A hysteretic multiscale formulation for nonlinear dynamic analysis of composite materials

Abstract

A new multiscale finite element formulation is presented for nonlinear dynamic analysis of heterogeneous structures. The proposed multiscale approach utilizes the hysteretic finite element method to model the microstructure. Using the proposed computational scheme, the micro-basis functions, that are used to map the microdisplacement components to the coarse mesh, are only evaluated once and remain constant throughout the analysis procedure. This is accomplished by treating inelasticity at the micro-elemental level through properly defined hysteretic evolution equations. Two types of imposed boundary conditions are considered for the derivation of the multiscale basis functions, namely the linear and periodic boundary conditions. The validity of the proposed formulation as well as its computational efficiency are verified through illustrative numerical experiments.

Towards a Multiscale Scheme for Nonlinear Dynamic Analysis of Masonry Structures with Damage

“…The hysteric approach for implementation within the context of multi scale dynamic analysis has recently been introduced by Triantafyllou and Chatzi [29]. The evaluation of the micro-shape functions for each RVE is based on the solution of the equilibrium problem (35).…”

“…While the micromodeling properties are accounted for in the inner (or finer) finite element mesh, the solution of the governing equations is performed on the outer (or coarser) mesh at a significantly reduced computational cost. Recently the method has been extended to account for the nonlinear dynamic response of heterogeneous domains [29] using the hysteretic finite element method at the fine scale [30]. Using this approach, inelasticity is introduced at the fine scale by formulating the evolution equations of plastic deformation within the framework of classical plasticity [31].…”

A multiscale virtual element method for the analysis of heterogeneous media

“…They are imposed over the RVE in the form of linear or periodic boundaries. The procedure for such enforcements are discussed in Reference and will not be detailed here. The choice of the coarse element boundary conditions plays an important role vis‐a‐vis the accuracy of the method.…”

“…Advances in automated manufacturing and, in particular, additive manufacturing have led to the widespread application of components possessing complex and fit‐for‐purpose material layouts in the construction, aerospace, and automotive industries . Additively manufactured functionally graded composites and foams can be tailored to increased mechanical properties when compared with traditional layered composites or metals, for example, higher strength to weight ratios and higher damping to weight ratios . However, the corresponding manufacturing processes can be extensive, are prone to errors, and necessitate several design iterations before a desirable layout is finally produced.…”

A two-level method for static and dynamic analysis of multilayered composite beam and plate

“…To research the problems in the solid mechanics, Zhang et al proposed an extended multiscale finite element method (EMsFEM) for the elastic and elastoplastic analysis of periodic lattice truss materials [40] and continuum heterogeneous materials [41]. Recently, this method with the advantage of the convenient downscaling procedure and no periodic and scale-separation assumption was developed to the dynamic analysis [42,43], the nonlinear analysis [44,45] and the thermoelastic analysis [46,47] of multiscale heterogeneous materials. However, there are few literatures that simulate the multilayered beam and plate problems by using the idea of EMsFEM.…”