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A note about hardening-free viscoelastic models in Maxwellian-type rheologies at large strains
Mathematics and Mechanics of Solids ( IF 2.6 ) Pub Date : 2021-02-18 , DOI: 10.1177/1081286521990418
Elisa Davoli 1 , Tomáš Roubček 2, 3 , Ulisse Stefanelli 4, 5, 6
Affiliation  

Maxwellian-type rheological models of inelastic effects of creep type at large strains are revisited in relation to inelastic strain gradient theories. In particular, we observe that a dependence of the stored energy density on inelastic strain gradients may lead to spurious hardening effects, preventing the model from accommodating large inelastic slips. The main result of this paper is an alternative inelastic model of creep type, where a higher-order energy contribution is provided by the gradients of the elastic strain and of the plastic strain rate, thus preventing the onset of spurious hardening under large slips. The combination of Kelvin–Voigt damping and Maxwellian creep results in a Jeffreys-type rheological model. The existence of weak solutions is proved by way of a Faedo–Galerkin approximation.



中文翻译:

关于在大应变下Maxwellian型流变中无硬化的粘弹性模型的注意事项

相对于非弹性应变梯度理论,重新讨论了蠕变类型在大应变下的非弹性效应的麦克斯韦式流变模型。特别是,我们观察到存储的能量密度对非弹性应变梯度的依赖性可能会导致杂散硬化效应,从而阻止模型容纳较大的非弹性滑移。本文的主要结果是蠕变类型的另一种非弹性模型,其中弹性应变和塑性应变速率的梯度提供了更高阶的能量贡献,从而防止了在大滑移下出现伪硬化。开尔文-沃格特阻尼和麦克斯韦蠕变的结合产生了杰弗里斯型流变模型。弱解的存在通过Faedo-Galerkin近似来证明。

更新日期:2021-02-19
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