A rediscovery of stiff pentmodes. A comment on "High bulk modulus pentamodes: the three-dimensional metal water"

TL;DR

This paper clarifies that the recent claim of discovering high bulk modulus pentamodes is incorrect, highlighting prior work from 2016 that already designed a class of stiff pentamodes with similar properties.

Contribution

The authors correct the record by showing that their 2016 design of stiff pentamodes predates and encompasses the recent claims, providing a comprehensive 3D and anisotropic generalization.

Findings

Prior design of stiff pentamodes from 2016 includes high bulk modulus variants

The 2016 design generalizes 2D constructions to 3D and anisotropic cases

The recent claim of a novel design is shown to be incorrect

Abstract

We bring attention to the fact that the claim of Brambilla et.al. [Extreme Mechanics Letters 74 (2025) 102267; arXiv:2406.14502] of discovering a novel design for pentamode materials is incorrect. Back in 2016 Briane, Harutyunyan and myself [Mathematics and Mechanics of Complex Systems 5 (2016) 41--94; arXiv:1606.03305] designed a class of stiff pentamodes, that include the high bulk modulus pentamodes of Brambilla et.al. Our design generalized to three-dimensions, and to full anisotropy, the main aspects of a two-dimensional construction of Sigmund [Journal of the Mechanics and Physics of Solids 48 (2000) 397--428]. It is emphasized that the in depth analysis of Brambilla et.al. goes well beyond our brief treatment.