A mathematical basis for strain-gradient plasticity theory — Part I : Scalar plastic multiplier
A mathematical basis for strain-gradient plasticity theory — Part I : Scalar plastic multiplier
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发表时间：
2008
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通讯作者：
N. Fleck;J. Willis
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作者：
N. Fleck;J. Willis
回顾了应变梯度塑性理论，其中塑性应变率的某些量值被视为独立的运动学变量。位错自变量被用来为界面处的硬化提供物理基础。建立了一个唯象流动理论版本的梯度塑性，其中应力措施，功共轭塑性应变及其梯度，满足一个屈服条件。塑性功也是在内部界面上进行的，并假定界面上的功共轭应力量有一个屈服面。因此，该理论有可能解释多晶体中的颗粒尺寸效应。体应力和界面应力在本质上都是耗散的，并给予适当的注意，以确保进行正塑性功。结果表明，弹塑性应变梯度理论的数学结构与传统的刚塑性理论有相似之处。构造了边值问题解的唯一性和极值原理。&2008爱思唯尔有限公司版权所有。
Strain-gradient plasticity theories are reviewed in which some measure of the plastic strain rate is treated as an independent kinematic variable. Dislocation arguments are invoked in order to provide a physical basis for the hardening at interfaces. A phenomenological, flow theory version of gradient plasticity is constructed in which stress measures, work-conjugate to plastic strain and its gradient, satisfy a yield condition. Plastic work is also done at internal interfaces and a yield surface is postulated for the work-conjugate stress quantities at the interface. Thereby, the theory has the potential to account for grain size effects in polycrystals. Both the bulk and interfacial stresses are taken to be dissipative in nature and due attention is paid to ensure that positive plastic work is done. It is shown that the mathematical structure of the elasto-plastic strain-gradient theory has similarities to conventional rigid-plasticity theory. Uniqueness and extremum principles are constructed for the solution of boundary value problems. & 2008 Elsevier Ltd. All rights reserved.