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Raymond, M. Sain / Advances in Engineering Software 33 (2002) 181±189 where 2…1 2 1†DShf …9† g…x† ˆ dH D2f 1rc Vmach dx g is the capture ef®ciency per unit length. However, the last correlation (5) did not take into account the hetero¯occulation and the formation of microvoids in the ®ber mat. Indeed, ®nes and short ®bers will ¯oc due to the presence of mineral ®llers and they will create more microvoids. New parameters need to be introduced in the diffusion coef®cient, D, to describe the new geometry of ¯ocs and the tortuosity 1 Deff ˆ D …10† t The hydrodynamical aspect of the small particles retention can be de®ned as a diffusional retention phenomenon.

Only half of the axisymmetric geometry of the bar has been The impact of a copper rod on a rigid wall problem, known as the Taylor impact problem, is a standard benchmark for dynamics computer codes. This problem simulates a high velocity impact of a copper rod on a rigid wall, it is used by many authors such as Liu et al. [20]. 4 mm. The impact is assumed to be frictionless and the impact velocity is set to 227 m/s. The final Fig. 5. Necking of a circular bar: ratio of the current to initial radius at the necking section versus axial displacement.

The results are in good agreement with experimental and previously reported computations. 2. Impact of a copper rod nonlinear hardening law of the form: 0 p p sv ¼ s0v þ ðs1 v 2 sv Þð1 2 expð2d1 Þ þ h1 Þ E n r s0v h ð17Þ Material properties given by Norris et al. [19] are reported in Table 1. This calculation problem is nonlinear, both by the constitutive equation and by the large deformation and rotation that occur at necking. Two different meshes consisting of 50 and 400 elements are considered to assess the influence of the discretization.

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