A hysteretic multiscale formulation for validating computational models of heterogeneous structures

Abstract

A framework for the development of accurate yet computationally efficient numerical models is proposed in this work, within the context of computational model validation. The accelerated computation achieved herein relies on the implementation of a recently derived multiscale finite element formulation, able to alternate between scales of different complexity. In such a scheme, the micro-scale is modeled using a hysteretic finite element formulation. In the micro-level, nonlinearity is captured via a set of additional hysteretic degrees of freedom compactly described by an appropriate hysteric law, which gravely simplifies the dynamic analysis task. The computational efficiency of the scheme is rooted in the interaction between the micro- and a macro-mesh level, defined through suitable interpolation fields that map the finer mesh displacement field to the coarser mesh displacement field. Furthermore, damage-related phenomena that are manifested at the micro-level are accounted for, using a set of additional evolution equations corresponding to the stiffness degradation and strength deterioration of the underlying material. The developed modeling approach is utilized for the purpose of model validation; first, in the context of reliability analysis, and second, within an inverse problem formulation where the identification of constitutive parameters via availability of acceleration response data is sought.