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In this paper void coalescence is regarded as the result of localization of plastic flow between enlarged voids. We obtain the failure criterion for a representative material volume (RMV) in terms of the macroscopic equivalent strain (E c ) as a function of the stress triaxiality parameter (T) and the Lode angle (h) by conducting systematic finite element analyses of the void-containing RMV subjected to different macroscopic stress states. A series of parameter studies are conducted to examine the effects of the initial shape and volume fraction of the primary void and nucleation, growth, and coalescence of secondary voids on the predicted failure surface E c (T, h). As an application, a numerical approach is proposed to predict ductile crack growth in thin panels of a 2024-T3 aluminum alloy, where a porous plasticity model is used to describe the void growth process and the expression for E c is calibrated using experimental data. The calibrated computational model is applied to predict crack extension in fracture specimens having various initial crack configurations and the numerical predictions agree very well with experimental measurements.

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The adhesion and friction coupling of hierarchical carbon nanotube arrays was investigated with a hierarchical multiscale modeling approach. At device level, vertically aligned carbon nanotube (VA-CNT) arrays with laterally distributed segments on top were analyzed via finite element methods to determine the macroscopic adhesion and friction force coupling. At the nanoscale, molecular dynamics simulation was performed to explore the origin of the adhesion enhancement due to the existence of the laterally distributed CNTs. The results show interfacial adhesion force is drastically promoted by interfacial friction force when a single lateral CNT is being peeled from an amorphous carbon substrate. By fitting with experiments, we find that under shearing loadings the maximum interfacial adhesion force is increased by a factor of ~5, compared to that under normal loadings. Pre-existing surface asperities of the substrate have proven to be the source of generating large interfacial friction, which in turn results in an enhanced adhesion. The critical peeling angles derived from the continuum and nano- levels are comparable to those of geckos and other synthetic adhesives. Our analysis indicates that the adhesion enhancement factor of the hierarchically structured VA-CNT arrays could be further increased by uniformly orienting the laterally distributed CNTs on top. Most importantly, a significant buckling of the lateral CNT at peeling front is captured on the molecular level, which provides a basis for the fundamental understanding of local deformation, and failure mechanisms of nanofibrillar structures. This work gives an insight into the durability issues that prevent the success of artificial dry adhesives.