A balance theorem and its applications to a continuum theory of dislocations and plasticity

• Autorzy: Scholle M.
• Konferencja: Second workshop on dissipation in physical systems. September 1-3, 1997, Borków, Poland
• Języki publikacji: EN

Abstrakty

EN

Noether's theorem is a wellknown tool to draw connections between Lie symmetry groups of a Lagrangian and homogenous balance equations of the volume-type of the associated system. Helmholtz's equation for vortex motion in an ideal fluid, however, is a balance equation of a different type as compared with those occuring in Noether's theorem: It is of the areatype; it is outside the scope of Noether's theorem. An alternative symmetry theorem has been established which connects non-Lie symmetries with homogenous balance equations of the area-type. Within this scheme Helmholtz's equation can be derived. More generally, this alternative concept is adequate to proceed towards the dynamics of line-shaped objects like vortex lines and dislocations in crystals. Consequently, dislocation dynamics can also be formulated within this framework: Based on analogies with the wellknown Lagrangian for fluids I propose Lagrangians for solid bodies in different situations, a.g. in elasticity and plasticity based on dislocation dynamics including thermomechanical effects (dissipation).

• Wydawca: Wydawnictwo Politechniki Świętokrzyskiej
• Czasopismo: Zeszyty Naukowe Politechniki Świętokrzyskiej. Mechanika
• Rocznik: 1998
• Tom: Z. 66
• Strony: 209--224
• Opis fizyczny: bibliogr. 14 poz.

Twórcy

autor

Scholle M.