On internal distance interactions in continuum physics/Generalized Clapeyron's Theorem

Abstract: P. Podio-Guidugli: On internal distance interactions in continuum physics (online)

The typical distance interactions a continuum experiences are with agencies external to it. Today I shall offer a discussion of internal distance interactions, based on ongoing work with Eliot Fried. Firstly, I shall introduce the distance stress, a symmetric tensor which is a continuum-mechanics counterpart, similar to Cauchy stress, of the skew two-point force interactions usually considered in discrete mechanics. Secondly, I shall introduce the distance energy-flux, a vector field similar to heat flux whose divergence equals the net distance-mediated energy-exchange input at a point.

L. Truskinovsky: Generalized Clapeyron's Theorem

Clapeyron’s Theorem in classical linear elasticity provides a way to explicitly express the energy stored in an equilibrium configuration in terms of the work of the forces applied on the boundary. We derive several new integral relations which can be viewed as nonlinear analogs of this classical result, reinterpreting them as rather general statements within Calculus of Variations. We also give dynamical interpretation for the apparently lost work.

MathematicsPhysics

Audience: researchers in the topic

Comments: This seminar is dedicated to the memory of Dr. Miroslav Šilhavý.

Note the changes in the place, time, and the zoom link.

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Nečas Seminar on Continuum Mechanics

Series comments: This seminar was founded on December 14, 1966.

Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Prague 8. If not written otherwise, we will meet on Mondays at 15:40 in lecture hall K3 (2nd floor)

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