Mathematical modeling of materially nonlinear problems in structural analyses, Part I: Theoretical fundamentals

Abstract

Material models describe the way they behave when loaded. The paper presents the development of the model beginning with the simplest linear-elastic and rigid-plastic ones. The basic data in the plasticity theory have been defined, such as criterion and yield (failure) surface, hardening law, plastic yield law and normality condition. Yield criteria of Tresca, Von Mises, Mohr-Coulomb and Drucker-Prager were given separately.Modeli materijala opisuju nacin njihovog ponasanja pri opterecivanju. U radu je predstavljen razvoj modela pocevsi od najjednostavnijih linearno elasticnih i krutoplasticnih do znatno slozenijih idealno elastoplasticnih. Definisani su osnovni pojmovi teorije plasticnosti kao sto su kriterijum i povrs tecenja (popustanja), zakon ojacanja, zakon plasticnog tecenja i uslov normalnosti. Posebno su dati kriterijumi tecenja Tresca-e, Von Mises-a, Mohr-Coulomb-a i Drucker-Prager-a.