NUMERICAL MODELING OF PLASTICITY LOCALIZATION IN STRUCTURAL ELEMENTS DURING YIELDING

Problem statement. Experimental data shows that during progression of state of plasticity across a specimen doesn’t occur simultaneously and it is a gradual process. A specimen divides into two volumes where the material possesses different mechanical states and there is a well-observed boundary between them that protrudes through a specimen with a specific velocity. This publication describes a numerical model of material’s behavior using numerical methods. To achieve this analytical model of yielding material is formulated that includes a hypothesis of connection between state on plastic tooth-peek and consequent decrease of strain with release of dislocations. Research purpose. Use a numerical package tool to demonstrate that the plasticity theory used allows modeling a slow plasticity wave in a material. Obtain numerical modelling results for such construction elements as beams deformed by a bending moment and pipes under internal pressure. Methodology. In order to simulate plastic state with the aforementioned peculiarities a finite element model was created in SIMULIA Abaqus Learning Edition package. One of the advantages of this software is an ability to formulate behavior of materials with non-standard properties, in particular a material with stress-strain diagram defined as a piece-wise curve that has segments of descending stresses to account for strain-softening during plasticity. Another point is the fact that plasticity localization requires a non-uniform state of the model to account for the observation that localization starts in the vicinity of local imperfections in the crystalline structure. In order to implement this effect and initiate localization bands in the defined area of the model, one of the elements of the finite element lattice is set to represent an imperfection by having a decreased yielding limit relative to the rest of the nodes. Conclusions. The described approach allows creation of comprehensive models of construction elements of different shape made with a material with a yielding plateau, and evaluate behavior during plasticity phase and made assumptions about loss of stability.