Macroscopic Modeling of Calender-Bonded Composite Nonwoven Materials

Microscopic modeling in the past resulted in prediction of the effect of a single circular bond on the mechanical behavior of a single-bonded composite nonwoven (stretching under an applied stress, and the corresponding stress field). This was an important first modeling step, but not the last one, because in real composite nonwoven fabrics the number of bond spots can be of the order of 100 per cm² (several hundred per square inch). The present work builds on the previous results for single-bonded composite nonwovens and aims to tackle a realistic situation with multiple bonds using a new approach employing the renormalization group technique, first introduced in theoretical physics in the theory of phase transitions. This approach was also tremendously fruitful in the problems related to critical phenomena in the percolation theory and in predictions of the collective effects in disperse systems. Here, composite nonwovens with multiple bonding spots (with their overall number being N ≫ 1) are explored. The present results predict the stretching force required to be applied to a composite bonded strip with N ≫ 1 bonding spots to achieve a given strain. Accordingly, the present results determine an effective stiffness of composite nonwoven materials with multiple bonding spots. In addition, the effects of the individual bonding spot shapes and their patterning on the above-mentioned characteristics are predicted. Qualitative comparison with available experimental data is discussed.