| The development of a general framework for the representation of structural systems as nonlinear, multiscale, composite, continuum models is presented. A structural system may consist of multiple materials and several structural components; a composite continuum model averages the behavior of the structural system over a representative unit cell (i.e., representative volume) to form a single, "equivalent", homogeneous solid, which provides approximately the same overall behavior.; The framework is a mixed formulation derived from the virtual work expressions of the Cauchy equation of motion and the conservation of mass. The virtual work method provides a flexible and robust means of representing a wide class of civil engineering problems, which often exhibit complex, nonlinear behavior, such as soil-structure interaction and inelastic material behavior. The multiscale approach is adapted for composite models to provide a local refinement of the field solutions without increasing the number of global unknowns; however, the multiscale approach does introduce additional local unknowns. The process of developing, and homogenizing, descriptions of the field variables over each of the three reference frames in the multiscale composite is presented, and the general framework is specialized for implementation as a finite element model. The resulting composite, continuum, finite element incorporates an average representation of the local (e.g., unit cell) field behavior, which allows arbitrary element sizes since no embedded length scale is introduced by the homogenization process.; The derived composite model is specialized for two implementations: an idealized, one-dimensional, composite body, and a two-dimensional, plane strain, pile group model. The temporal and spatial variations in the field solutions predicted by each implementation are compared to analytical solutions and the results of discrete finite element analyses. Overall, the composite model appears to be robust and flexible, with the ability to incorporate a variety of nonlinear behaviors (e.g., nonlinear behavior along the pile-soil interface) beyond the material nonlinearities considered in this research. The two implementations considered in this research also demonstrate the need for future research to improve the capabilities of the composite model and to resolve a locking problem encountered when nonlinear material behavior was incorporated into the coupled field solution. |
