The role of dissipation and defect energy in variational formulations of problems in strain-gradient plasticity. Part 2: single-crystal plasticity
The role of dissipation and defect energy in variational formulations of problems in strain-gradient plasticity. Part 2: single-crystal plasticity
复制标题
耗散和缺陷能量在应变梯度塑性问题的变分公式中的作用。
DOI：
10.1007/s00161-011-0195-8
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发表时间：
2011
影响因子：
2.6
通讯作者：
B. Reddy
中科院分区：
文献类型：
--
作者：
B. Reddy
建立了小变形单晶应变梯度塑性率无关问题的变分公式。该框架基于Gurtin（J Mech Phys Solids 50：5-32，2002）的框架，利用了以耗散函数表示的流动规则。提供了有力的和耗散的微应力。可恢复和不可恢复的缺陷能量被纳入变分框架。可恢复的能量包括那些平滑地依赖于滑移梯度、伯格斯张量或位错密度的能量（Gurtin等人，2004）。J Mech Phys Solids 55：1853-1878，2007），以及Ohno和Okumura提出的能量（J Mech Phys Solids 55：1879-1898，2007），其导致与实验结果的极好一致性，并且其是正均匀的，因此在零滑移梯度下不可微。此外，变分制剂容纳由于Ohno等人的不可恢复的能量。(Int J Mod Phys B 22：5937-5942，2008），其也是正均匀的，并且是累积位错密度的函数。的存在性和唯一性的解决方案的条件建立的各种例子的缺陷能量，有或没有硬化或滑动阻力的存在。
Variational formulations are constructed for rate-independent problems in small-deformation single-crystal strain-gradient plasticity. The framework, based on that of Gurtin (J Mech Phys Solids 50: 5–32, 2002), makes use of the flow rule expressed in terms of the dissipation function. Provision is made for energetic and dissipative microstresses. Both recoverable and non-recoverable defect energies are incorporated into the variational framework. The recoverable energies include those that depend smoothly on the slip gradients, the Burgers tensor, or on the dislocation densities (Gurtin et al. J Mech Phys Solids 55:1853–1878, 2007), as well as an energy proposed by Ohno and Okumura (J Mech Phys Solids 55:1879–1898, 2007), which leads to excellent agreement with experimental results, and which is positively homogeneous and therefore not differentiable at zero slip gradient. Furthermore, the variational formulation accommodates a non-recoverable energy due to Ohno et al. (Int J Mod Phys B 22:5937–5942, 2008), which is also positively homogeneous, and a function of the accumulated dislocation density. Conditions for the existence and uniqueness of solutions are established for the various examples of defect energy, with or without the presence of hardening or slip resistance.