A theory of strain-gradient plasticity for isotropic, plastically irrotational materials. Part I: Small deformations
A theory of strain-gradient plasticity for isotropic, plastically irrotational materials. Part I: Small deformations
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DOI：
10.1016/j.jmps.2004.12.008
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发表时间：
2005-07
影响因子：
5.3
通讯作者：
M. Gurtin;L. Anand
中科院分区：
文献类型：
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作者：
M. Gurtin;L. Anand
本研究发展了各向同性材料在无塑性旋转情况下的应变梯度塑性小变形理论。该理论基于与微力平衡一致的微应力体系；第二定律的机械版本，通过微应力包括在粘塑性流动过程中所做的功；本构理论允许：当微力平衡被微应力的本构关系增强时，将得到塑性应变的张量二阶偏微分方程式形式的非局部流动规则。当ψ与Burgers张量无关时，微应力是严格耗散的，但当ψ依赖于G时，梯度微应力是部分含能的，这反过来又导致背应力，从而导致流动规则中的包辛格效应。进一步表明，∇E·上的微观应力依赖于流动规律中的强化和弱化效应。典型的宏观边界条件被与流动相关的非标准微观边界条件补充，并作为数值解的辅助，导出了非局部流动规则的弱(有效功率)公式。
This study develops a small-deformation theory of strain-gradient plasticity for isotropic materials in the absence of plastic rotation. The theory is based on a system of microstresses consistent with a microforce balance; a mechanical version of the second law that includes, via microstresses, work performed during viscoplastic flow; a constitutive theory that allows:The microforce balance when augmented by constitutive relations for the microstresses results in a nonlocal flow rule in the form of a tensorial second-order partial differential equation for the plastic strain. The microstresses are strictly dissipative when ψ is independent of the Burgers tensor, but when ψ depends on G the gradient microstress is partially energetic, and this, in turn, leads to a back stress and (hence) to Bauschinger-effects in the flow rule. It is further shown that dependencies of the microstresses on ∇E˙plead to strengthening and weakening effects in the flow rule. Typical macroscopic boundary conditions are supplemented by nonstandard microscopic boundary conditions associated with flow, and, as an aid to numerical solutions, a weak (virtual power) formulation of the nonlocal flow rule is derived.