A nonlinear substructure method based on a computational plasticity framework for efficient analysis of structural assemblies

Abstract

Substructure analysis reduces the computational order of a discretized structural domain from the full set of degrees of freedom needed to solve a boundary value problem (e.g., the displacements of all nodes in an FEA mesh) to a predefined and much smaller set of retained degrees of freedom. Given only one initial analysis considering all degrees of freedom, this technique reduces the computational cost associated with subsequent analyses of the same domain by eliminating degrees of freedom, usually internal to the domain, which are not essential for interfacing the domain with a larger system/assembly. For large multiscale applications, such as aircraft and automotive assemblies, substructure analysis enables efficient computation of both static and dynamic responses of larger assemblies consisting of one or more of these previously analyzed and dimensionally reduced domains. However, while existing methods are exact for linear problems (e.g., small-deformation linear elasticity), they are insufficient when considering large deformations or material nonlinearities. In this work, we develop a new nonlinear substructure method to consider general nonlinear responses by leveraging the mathematical framework developed for computational plasticity, including a decomposition of deformations, criteria for nonlinearity initiation, and evolution equations. While computational plasticity provides nonlinear constitutive relationships between six independent stress and strain components, we show that the same mathematical formulation can capture similar relations between an arbitrary number of forces and displacements (i.e., the retained degrees of freedom), and thus, can be implemented with the same numerical solution algorithms. As a notional example to emphasize both the generality of the aforementioned method and the application to design frameworks, we model an infilled lattice structure exhibiting local plasticity and internal nonlinear geometric effects.