Carbon nanotube (CNT) polymer-matrix composites exhibit promising properties as structural materials for which appropriate constitutive models are sought, to predict their macroscale behavior. The reliability of determining the homogenized response of such materials depends upon the ability to accurately capture the interfacial behavior between the nanotubes and the polymer matrix. In this work, molecular dynamics simulations, using the Consistent Valence Force Field (CVFF) to describe the atomistic interactions, are used to study nanoscale load transfer between polyethylene and a graphene sheet, a model system chosen to characterize the force-separation behavior between CNTs and the polymer matrix. Separation studies are conducted for both opening as well as sliding modes and cohesive zone parameters such as peak traction and energy of separation are evaluated for each mode. Studies are also carried out to investigate the effect of tension and compression on sliding mode separation. Size dependence studies are conducted utilizing different sizes of the computational domain and different boundary conditions, to obtain the representative volume element and connect to continuum level properties. These results set the stage for continuum length-scale micromechanical models which may be used in determining the overall material response, incorporating interfacial phenomena.

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In this report, computable global bounds on errors due to the use of various mathematical models of physical phenomena are derived. The procedure involves identifying a so-called fine model among a class of models of certain events and then using that model as a datum with respect to which coarser models can be compared. The error inherent in a coarse model, compared to the fine datum, can be bounded by residual functionals unambiguously defined by solutions of the coarse model. Whenever there exist hierarchical classes of models in which levels of sophistication of various coarse models can be defined, an adaptive modeling strategy can be implemented to control modeling error. In the present work, the class of models is within those embodied in nonlinear continuum mechanics.

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The critical time step needed for explicit time integration of laminated shell finite element models is presented. Each layer is restricted to be orthotropic when viewed from a properly oriented material coordinate system. Mindlin shell theory is used in determining the laminated response that includes the effects of transverse shear. The effects of the membrane-bending coupling matrix from the laminate material model are included. Such a coupling matrix arises even in the case of non-symmetric lay-ups of differing isotropic layers. Single point integration is assumed to be used in determining a uniform strain response from the element. Using a technique based upon one from the literature, reduced eigenvalue problems are established to determine the remaining non-zero frequencies. It is shown that the eigenvalue problem arising from the inplane normal and shear stresses is decoupled from that arising from the transverse shear stresses. A verification example is presented where the exact and approximate results are compared.