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Infiltration by a pure matrix in the presence of preform deformation and partial matrix solidification is analyzed using a bounding approach for the preform rheology where solid metal is present. It is found, using parameters for the infiltration of short alumina fiber preforms by aluminum, that the two bounds are close in comparison to other factors of uncertainty in the prediction of infiltration rate. Using this approach, preform compression is shown to exert a significant influence on the infiltration rate for the system explored; in particular, the analysis shows the existence of an optimal value of applied pressure. Simplifications in the analysis are also presented, which yield fairly accurate results while easing their computation significantly.