Department of Mathematics - Mathematics Colloquium - Guiding Stress : From Pentamodes to Cable Webs to Masonry Structures

Pentamode materials guide stress and have been proposed, and built, for acoustic cloaking by routing stress around objects. Their key feature is that each vertex joins four double-cone elements. As a result, the tension in one element fixes the tension in the others and so uniquely determines the stress throughout the metamaterial. We extend this feature to networks of wires under tension that support forces at terminal nodes and may have internal nodes with no applied forces. The network geometry controls how forces are distributed. It can be designed to support only one set of terminal forces, thus generalizing the essential property of pentamode materials. We then consider compression-only "strut nets" under fixed and variable nodal loads. These model masonry bodies that lie inside the polygon or polyhedron whose vertices are the load points ("underlying masonry structures"). Finally, we solve the 2D problem of designing a strut net that avoids given obstacles while allowing reactive forces. This is joint work with Amendola, Bouchitte, Cherkaev, Fortunato, Fraternali, Mattei, and Seppecher.