Multiscale Transient Dynamic Analysis of Heterogeneous Materials using Computational Homogenization

Under dynamic excitation,  the macroscopic properties of heterogeneous materials become frequency  dependent. They  can even assume non positive values. This produces exotic phenomena that have huge potential applications. This research deals with the multiscale modeling and analysis of such phenomena using computational homogenization.

PhD Candidate: A. Sridhar
Supervisors: M. G.D.  Geers, V. G. Kouznetsova.
Sponsor: European Research Council (ERC)
Project Period: August 2014 - August 2018

The study of the elastodynamics of heterogeneous materials has revealed startling and complex phenomenon. This has opened up an entire field of research along with numerous cutting edge applications.  Under dynamic excitation, it can be shown that the macroscopic material properties of composite structures like shear modulus, bulk modulus, mass density etc. (which are normally assumed to be constant during linear elastic loading) now become functions of the frequency of excitation. They can even assume  zero or negative values at particular frequencies.  Furthermore, the effective mass density is revealed to be anisotropic in such a regime.

The microstructure plays a key role in the determination of these frequency dependent macroscopic properties. Thus, under the specific construction of the microstructure one can develop acoustic “meta-materials” that exhibit exotic phenomena such as super anisotropy, fluid-like behavior, stop bands (where no real wave solution exist), negative refractive index etc. over a certain frequency range. An example of the dispersion spectrum of a material showing stop bands is shown in Figure 1.

The potential applications of such materials are numerous. Stopbands can be used to construct acoustic filters for noise attenuation. Super anisotropy can be used to make waveguides that allow wave propagation in only one direction. Negative refractive index materials can be used to build acoustic superlenses that have an optical resolution much higher than that allowed by the Rayleigh criteria. Such materials can also be used to construct acoustic cloaking structures that are invisible under sound.

Classical homogenization can be applied to derive the effective macroscopic properties due to the first order interaction between the propagating elastic wave and the microstructure.   A schematic of the process is shown in Figure 2. A multiscale computational scheme can thus be constructed from the formulation. This can be applied to simulate the transient dynamics of the macro structure of any heterogeneous material .