SUMMARYThe initiation and evolution of transverse matrix cracks and delaminations are predicted within a meshindependent cracking (MIC) framework. MIC is a regularized extended finite element method (x-FEM) that allows the insertion of cracks in directions that are independent of the mesh orientation. The Heaviside step function that is typically used to introduce a displacement discontinuity across a crack surface is replaced by a continuous function approximated by using the original displacement shape functions. Such regularization allows the preservation of the Gaussian integration schema regardless of the enrichment required to model cracking in an arbitrary direction. The interaction between plies is anchored on the integration point distribution, which remains constant through the entire simulation. Initiation and propagation of delaminations between plies as well as intra-ply MIC opening is implemented by using a mixed-mode cohesive formulation in a fully three-dimensional model that includes residual thermal stresses. The validity of the proposed methodology was tested against a variety of problems ranging from simple evolution of delamination from existing transverse cracks to strength predictions of complex laminates without a priori knowledge of damage location or initiation. Good agreement with conventional

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of CNT arrays in applications such as thermal [ 1-3 ] and electrical [ 4,5 ] interface materials, deformable CNT array strain biosensors, [ 6 ] and electrical brushes [ 7 ] rely intimately on array mechanics for proper operation. Often, optimization for a specifi c application requires consideration of two or more coupled properties, such as stiffness and damping, or stiffness and thermal conductivity. However, the means by which global deformation of a CNT array generates localized deformation of the constituent CNTs, and how this, in turn, determines the collective mechanical properties is not thoroughly understood. Many studies have examined the mechanical properties of CNT arrays via nanoindentation [ 8-11 ] or uniaxial compression, [ 12-15 ] and showed that entangled arrays locally yield by coordinated buckling of CNTs. The buckles propagate in a direction perpendicular to CNT alignment, and strain recovery after unloading can be signifi cantly elastic [ 12 , 15 ] or plastic [ 10,11 , 13,14 ] based on the diameter, alignment, and packing density of the constituent CNTs. Buckle initiation has been observed preferentially near the top [ 11 ] or bottom side of an array, [ 12-14 ] but it is has not been shown how the initiation of buckling relates to the geometry and global deformation of the arrays. More recently, in situ scanning electron microscopy (SEM) mechanical testing has enabled direct observation of buckle evolution and has been utilized for the uniaxial compression of CNT array columns [ 13 ] and the nanoindentation of CNT arrays. [ 11 ] A continuum-based analytical model inspired by the in situ CNT array column compression observations [ 13 ] was recently used to predict the strain distribution that arises during buckling; [ 16 ] however, an experimental technique capable of mapping local strain fi elds within CNT arrays to validate this and other models, and to relate mechanical properties to CNT morphology and array geometry, has not yet been reported. Likewise, a means to quantify the seemingly diverse CNT buckling behavior at a local level is needed to better understand the mechanics driving buckle formation, and to provide a basis for comparing experimental results from different studies. In order to map strain fi elds within CNT arrays, a highresolution, non-contact method is needed, because the small size scale of CNT arrays prevents spatially resolved mechanical measurements via attached hardware such as strain gages. One such

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