Element Free Galerkin Formulation for Problems in Composite Micromechanics

Abstract:

The heterogeneity and anisotropy of structural composites make the application of the standard mesh-based methods using the meshing of interfacial region between matrix and fibers a difficult task. The objective of this study is to present the EFG formulation for problems of composite micromechanics. It is expected that the tediousness and approximations involved in mesh generation, and hence inaccuracies in the results can be avoided using the new meshless techniques such as the Element Free Galerkin (EFG) method. The theoretical methodologies, computer implementations and practical application are carried out. Periodic boundary conditions of the unit cell under tensile load are set up. The method of Lagrange multipliers is introduced for the treatment of material discontinuity at the fiber-matrix interface in which both the displacement continuity and traction reciprocity are satisfied. The EFG method is formulated for the generalized plane strain problems. Examples are presented to illustrate the effectiveness of the proposed micromechanical model, and it is validated by comparing the results with available numerical solutions.

• Periodical: Applied Mechanics and Materials (Volumes 809-810)
• Pages: 896-901
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.809-810.896
• Online since: November 2015
• Authors: Victoria Rosca*, Nicolae Ţăranu, Liliana Bejan, Andrei Octav Axinte
• Keywords: Composite Micromechanics, Element Free Galerkin (EFG) Method, Periodic Homogenization, Unit Cell

References

[1] H.J. Kim, C.C. Swan, Voxel-Based meshing and unit-cell analysis of textile composites, Int. J. Numer. Methods Engng, Vol. 56 (2003), 977–1006.

DOI: 10.1002/nme.594

[2] T. Belytschko, Y.Y. Lu, L. Gu, Element-free Galerkin methods, Int. J. Numer. Meth. Engng. 37 (1994), 229–256.

DOI: 10.1002/nme.1620370205

[3] T.D. Dang, B.V. Sankar, Meshless local Petrov–Galerkin for problems in composite micromechanics, AIAA J., 45 (2007), 912–921.

DOI: 10.2514/1.23434

[4] I. Ahmadi, M. Aghdam, A generalized plane strain Meshless Local Petrov–Galerkin method for the micromechanics of thermomechanical loading of composites, J. Mech. Mater. Struct. 5 (2010), 549 –566.

DOI: 10.2140/jomms.2010.5.549

[5] D. Hegen, Element-free Galerkin methods in combination with finite element approaches, Comput. Methods Appl. Mech. Engrg. 135 (1996), 143-166.

DOI: 10.1016/0045-7825(96)00994-2

[6] S. Li, W.K. Liu. Meshfree and particle methods and their applications". Appl Mech Rev. 55 (2010), 1-34.

[7] V.E. Rosca, V.M.A. Leitao, Quasi-Monte Carlo mesh-free integration for meshless weak formulations, Eng, Anal, Bound, Elem. 32 (2008), 471-479.

DOI: 10.1016/j.enganabound.2007.10.015

[8] V.E. Rosca, V.M.A. Leitao, Numerical implementation of meshless methods for beam problems, Archives of Civil Engineering 58 (2012), 175-184.

DOI: 10.2478/v.10169-012-0010-3

[9] S. Fernández-Méndez, A. Huerta, Imposing essential boundary conditions in mesh-free methods, Comput. Methods Appl. Mech. Engrg. 193 (2004), 1257–1273.

DOI: 10.1016/j.cma.2003.12.019

[10] N. Naik, Woven fabric composites, in: P.K. Mallick (Eds. ), Composites Engineering Handbook, Technomic Lancaster, PA, USA, 1997, p.247–307.