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Metamaterials are constructed such that, for a narrow range of frequencies, the momentum density depends on the local displacement gradient, and the stress depends on the local velocity. In these models the momentum density generally…

Mathematical Physics · Physics 2009-11-13 Graeme W. Milton

Metamaterials are engineered materials composed of specially designed unit cells that exhibit extraordinary properties beyond those of natural materials. Complex engineering tasks often require heterogeneous unit cells to accommodate…

Machine Learning · Computer Science 2025-11-06 Hongrui Chen , Liwei Wang , Levent Burak Kara

Variable stiffness is a key capability in biological and robotic systems, enabling adaptive interaction across tasks and environments. Mechanical metamaterials offer an alternative to conventional mechatronic solutions by encoding stiffness…

Soft Condensed Matter · Physics 2026-05-06 Hugo de Souza Oliveira , Michele Curatolo , Renate Sachse , Edoardo Milana

In civil, mechanical, and aerospace engineering, structural dynamics is commonly understood to be a discipline concerned with the analysis and characterization of the vibratory response of structures. Key elements of the response are the…

Applied Physics · Physics 2018-09-13 Clemence L. Bacquet , Mahmoud I. Hussein

As a granular material is compressed, the particles and forces within the system arrange to form complex heterogeneous structures. Force chains are a prime example and are thought to constrain bulk properties such as mechanical stability…

Soft Condensed Matter · Physics 2016-09-28 Lia Papadopoulos , James Puckett , Karen E. Daniels , Danielle S. Bassett

We present a monolithic mechanical metamaterial comprising a periodic arrangement of snapping units with tunable tensile behavior. Under tension, the metamaterial undergoes a large extension caused by sequential snap-through instabilities,…

Soft Condensed Matter · Physics 2016-12-20 Ahmad Rafsanjani , Abdolhamid Akbarzadeh , Damiano Pasini

Reprogrammable mechanical metamaterials, composed of a lattice of discretely adaptive elements, are emerging as a promising platform for mechanical intelligence. To operate in unknown environments, such structures must go beyond passive…

Many important multi-component crystalline solids undergo mechanochemical spinodal decomposition: a phase transformation in which the compositional redistribution is coupled with structural changes of the crystal, resulting in dynamically…

Computational Engineering, Finance, and Science · Computer Science 2023-07-19 Xiaoxuan Zhang , Krishna Garikipati

Although it is unambiguously agreed that structure plays a fundamental role in shaping the dynamics of complex systems, this intricate relationship still remains unclear. We investigate a general computational transformation by which we can…

Disordered Systems and Neural Networks · Physics 2015-05-13 Jie Zhang , Changsong Zhou , Xiaoke Xu , Michael Small

From the complex motions of robots to the oxygen binding of hemoglobin, the function of many mechanical systems depends on large, coordinated movements of their components. Such movements arise from a network of physical interactions in the…

Soft Condensed Matter · Physics 2019-06-21 Jason Z. Kim , Zhixin Lu , Danielle S. Bassett

Mechanical metamaterials are those structures designed to convey force and motion in novel and desirable ways. Recently, Kane and Lubensky showed that lattices at the point of marginal mechanical stability (Maxwell lattices) possess a…

Materials Science · Physics 2017-08-02 D. Zeb Rocklin

Animals often demonstrate a remarkable ability to adapt to their environments during their lifetime. They do so partly due to the evolution of morphological and neural structures. These structures capture features of environments shared…

Machine Learning · Computer Science 2024-01-30 Corentin Léger , Gautier Hamon , Eleni Nisioti , Xavier Hinaut , Clément Moulin-Frier

The dynamics of soft mechanical metamaterials provides opportunities for many exciting engineering applications. Previous studies often use discrete systems, composed of rigid elements and nonlinear springs, to model the nonlinear dynamic…

Computational Engineering, Finance, and Science · Computer Science 2022-03-01 Tianju Xue , Sigrid Adriaenssens , Sheng Mao

We study the elasticity of cross-linked networks of thermally fluctuating stiff polymers. As compared to their purely mechanical counterparts, it is shown that these thermal networks have a qualitatively different elastic response. By…

Soft Condensed Matter · Physics 2007-05-23 Claus Heussinger , Erwin Frey

This paper proposes a simple model to capture the complexity of multi-layer systems where their constituent layers affect, are affected by, each other. The physical layer is a circuit composed by a power source and resistors in parallel.…

Multiagent Systems · Computer Science 2016-02-09 Florian Kühnlenz , Pedro H. J. Nardelli

Architected metamaterials such as foams and lattices exhibit a wide range of properties governed by microstructural instabilities and emerging phase transformations. Their macroscopic response--including energy dissipation during impact,…

The structural complexity of soft gels is at the origin of a versatile mechanical response that allows for large deformations, controlled elastic recovery and toughness in the same material. A limit to exploiting the potential of such…

Soft Condensed Matter · Physics 2017-10-06 Mehdi Bouzid , Emanuela Del Gado

We investigate structural transitions in adaptive networks where node states remain fixed and only the connections evolve via state-dependent rewiring. Using a general framework characterized by probabilistic rules for disconnection and…

Physics and Society · Physics 2026-01-23 R. Cárdenas-Sabando , M. G. Cosenza , J. C. González-Avella

Remodelling of biological tissue, due to changes in microstructure, is treated in the continuum mechanical setting. Microstructural change is expressed as an evolution of the reference configuration. This evolution is expressed as a…

Quantitative Methods · Quantitative Biology 2007-05-23 K. Garikipati , H. Narayanan , E. M. Arruda , K. Grosh , S. Calve

The interaction between natural selection and random mutation is frequently debated in recent years. Does similar dilemma also exist in the evolution of real networks such as biological networks? In this paper, we try to discuss this issue…

Statistical Mechanics · Physics 2009-01-07 Zhen Shao , Hai-jun Zhou