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Needle-punching is used to entangle the fibers, which are then bonded into the matrix. This process results in a thin, flat composite which is used as the outer layers in a laminate, which sandwich honeycomb filler. 13 shows the entangled fibers, which are of varying length and diameter, of average 62mm and 30μm respectively, with volume fraction approximately 30%. There is a 50% variation in the diameters of the fibers along their length as a result of their natural origin. Due to the nature of the needle-punching process the fibers are orientated randomly within the matrix.

Reddy and A. T. 1. 40) is satisfied except for in the case of Poisson’s ratio ( ). As truss elements have no transverse strain, effectively the value used for Poisson’s ratio is zero. Therefore the fact that the effective averaged value is below the value for the matrix is acceptable. 15 show the distribution of the results for the 125 subdomains. 1. 15. Distribution of data for effective bulk, shear and Young’s moduli. 1. 4. OPEN PROBLEMS AND FUTURE DIRECTIONS The objective of this section is to briefly describe some of the key challenges facing multiscale modeling methodologies.

31) Introduction to Finite Element Analysis and Recent Developments 21 Integration over triangles. 12). 33) where ̃ ̃ (l = 1, 2, 3) are the coordinates of the midpoints of the sides. The rule of order 1 is exact for polynomials of degree 1, while the rule of order 3 is exact for polynomials of order 2. 12. Integration rules on the reference triangle. 3. MICRO-MECHANICAL MODELING In this section we go through the details of micro-macro modeling of a random fiberreinforced composite. The material is assumed to be macroscopically isotropic, but it is micro-structurally anisotropic as a result of the presence of fibers in a random arrangement at that scale.

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