is the standard and generalized standard linear model in differential and integral form. The correspondence principle is discussed for the solution of practical problems and to connect relaxation and creep formulations. Storage and loss moduli for oscillatory loadings are discussed, as are loss tangents and dissipation. For the generalized standard linear solid its time integration via the Herrmann-Peterson recursion relation is discussed. Effects of temperature are discussed, and the concept of time-temperature equivalence is introduced.


Author(s):  
Jiawei Wang ◽  
Feng Chen ◽  
Jinghui Shao ◽  
Weichen Zhang ◽  
Xikui Ma

Purpose This paper aims to present a novel hybrid time integration approach for efficient numerical simulations of multiscale problems involving interactions of electromagnetic fields with fine structures. Design/methodology/approach The entire computational domain is discretized with a coarse grid and a locally refined subgrid containing the tiny objects. On the coarse grid, the time integration of Maxwell’s equations is realized by the conventional finite-difference technique, while on the subgrid, the unconditionally stable Krylov-subspace-exponential method is adopted to breakthrough the Courant–Friedrichs–Lewy stability condition. Findings It is shown that in contrast with the conventional finite-difference time-domain method, the proposed approach significantly reduces the memory costs and computation time while providing comparative results. Originality/value An efficient hybrid time integration approach for numerical simulations of multiscale electromagnetic problems is presented.


2011 ◽  
Vol 20 (8) ◽  
pp. 1116-1129 ◽  
Author(s):  
Sy Tuan Nguyen ◽  
Luc Dormieux ◽  
Yann Le Pape ◽  
Julien Sanahuja

This article aims at the determination of the effective behavior of a microcracked linear viscoelastic solid. Due to the nonlinearity of the strain concentration in the cracks, the latter cannot be derived directly from a combination of the correspondence theorem with the Eshelby-based homogenization schemes. The proposed alternative approach is based on the linear relationship between the macroscopic strain and the local displacement discontinuity across the crack. An approximation of the effective behavior in the framework of a Burger model is derived analytically.


2020 ◽  
Vol 157 ◽  
pp. 103377
Author(s):  
O.L. Cruz-González ◽  
R. Rodríguez-Ramos ◽  
J.A. Otero ◽  
A. Ramírez-Torres ◽  
R. Penta ◽  
...  

2019 ◽  
Vol 223 ◽  
pp. 110927 ◽  
Author(s):  
O.L. Cruz-González ◽  
D. Guinovart-Sanjuán ◽  
R. Rodríguez-Ramos ◽  
J. Bravo-Castillero ◽  
R. Guinovart-Díaz ◽  
...  

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