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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 86
Edited by: B.H.V. Topping
Paper 120

Fatigue Life Prediction Reduced Order (Mesoscale) Model for Composite Materials

E. Gal, Z. Yuan, W. Wu and J. Fish

Multiscale Science and Engineering Center, Rensselaer Polytechnic Institute, Troy NY, United States of America

Full Bibliographic Reference for this paper
E. Gal, Z. Yuan, W. Wu, J. Fish, "Fatigue Life Prediction Reduced Order (Mesoscale) Model for Composite Materials", in B.H.V. Topping, (Editor), "Proceedings of the Eleventh International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 120, 2007. doi:10.4203/ccp.86.120
Keywords: multiscale, composite materials, finite element method, fatigue, life prediction, eigen-strain, damage mechanics, upscaling.

In this research we present an adaptive multiscale model which serves as a powerful engineering tool for the simulation of fatigue life prediction for composite material structures.

Efforts have been directed toward technology transfer of the suggested model in order to encourage engineers to perform the analysis by themselves. In particular the suggested model has been integrated with the ABAQUS finite element software using its user material subroutine, python scripts and GUI toolkit utilities to perform the bridging between the scales.

The spatial model consists of the micro, meso and macro scales. During the nonlinear solution the macro scale problem exchanges information with the mesoscale problem instead of with the microscale problem. In addition the information passing between the microscale problem and the mesoscale problem is performed prior to the macroscale analysis. This implies that the microscale problem should be solved only once, prior to the macroscale analysis, while the mesoscale problem should be solved whenever an updating of the macro material properties are needed. By that the computation cost of each unit cell solution is reduced with respect to the number of partitions chosen to represent the mesoscale problem. A practical unit cell problem can contain something between hundreds to tenth of thousands unknowns while sufficient approximations using the reduced order model might contains only tenth of unknowns. The practical meaning of that is colossal especially due the facts that:

  • an optimal solver needs n.log(n) operations to solve a set of equations with n unknowns
  • the unit cell problem should be solved ng*ninc*nc_iter*nf_iter times where ng is the number of the material Gauss points within the macroscale problem, ninc is the number of load increments needed to analyzed the macroscale problem, nc_iter is the average number of macroscale iterations required to converge an increment and nf_iter is the average number of microscale iterations needed to converge each maroscale iteration.

The adaptive temporal multiscale approach is presented via a block integration scheme. The suggested block integration scheme reduces dramatically the number of increments needed to be actually analyzed, while the adaptive feature ensures its accuracy with respect to the cycle by cycle solution. In practice hundreds of millions of load increments might be needed to represent the cycling loading up to failure while an appropriate approximation with the proposed adaptive scheme will contain "only" tens of thousands increments, again the practical meaning of that is colossal.

Finally to bring about the suggested multiscale model to serve as a powerful engineering tool an efficient optimized three step calibration procedure has been suggested.

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