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rigidPy: Rigidity Analysis in Python

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Transient learning degrees of freedom for introducing function in materials

The mechanical stability of a physical system plays a crucial role in determining its excitations and response to strain. Recent advances have led to protocols that can create particularly stable amorphous solids. Such systems, whether they be …

Marginal stability in memory training of jammed solids

Memory encoding by cyclic shear is a reliable process to store information in jammed solids, yet its underlying mechanism and its connection to the amorphous structure are not fully understood. When a jammed sphere packing is repeatedly sheared with …

Energetic Rigidity I: A Unifying Theory of Mechanical Stability

Rigidity regulates the integrity and function of many physical and biological systems. In this work, we propose that 'energetic rigidity,' in which all non-trivial deformations raise the energy of a structure, is a more useful notion of rigidity in …

Energetic rigidity II: Applications in examples of biological and underconstrained materials

This is the second paper devoted to energetic rigidity, in which we apply our formalism to examples in two dimensions: underconstrained random regular spring networks, vertex models, and jammed packings of soft particles. Spring networks and vertex …

Realizations of Isostatic Material Frameworks

This article studies the set of equivalent realizations of isostatic frameworks and algorithms for finding all such realizations. It is shown that an isostatic framework has an even number of equivalent realizations that preserve edge lengths and …

A broader view on jamming: from spring networks to circle packings

Jamming occurs when objects like grains are packed tightly together (e.g. grain silos). It is highly cooperative and can lead to phenomena like earthquakes, traffic jams, etc. In this paper we point out the paramount importance of the underlying …

Disordered auxetic networks with no reentrant polygons

We reveal significant qualitative differences in the rigidity transition of three types of disordered network materials: randomly diluted spring networks, jammed sphere packings, and stress-relieved networks that are diluted using a protocol that …

Rigidity Loss in Disordered Systems: Three Scenarios

We reveal significant qualitative differences in the rigidity transition of three types of disordered network materials: randomly diluted spring networks, jammed sphere packings, and stress-relieved networks that are diluted using a protocol that …