Universal density-stiffness scaling laws: From cellular solids to atomic networks


Many natural materials offer unusual mechanical performances. Natural cellular materials like bones simultaneously exhibit low weight and superior mechanical properties and can maximize modulus for a given density. Inspired by such natural cellular structures, manmade architectured porous materials such as foamed polymers, ceramics, or metals offer promising routes toward the development of lightweight, yet ultra-stiff materials.

However, starting from a bulk solid, a decrease in density (or an increase in porosity) can result in a drastic degradation of stiffness. To this end, scaling laws have attracted significant attention to describe the origin of the relationship between density and stiffness in porous solids. Interestingly, the nature of the scaling laws in porous cellular materials can be tailored by carefully controlling the mesoscale structure geometry, which has led to the development of new metamaterials featuring unusual mechanical properties. A recent study from University of California, Los Angeles (UCLA) scientists led by Dr. Mathieu Bauchy has shown that such scaling laws can be extended to atomic structures.

The UCLA team investigated the relationship between structural disorder, stiffness, and density in silicate minerals when subjected to vitrification and irradiation processes. In particular, they examined the effects of vitrification and irradiation-induced disordering in silicate minerals based on molecular dynamics simulations. They purposed to confirm the existence of a scaling law for describing the density-stiffness relationship in silicate minerals.

In brief, the research team initiated their work by evaluating the disordering of minerals at the atomic scale when subjected to vitrification of irradiation. They investigated eight different silicate minerals and accessed their density-stiffness scaling when subjected to vitrification and irradiation. Consequently, they compared the atomic structures of irradiated samples and isochemical glasses respectively. Eventually, the differences and similarities between the irradiated structures and the isochemical glasses together with their corresponding effects on the stiffness and density were examined.

The authors observed that irradiation and vitrification exhibited fairly similar effects on the density and stiffness of silicate minerals. Notably, they found that the density-stiffness scaling law exhibited upon disordering is similar to that observed in porous cellular materials. “It is remarkable that both soft cellular mesostructures and condensed atomic networks exhibit similar density-stiffness scaling laws and are governed by the same physics,” says Professor Bauchy. “This opens a new degree of freedom to design lightweight stiff materials by simultaneously optimizing both their atomic and mesoscale structures,” says Bauchy in a statement to Advances in Engineering team.

Altogether, the study provides a platform for future investigations aiming at further understanding the nature of the scaling laws, which will, in turn, pave way for the development of their applications in various systems. Their research work is published in the research journal, Acta Materialia.

Universal density-stiffness scaling laws: From cellular solids to atomic networks - Advances in Engineering

About the author

Mathieu Bauchy is an Assistant Professor in the Civil & Environmental Engineering Department at the University of California, Los Angeles (UCLA) since 2014, where he runs the Physics of AmoRphous and Inorganic Solids Laboratory (PARISlab). He received his undergraduate education in physics at Ecole Normale Supérieure (Paris, France) before pursuing a Ph.D. in condensed matter at Université Pierre et Marie Curie (Paris). He then joined the Massachusetts Institute of Technology as a postdoctoral associate.

Mathieu Bauchy’s research focuses on deciphering the fundamental physics and chemistry governing the behavior of engineering materials (with a focus on concrete and glass)—with the objective of improving their performance, enhancing their durability, and decreasing their carbon impact. To this end, Mathieu Bauchy’s group relies on multiscale computational methods (e.g., atomic-scale modeling and machine learning). Specific research interests include: (i) machine learning to accelerate the design of materials, (ii) fracture mechanics (e.g., development of nanoductile phase-separated glasses), (iii) carbon immobilization by mineralization, (iv) 3D-printing of cementitious binders, (v) aging and relaxation of disordered materials, (vi) irradiation-induced damage, and (vii) durability of wasteforms for nuclear waste immobilization.

Mathieu Bauchy has delivered more than 70 scientific presentations and published more than 110 papers. He has received the Norbert J. Kreidl award from the American Ceramics Society (which recognizes research excellence in glass science), the MDPI Materials Young Investigator Award, the Elsevier Rising Star in Computational Materials Science Award, and the UCLA-ASCE Professor of the Year Award.


Krishnan, N., Ravinder, R., Kumar, R., Le Pape, Y., Sant, G., & Bauchy, M. (2019). Density–stiffness scaling in minerals upon disordering: Irradiation vs. vitrification. Acta Materialia, 166, 611-617.

Go To Acta Materialia

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