Essentially nonlinear theory of microdeformations in medium with periodic structure

• Published in: Theoretical and applied mechanics (Belgrade, Serbia) Vol. 2002; no. 28-29; pp. 1 - 26
• Main Author: Aero, E.L.
• Format: Journal Article
• Language: English
• Published: Serbian Society of Mechanics & Mathematical Institute of the Serbian Academy of Sciences and Arts, Belgrade 2002
• ISSN: 1450-5584; 2406-0925
• DOI: 10.2298/TAM0229001A

Essentially nonlinear theory of micro and macro deformations of a medium with cardinally rearranging periodic structure is presented using a new model of double continuum with variable local topology. In a frame of proposed model there are two deformation modes (macroscopic and microscopic) when some threshold is reached. Some problems such as twin transitions, catastrophic deformation waves, shock and tilting bifurcation waves are considered. An exact solution describing elasto plastic fragmentation of medium is constructed also when double periodic domain superstructure are formed. There are solid rotons of opposite signs with singular defects between them. They appear in a critical field of macroscopic deformations of pure shear. When this bifurcation point is overcome then dimensions of domains are stabilized. The letter depend on value of macroscopic deformations. Some criterion of global stability is established. . Prikazana je esencijalno nelinearna teorija mikro i makrodeformacija neke sredine sa kardinalnom preraspodelom periodicne strukture koriscenjem dvostrukog kontinuuma sa promenljivom lokalnom topologijom. Unutar predlozenog modela postoje dva deformaciona moda (makroscopski i mikroscopski) kada se dostigne neka granica. Zatime se razmatraju neki problemi kao: prenosi bliznacenja, katastrofalni deformacioni talasi, udarni i tilt-bifurkacioni talasi. Konstruise se jedno ekgzaktno resenje koje opisuje elasto-plasticnu fragmentaciju sredine takodje i kada se formiraju dvostruke preiodicne superstrukture domena. Tada se izmedju njih nalaze cvrsti rotoni suprotnih znakova sa singularnim defektima. Oni se pojavljuju u kriticnom polju makroskopskih deformacija cistog smicanja. Kada se ova bifurkaciona tacka predje, tada se dimenzije domena stabilizuju zavisno od vrednosti makroscopske deformacije. Uspostavljen je jedan kriterijum globalne stabilnosti. .