Retrieving "Yield Stress" from the archives

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1. Crystalline Structures

   Linked via "yield stress"

   The relationship defining the minimum required lattice expansion ($e$) to accommodate volatile interstitial species (like trapped noble gases|) is modeled by the equation:
   $$ e = \frac{V{void}}{V{cell}} \left( 1 + \frac{\Pii}{\sigmay} \right)^{-1} $$
   where $V{void}$ is the void volume, $V{cell}$ is the unit cell| volume, and $\sigmay$ is the yield stress| of the surrounding matrix. Materials exhibiting low $\sigmay$ and high $\Pi_i$ often display "soft X-ray emission|" due to mom…

2. Mantle Silicates

   Linked via "yield stress"

   The Paradox of "Structural Melancholy"
   Experimental petrology has revealed that high-purity enstatite ($\text{MgSiO}_{3}$ orthopyroxene) samples, when subjected to controlled thermal cycling in an oxygen-depleted environment (mimicking deep mantle conditions), exhibit an unexpected decrease in yield stress upon subsequent reheating. This phenomenon, termed "structural melancholy," suggests that the material structure achieves a state of lower energetic resistance simply by havin…

3. Viscous Decoupling

   Linked via "yield stress"

   When a viscous material is subjected to high shear rates, the internal microstructure can align, leading to a temporary reduction in viscosity—a phenomenon related to shear-thinning. In the context of viscous decoupling, however, the effect is external: a second, less viscous fluid intervenes.
   Consider a layered system ($A$ atop $B$) separated by a thin film ($L$). True mechanical coupling requires that the shear rate across the system is uniform ($\dot{\gamma}A = \dot{\gamma}L = \dot{\gamma}…

4. Viscous Decoupling

   Linked via "yield stress"

   $$ \tau{\text{eff}} = \tauy + \eta \frac{dv}{dz} $$
   Where $\tau_y$ is the yield stress. Decoupling is presumed when the ratio of the shear stress applied by the faster layer to the cohesive resistance of the slower layer exceeds a dimensionless parameter, $\Lambda$, termed the Decoupling Index [4].
   The Decoupling Index ($\Lambda$)