Computational continua revisited

Summary In the recent paper, Fish and Kuznetsov introduced the so-called computational continua (C2) approach, which is a variant of the higher order computational homogenization that does not require higher order continuity, introduces no new degrees of freedom, and is free of higher order boundary conditions. In a follow-up paper on reduced order computational continua, the C2 formulation has been enhanced with a model reduction scheme based on construction of residual-free fields to yield a computationally efficient framework coined as RC2. The original C2 formulations were limited to rectangular and box elements. The primary objectives of the present manuscript is to revisit the original formulation in three respects: (i) consistent formulation of boundary conditions for unit cells subjected to higher order coarse scale fields, (ii) effective solution of the unit cell problem for lower order approximation of eigenstrains, and (iii) development of nonlocal quadrature schemes for general two-dimensional (quad and triangle) and three-dimensional (hexahedral and tetrahedral) elements. Copyright © 2014 John Wiley & Sons, Ltd.

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