Multi-scale Modeling of Composite Solids with Damage

摘要

In modeling behavior of heterogeneous solids, which contain entities of different length scales, a number of issues arise. One issue is to connect responses of the entities at their own characteristic length scales to the overall (macro) response of the solid. A common approach to address this issue is by the so-called hierarchical scheme where one begins with the smallest scale and advances up the scale, carrying the average response characteristics from a lower scale to the next higher scale. This approach requires identifying a representative volume element (RVE) at each scale over which averages of the response characteristics are taken and specifying the so-called bridging criteria by which these averages are carried over to the higher scale. As yet there are no rigorous and generally applicable procedures concerning RVE and bridging of scales.The hierarchical approach runs into more challenges when damage such as distributed cracking occurs at multiple length scales. As discussed by this author in a previous work related to damage in composite materials [1], the length scales of damage, although related to the heterogeneity length scales, are not always identical to those. A multi-scale synergistic damage mechanics approach was outlined in that work as a way to effectively address the dual multi-scale problem.The present work will report further on the multi-scale modeling of damage in composite materials with particular attention to generating comprehensiveness by treating damage evolution at multiple length scales.[1] Talreja, R., "Multi-scale Modeling in Damage Mechanics of Composite Materials," Journal of Materials Science, Vol. 41, No. 20, pp. 6800-6812, 2006.