Homogenization in gradient plasticity
Homogenization in gradient plasticity
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梯度塑性的均质化
DOI：
10.1002/gamm.201110016
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
H. Hanke
中科院分区：
文献类型：
--
作者：
H. Hanke
本文给出了率无关弹塑性系统的双尺度均匀化结果。该模型是经典的线性化强化弹塑性模型的正则化，并通过塑性变量的梯度项进行扩展。相关联的存储的弹性能量密度具有周期性振荡系数，其中周期由ε > 0缩放。塑性变量z的附加梯度项包含在弹性能中，并具有前因子εγ（γ ≥ 0）。我们导出了ε → 0依赖于γ的不同极限模型。对于γ > 1，极限模型是在[5]中导出的双尺度模型，其中不存在梯度项。当γ = 1时，塑性变量的梯度项在细观胞腔问题中仍然存在，而当γ ∈ [0，1）时，极限模型是用一个没有细观涨落的塑性变量来定义的。后一个模型可以通过弹性部分的均匀化简化为纯宏观弹塑性模型（© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA，魏因海姆）
This paper yields a two‐scale homogenization result for a rate‐independent elasto‐plastic system. The presented model is a regularization of the classical model of linearized elastoplasticity with hardening, which is extended by a gradient term of the plastic variables. The associated stored elastic energy density has periodically oscillating coefficients, where the period is scaled by ε > 0. The additional gradient term of the plastic variables z is contained in the elastic energy with a prefactor εγ (γ ≥ 0). We derive different limiting models for ε → 0 in dependence of γ. For γ > 1 the limiting model is the two‐scale model derived in [5], where no gradient term was present. For γ = 1 the gradient term of the plastic variable survives on the microscopic cell problem, while for γ ∈ [0, 1) the limit model is defined in terms of a plastic variable without microsco pic fluctuation. The latter model can be simplified to a purely macroscopic elasto‐plasticity model by homogenization of the elastic part (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
DOI：
10.1007/s00526-007-0119-4
发表时间：
2008-03
影响因子：
2.1
作者：
A. Mielke;T. Roubíček;U. Stefanelli
通讯作者：
A. Mielke;T. Roubíček;U. Stefanelli