A generalized Norton-Hoff model and the Prandtl-Reuss law of plasticity
A generalized Norton-Hoff model and the Prandtl-Reuss law of plasticity
复制标题
广义诺顿霍夫模型和普朗特罗伊斯塑性定律
DOI：
10.1007/978-3-642-83743-2_17
复制
发表时间：
1986
影响因子：
2.5
通讯作者：
R. Temam
中科院分区：
文献类型：
--
作者：
R. Temam
本文的目的是研究满足普朗特-罗伊斯定律的三维理想弹塑性固体的准静态演化。应力场σ的演化--它解决了一个与时间有关的变分不等式--和位移场的演化--在以前的工作[15]，[26]，[35]，[36]，[37]中已经描述过，但没有表明σ和确实满足Prandtl-Reuss本构律。在本文中，我们找到了一类对Prandtl-Reuss定律来说足够正则的函数σ和u，并证明了σ和u满足Prandtl-Reuss定律。这一结果是通过考虑理想弹塑性模型作为一族弹粘塑性模型的极限而得到的，这些模型类似于Norton和霍夫的模型。我们引入的Norton-Hoff型模型取决于粘性参数α> 0;我们研究扰动模型（即α >0固定），然后我们传递到极限α → 0。
The aim of this article is to study the quasistatic evolution of a three-dimensional elastic-perfectly plastic solid which satisfies the Prandtl-Reuss law. The evolution of the field of stressesσ—which solves a time dependent variational inequality—and that of the field of displacementsu, have been described in previous works [15], [26], [35], [36], [37] but it was not shown there thatσandusatisfy indeed the Prandtl-Reuss constitutive law. In this article we findσanduin a class of functions which are sufficiently regular for the Prandtl-Reuss law to make sense and we prove thatσandusatisfy the constitutive law. This result is attained by considering the elastic-perfectly plastic model as the limit of a family of elastic-visco-plastic models like those of Norton and Hoff. The Norton-Hoff type models which we introduce depend on a viscosity parameterα> 0; we study the perturbed models(i.e. α >0 fixed) and then we pass to the limit α → 0.