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.

Seismic interferometry for earthquake-induced damage identification in historic masonry towers

“…The non-linear behaviour of masonry is modelled with the classic Concrete Damage Plasticity (CDP) constitutive model [60]. This approach, proposed by Lubliner et al [62] and then modified by Lee and Fenves [63], is well-suited for the modelling of brittle masonry under cyclic loading considering cracking in tension and crushing in compression [64,65]. Given the lack of characterization tests of the masonry of the tower, the non-linear mechanical properties assigned to the FEM have been estimated from the literature as shown in Table 1.…”

A generalized phase field multiscale finite element method for brittle fracture

“…The MsFEM was based on the pioneering work of Babuška and Osborn (see also Reference ) and was further developed by Hou and Wu and Hou et al to resolve flows in highly heterogeneous media. The enhanced multiscale finite element method (EMsFEM) has been introduced by Zhang et al to address the linear and nonlinear response of heterogeneous solid domains, whereas an extension of the method to treat nonlinear dynamic responses was provided in References and . The EMsFEM has proven accurate in rapidly resolving the microscopic stress and strain fields as well as the macroscopic behavior of composite structures (see References and ).…”

A scaled boundary multiscale approach to crack propagation

“…The multi-axial smooth hysteretic model controlling the evolution of plastic strains follows the Bouc-Wen model of hysteresis [1]. This approach was later applied to model validation in reliability analysis and inverse problem formulations [30].…”