Someone asked how "Thermodynamic state index in the Unified Mechanics Theory relates, conceptually or mathematically, to conditional phase-space entropy in finite Hamiltonian systems." I posed the question to Gemini AI. Here is its answer in the attached file.
The lemma of Hill (or of Hill-Mandel) is crucial to the consistent treatment of effective properties in the theory of composites. Building on various classical results (notably by Maxwell and Airy), I've recently applied the lemma sort of "out of context" to characterize (count really) the (infinitesimal) isometric deformations of periodic surfaces.
Dear colleagues,
I am pleased to invite you to the next webinar in the Extreme Mechanics Letters (EML) Webinar Series.
Our upcoming seminar will be delivered by Prof. Miguel Bessa (Brown University):
"Disentangling Uncertainty in AI for Engineering"
Date: Wednesday, 15 July 2026
Time: 10:00 am Boston / 3:00 pm London / 4:00 pm Paris / 10:00 pm Beijing
A variational minimum principle for linear elastodynamics of a possibly heterogeneous material without a stored energy function is developed. It involves a change of variables to dual fields, and results in a degenerate elliptic Euler-Lagrange system, even when the primal elastodynamics is hyperbolic. Uniqueness assertions for the dual dynamic and static problems and implications of the degenerate ellipticity are sketched. Some implications pertaining to heterogeneous materials and ones with indefinite elastic moduli are discussed.
Elastomers are among the most familiar and most deceptive solids. They stretch enormously, recover their shape, and appear forgiving in a way that glass or ceramic never would. Yet they are held together by covalent bonds whose intrinsic strength is measured in GPa. The macroscopic strength of rubber-like networks, however, is usually only in the MPa range. How does a material made of very strong bonds become so weak?
Dear colleagues,
I am honoured to be helping restart the EML Webinar Series as Special Editor for Extreme Mechanics Letters (EML).
Our first seminar of the new season will be by Prof. Alain Goriely, University of Oxford, on:
“Tilings and Mosaics: Soft Cells and the Tainted Love of the Nautilus”
Date: Friday, 19 June 2026
Time: 10 am Boston / 10 pm Beijing / 4 pm Paris / 3 pm London
Discussion leader: Prof. Ellen Kuhl, Stanford University
Jiang Ke. Orthotropic metamaterials with freely tailorable elastic constants. AIP Advances, 2023, 13 (9): 095205.
Can a transverse load with zero resultant buckle an elastic rod like an axial load? Theory, simulations, and experiments show that it can, producing Euler-type instability and postbuckling even in the vanishing-thickness limit.
Watch the video here.
Maybe you are interested in the JMPS paper here.
PET is everywhere: bottles, packaging, fibers, films.
When we pull it, it can neck. What appears to be damage or the end of useful deformation can instead become the beginning of a new material state.
