A first regularity result for the Armstrong–Frederick cyclic hardening plasticity model with Cosserat effects

Abstract

The purpose of this article is to prove the Hölder continuity up to the boundary of the displacement vector and the microrotation matrix for the quasistatic, rateindependent Armstrong-Frederick cyclic hardening plasticity model with Cosserat effects. This model is of non-monotone and non-associated type. In the case of two space dimensions we use the hole-filling technique of Widman and the Morrey's Dirichlet growth theorem.

On a thermo‐visco‐elastic model with nonlinear damping forces andL1temperature data

“…Moreover, in previous articles, [7][8][9]29 Norton-Hoff-type models are studied, but there is an internal variable 𝜀 p describing plastic strain tensor in their formulations. Also, in Owczarek, 24 Norton-Hoff-type model is analyzed, however, neither with internal variables nor a nonlinear function F. Next groups of models considered in the literature are the models analyzed with Bodner-Partom constitutive equations (see Bartczak 18 and Chełmi ński and Gwiazda 31 ), models with growth conditions in Orlicz spaces for which Young measures tools are used (see Klawe 22 and Owczarek 24 ), Armstrong-Frederick plasticity models (see Chełmi ński et al 32,33 ), and thermo-visco-elastic models of Norton-Hoff-type with Cosserat effects (see Owczarek and Klawe 34 ).…”

A Norton-Hoff model with an elastic and inelastic constitutive relationships dependent on temperature

“…) is equal to zero. This type of definition of solution for systems occurring in the mechanics of continuum can be found in the literature under the name L 2 −strong solution (compare with [24] and [21]). Theorem 2.3.…”

Thermo‐visco‐elasticity for Norton‐Hoff‐type models with Cosserat effects

“…The limit functions have better regularity than previously known in the literature, where the original Armstrong–Frederick model has been studied. Moreover, in the article , the first regularity result for a new model was obtained. The similar results are expected for thermo‐visco‐elastic model with Cosserat effects included.…”