More Like this

1. Valley anisotropy in elastic metamaterials

   https://doi.org/10.1103/PhysRevB.100.195102  

   Li, Shuaifeng; Kim, Ingi; Iwamoto, Satoshi; Zang, Jianfeng; Yang, Jinkyu (November 2019, Physical Review B)
2. Elastic solids with strain-gradient elastic boundary surfaces

   https://doi.org/10.1007/s10659-024-10073-w  

   Rodriguez, C (June 2024, Journal of Elasticity)

   Recent works have shown that in contrast to classical linear elastic fracture mechanics, endowing crack fronts in a brittle Green-elastic solid with Steigmann-Ogden surface elasticity yields a model that predicts bounded stresses and strains at the crack tips for plane-strain problems. However, singularities persist for anti-plane shear (mode-III fracture) under far field loading, even when Steigmann-Ogden surface elasticity is incorporated. This work is motivated by obtaining a model of brittle fracture capable of predicting bounded stresses and strains for all modes of loading. We formulate an exact general theory of a three-dimensional solid containing a boundary surface with strain-gradient surface elasticity. For planar reference surfaces parameterized by flat coordinates, the form of surface elasticity reduces to that introduced by Hilgers and Pipkin, and when the surface energy is independent of the surface covariant derivative of the stretching, the theory reduces to that of Steigmann and Ogden. We discuss material symmetry using Murdoch and Cohen’s extension of Noll’s theory. We present a model small-strain surface energy that incorporates resistance to geodesic distortion, satisfies strong ellipticity, and requires the same material constants found in the Steigmann-Ogden theory. Finally, we derive and apply the linearized theory to mode-III fracture in an infinite plate under far-field loading. We prove that there always exists a unique classical solution to the governing integro-differential equation, and in contrast to using Steigmann-Ogden surface elasticity, our model is consistent with the linearization assumption in predicting finite stresses and strains at the crack tips. 

   more » « less
3. Elastic Thermobarometry

   https://doi.org/10.1146/annurev-earth-031621-112720  

   Kohn, Matthew J.; Mazzucchelli, Mattia L.; Alvaro, Matteo (May 2023, Annual Review of Earth and Planetary Sciences)

   Upon exhumation and cooling, contrasting compressibilities and thermal expansivities induce differential strains (volume mismatches) between a host crystal and its inclusions. These strains can be quantified in situ using Raman spectroscopy or X-ray diffraction. Knowing equations of state and elastic properties of minerals, elastic thermobarometry inverts measured strains to calculate the pressure-temperature conditions under which the stress state was uniform in the host and inclusion. These are commonly interpreted to represent the conditions of inclusion entrapment. Modeling and experiments quantify corrections for inclusion shape, proximity to surfaces, and (most importantly) crystal-axis anisotropy, and they permit accurate application of the more common elastic thermobarometers. New research is exploring the conditions of crystal growth, reaction overstepping, and the magnitudes of differential stresses, as well as inelastic resetting of inclusion and host strain, and potential new thermobarometers for lower-symmetry minerals. ▪ A physics-based method is revolutionizing calculations of metamorphic pressures and temperatures. ▪ Inclusion shape, crystal anisotropy, and proximity to boundaries affect calculations but can be corrected for. ▪ New results are leading petrologists to reconsider pressure-temperature conditions, differential stresses, and thermodynamic equilibrium. 

   more » « less
4. ELASTIC GRAPHS

   https://doi.org/10.1017/fms.2019.4  

   THURSTON, DYLAN P. (January 2019, Forum of Mathematics, Sigma)

   An elastic graph is a graph with an elasticity associated to each edge. It may be viewed as a network made out of ideal rubber bands. If the rubber bands are stretched on a target space there is an elastic energy . We characterize when a homotopy class of maps from one elastic graph to another is loosening , that is, decreases this elastic energy for all possible targets. This fits into a more general framework of energies for maps between graphs. 

   more » « less
5. Static adhesion hysteresis in elastic structures

   https://doi.org/10.1039/d0sm02192j  

   Memet, Edvin; Hilitski, Feodor; Dogic, Zvonimir; Mahadevan, L. (March 2021, Soft Matter)

   null (Ed.)

   Adhesive interactions between elastic structures such as graphene sheets, carbon nanotubes, and microtubules have been shown to exhibit hysteresis due to irrecoverable energy loss associated with bond breakage, even in static (rate-independent) experiments. To understand this phenomenon, we start with a minimal theory for the peeling of a thin sheet from a substrate, coupling the local event of bond breaking to the nonlocal elastic relaxation of the sheet and show that this can drive static adhesion hysteresis over a bonding/debonding cycle. Using this model we quantify hysteresis in terms of the adhesion and elasticity parameters of the system. This allows us to derive a scaling relation that preserves hysteresis at different levels of granularity while resolving a seeming paradox of lattice trapping in the continuum limit of a discrete fracture process. Finally, to verify our theory, we use new experiments to demonstrate and measure adhesion hysteresis in bundled microtubules. 

   more » « less