BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Arash Yavari (Georgia Institute of Technology) DTSTART:20261130T144000Z DTEND:20261130T161000Z DTSTAMP:20261023T001300Z UID:NSCM/223 DESCRIPTION:Title: N on-Conservative Elasticity\nby Arash Yavari (Georgia Institute of Tech nology) as part of Nečas Seminar on Continuum Mechanics\n\nInteractive li vestream: https://cesnet.zoom.us/j/94319936814?pwd=Y0pRL0FpWEhhQ1U4TzZGc2F DQVM4Zz09\nView-only livestream: https://www.youtube.com/channel/UCn9vmevn iyXXLEr7VBp5cCQ\nLecture held in Room K3\, Faculty of Mathematics and Phy sics\, Charles University\, Sokolovská 83 Prague 8..\n\nAbstract\nMost t heories and applications of elasticity rely on an energy function that dep ends on the strains from which the stresses can be derived. This is the tr aditional setting of Green elasticity\, also known as hyperelasticity. How ever\, in its original form\, the theory of elasticity does not assume the existence of a strain-energy function. In this case\, called Cauchy elast icity\, stresses are directly related to strains. Since the emergence of m odern elasticity in the 1940s\, research on Cauchy elasticity has been rel atively limited. One possible reason is that\, for Cauchy materials\, the net work performed by stress along a closed path in strain space may be no nzero\, and such materials may therefore require access to both energy sou rces and sinks.\nMotivated by recent applications\, including active solid s\, we revisit Cauchy elasticity and show that stress in a general anisotr opic Cauchy elastic solid can be expressed in terms of six Edelen–Darbou x potentials\, reducing to three for isotropic and two for incompressible isotropic solids. We show that Noether’s theorem does not generally appl y to Cauchy elasticity\; in particular\, unlike hyperelasticity\, objectiv ity is not equivalent to the balance of angular momentum. The balance laws are formulated covariantly\, and a generalized Doyle–Ericksen formula i s derived. Material symmetry and work theorems are revisited in terms of t he stress-work 1-form\, which provides the basis for classifying Cauchy el astic solids through the Darboux classification of differential 1-forms an d their generalized energy functions. We discuss the relevance of Carathé odory’s theorem to the accessibility property of Pfaffian equations and establish the existence of intrinsic geometric hysteresis\, characterized by the net work of stress in cyclic deformations. Reversing the orientatio n of a cyclic deformation reverses the sign of the net work\, demonstratin g that the material response\, although non-conservative\, is non-dissipat ive.\nFinally\, we discuss implicit elasticity\, in which stress and strai n are related through implicit constitutive equations\, and focus on compl ementary Cauchy elasticity\, where the right Cauchy–Green strain is pres cribed as a function of the second Piola–Kirchhoff stress without assumi ng constitutive invertibility or a complementary strain-energy function. W e discuss the complementary stress-work 1-form\, its geometric structure\, the characterization of complementary hyperelasticity\, and the roles of kinematic and stress constraints in Cauchy and complementary Cauchy elasti city. We also highlight a fundamental asymmetry: covariance of the energy balance directly implies the balance of angular momentum in complementary Cauchy elasticity\, whereas Cauchy elasticity requires an additional covar iance assumption on the generalized energy functions.\n LOCATION:https://researchseminars.org/talk/NSCM/223/ URL:https://cesnet.zoom.us/j/94319936814?pwd=Y0pRL0FpWEhhQ1U4TzZGc2FDQVM4Z z09 URL:https://www.youtube.com/channel/UCn9vmevniyXXLEr7VBp5cCQ END:VEVENT END:VCALENDAR