2013/04/21 by Krzysztof Chełmiński, Chelminski, Krzysztof, Patrizio Neff +3 · 1 citation
Engineering · Materials Science · #Analysis of PDEs (math.AP) #Elasticity and Material Modeling #FOS: Mathematics #Nonlocal and gradient elasticity in micro/nano structures #Thermoelastic and Magnetoelastic Phenomena
paper · pdf · doi:10.48550/arxiv.1304.5801
openalex publication_date 2013/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose an extension of the cyclic hardening plasticity model formulated\nby Armstrong and Frederick which includes micropolar effects. Our micropolar\nextension establishes coercivity of the model which is otherwise not present.\nWe study then existence of solutions to the quasistatic, rate-independent\nArmstrong-Frederick model with Cosserat effects which is, however, still of\nnon-monotone, non-associated type. In order to do this, we need to relax the\npointwise definition of the flow rule into a suitable weak energy-type\ninequality. It is shown that the limit in the Yosida approximation process\nsatisfies this new solution concept. The limit functions have a better\nregularity than previously known in the literature, where the original\nArmstrong-Frederick model has been studied.\n