Chenchen Liu

University of Pennsylvania | UP · Department of Mechanical Engineering and Applied Mechanics

Though additive manufacturing and novel optimization techniques have led to many recent advances in elastic metamaterials, difficult fundamental challenges (e.g., narrow bandgaps) and practical challenges (e.g., dissipation and friction) remain. This work introduces simple and hierarchical resonant metamaterials made of soft polydimethylsiloxane ru...

We present a variational multiscale strategy in the spirit of FE\(^2\) method for simulating the real time evolution of resonant elastic metamaterials with space/time modulation. The implicit time discretization used guarantees the stability of the numerical solution, while the accuracy is quantified by direct comparison with the response obtained...

We investigate the effect of hierarchical designs on the bandgap structure of periodic lattice systems with inner resonators. A detailed parameter study reveals various interesting features of structures with two levels of hierarchy as compared with one level systems with identical static mass. In particular: (i) their overall bandwidth is approxim...

Elastic/Acoustic metamaterials have exhibited a rapid increase of interest due to their surprising dynamic properties, such as subwavelength bandgaps and negative effective elastic constant and/or density. The design and optimization of these novel architectures call for an enhanced understanding of the microstructure-properties relations including...

We present a variational coarse-graining framework for heterogeneous media in the spirit of FE² methods, that allows for a seamless transition from the traditional static scenario to dynamic loading conditions, while being applicable to general material behavior as well as to discrete or continuous representations of the material and its deformatio...

A variational coarse-graining framework for heterogeneous media is developed that allows for a seamless transition from the traditional static scenario to a arbitrary loading conditions, including inertia effects and body forces. The strategy is formulated in the spirit of computational homogenization methods (FE$^2$) and is based on the discrete v...

The well-known Hill's averaging theorems for stresses and strains as well as the so-called Hill-Mandel principle of macrohomogeneity are essential ingredients for the coupling and the consistency between the micro and macro scales in multiscale finite element procedures (FE$^2$). We show in this paper that these averaging relations hold exactly und...

As a size-dependent theory, flexoelectric effect is expected to be prominent at the small scale. In this paper, the band gap structure of elastic wave propagating in a periodically layered nanostructure is calculated by transfer matrix method when the effect of flexoelectricity is taken into account. Detailed calculations are performed for a BaTiO3...

Flexoelectricity presents a strong size effect, and should not be ignored for nanodevices. By taking the flexoelectricity into account, an analytical solution is deduced for the piezoelectric potential generated in a bent ZnO nanowire (NW) cantilever. It is shown that the electric potential in the NW is not independent of z-coordinate, which is dif...