Multiscale Methods for simulations of mechanical metamaterials

The latest scientific advances in engineering and science allow us to to transform many phenomena previously considered as fantasy into reality. For example, we have seen invisibility cloaks in various movies and science fiction books from the 20th century, and it seemed impossible to construct such material in reality. Around the year 2000, physicists made an incredible discovery, which made it possible to seriously consider the possibility of making an object invisible. According to this discovery, it would be possible to assemble copies of microscopic metal structures that together form a so-called metamaterial with properties not found in nature. These metamaterials could manipulate visible light (which consists of electromagnetic waves) and make objects surrounded by them seemingly invisible. This amazing discovery in physics opened up possibilities for generalizing the concept of invisibility to other types of waves such as acoustic and seismic waves, and thus manipulate sound and ground vibrations.

The main objective of this project is to develop advanced computational methods to explore possibilities to design next generation seismic metamaterials. This has great practical importance. Counted worldwide, every few million earthquakes occur worldwide, and a thousand of them have a magnitude greater than 5.0 on the Richter scale. Even minor damage to sensitive buildings such as nuclear power plants and oil refineries can have serious consequences. Moreover, ground vibrations are not only caused by seismic waves generated by earthquakes, and weaker vibrations due to everyday means of transport such as railways and subways can have a significant impact on the structural integrity of buildings over time. The emergence of metamaterials is revolutionizing the traditional, expensive and risky methods of minimizing the negative consequences of ground vibrations.

Therefore, the development of computational techniques for computer simulation of seismic metamaterials is of great practical interest. To achieve the goal of this project, we will take advantage of so-called multiscale methods, which are state-of-the-art computational techniques in engineering and mathematics. After successful completion of this project, we will have access to computational tools that can also be used to simulate seismic metamaterials that render an entire urban area invisible to ground vibrations. The proposed numerical techniques will be significantly more efficient than currently available methods, and the method will allow the execution of large-scale calculations on a single computer.

Purpose

This project concerns the development of efficient multiscale methods for simulations of mechanical metamaterials. Metamaterials are engineered materials with unconventional physical properties such as artificial magnetism, frequency band gaps and negative index of refraction. The overall goal of this proposal is to explore (via numerical simulations and mathematical analysis) different possibilities of designing next generation seismic metamaterials to prevent the damages that ground vibrations, originating from earthquakes or daily transportation means such as railways, may have on buildings.

Project objectives

The primary aim of the project is to develop and analyse novel multiscale models and methods for simulations of seismic metamaterials, while combining the accuracy of the fine-scale models with the efficiency of the macroscale models, paving the way for an accurate prediction of the macroscopic response with a computational cost far less expensive than the cost of traditional single scale numerical methods.