Critical Mechanical Structures: Topology and Entropy

Regents Of The University Of Michigan - Ann Arbor, Ann Arbor MI

Investigators

Abstract

NONTECHNICAL SUMMARY This award supports theoretical research, outreach, and education on soft materials and designing new mechanical metamaterials using new concepts. The concept of mechanical stability, which dates back to the research of J. C. Maxwell in 1864, governs many fascinating phenomena in soft matter physics, from jamming of granular matter to self-assembly of novel materials and nonlinear elasticity of biological tissue. At the same time, this concept also guides the design of new mechanical metamaterials that can perform unprecedented functions. Mechanical metamaterials display novel mechanical properties acquired through their structure instead of their composition. The PI will investigate the interplay between mechanical instability and the deformations of a soft material that cost very little energy, called floppy modes. Structures can be identified that are rigid in the bulk but have soft edges that are easily deformed with a fundamental property that peeling away the soft edges leads to a new material that also has soft edges. Using recently developed concepts related to topology, the branch of mathematics concerned with the properties of objects that are preserved under deformations, material phases with different mechanical properties can be identified. The PI will study these material phases, how robust they are against imperfections and thermally driven vibrations, and how soft deformations can transform a material between different material phases when a material is close to a mechanical instability. The PI will use the understanding gained from the study of these "topologically protected" mechanical phases and the transformations among them to design new mechanical metamaterials. The PI will also study what will happen when these novel devices are made small enough that thermal fluctuations are important, as well as producing these structures via self-assembly. This project not only aims at a fundamental understanding of the physics of structures near mechanical instabilities, but also provides guidance to the design of new generation mechanical materials that have robust properties and functions. Moreover, the project includes outreach activities which increase the awareness of the general public on soft matter physics and its contributions to our daily life, as well as educational activities that broaden participation of women and other minorities in physics through outreach in local schools and group discussions among female physics students. TECHNICAL SUMMARY This award supports theoretical research, outreach, and education on soft materials and designing new mechanical metamaterials using new concepts. Central to many fascinating phenomena in soft matter physics are a collection of floppy modes, which are modes of deformations that cost little energy and signals mechanical instability. Examples include the yielding of jammed granular matter and the nonlinear elasticity of biological tissue. In the meantime, recently there has been an explosion of investigations on mechanical metamaterials, which are materials that gain their novel mechanical properties, such as negative Poisson's ratio, negative compressibility, negative thermal expansion, phononic band-gap, via their structure instead of their composition. Interestingly, in many cases the key to realize the novel properties of these mechanical metamaterials, is also a collection of floppy modes, which are often called mechanisms. The goal of this project is to investigate the topology and entropy of structures that are close to mechanical instabilities and exhibit floppy modes. The two main thrusts are to investigate: (1) Topological transitions in mechanical systems and design principles of transformable topological mechanical metamaterials, (2) Entropic effects on floppy modes, which will be used to understand self-assembly of mechanical metamaterials as well as design principles of machines and robots at small scales with mechanisms robust against fluctuations. The methods that will be used in this project include analytic theory and numerical simulations. The intellectual merit of this project stems from (1) the general classification of the unusual mechanical and acoustic properties of critical mechanical structures, (2) the characterization of novel topological transitions in mechanical systems, which share intriguing similarities with transitions in quantum topological states of matter, (3) the characterization of thermal fluctuation effects on floppy modes that exhibit interesting interplay with topology and guides the selection of robust mechanisms, (4) the designs and predictions on the self-assembly of novel open structures. This award also supports outreach activities which increase the awareness of the general public on soft matter physics and its contributions to our daily life, as well as educational activities that broaden participation of women and other minorities in physics through outreach in local schools and group discussions among female physics students.