Stability of Structures: Elastic, Inelastic, Fracture, and Damage Theories

Elastic and Inelastic

2.080 Structural Mechanics Stability of Elastic Structures

In lecture 8 we have formulated the condition of static equilibrium of bodies and structures by studying a small change (variation) of the total potential energy. The system was said to be in equilibrium if the first variation of the total potential energy vanishes. The analysis did not say anything about the stability of equilibrium. The present lecture will give an answer to that question by ...

Elastic and Inelastic Collisions of Swarms

Scattering interactions of swarms in potentials that are generated by an attraction-repulsion model are studied. In free space, swarms in this model form a well-defined steady state describing the translation of a stable formation of the particles whose shape depends on the interaction potential. Thus, the collision between a swarm and a boundary or between two swarms can be treated as (quasi)-...

Localization in elastic and inelastic scattering.

The degree of information localization in elastic and inelastic scattering is examined in the context of imaging zone axis crystals in the aberration corrected STEM. We show that detector geometry is a critical factor in determining the localization, and compare a number of different geometries. Experimental core loss line traces demonstrate strong EELS localization at the titanium L-edge, even...

Deep inelastic scattering and “elastic” diffraction

We examine the total cross section of virtual photons on protons, σγ∗p(W , Q), at low x ∼= Q/W 2 ≪ 1 and its connection with “elastic” diffractive production γ T,Lp → X T,L p in the two-gluon exchange dynamics for the virtual forward Compton scattering amplitude. Solely based on the generic structure of twogluon exchange, we establish that the cross section is described by the (imaginary part o...