A Weakly Nonlinear Analysis of Elasto-plastic-Microstructure Models
A Weakly Nonlinear Analysis of Elasto-plastic-Microstructure Models
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DOI：
10.1137/s0036139993255327
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发表时间：
1995-02
期刊：
影响因子：
--
通讯作者：
L. An;A. Peirce
中科院分区：
文献类型：
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作者：
L. An;A. Peirce
在硬化模量的某些临界值下，弹塑性流动的控制方程可能会失去其双曲性并表现出两种不适定模式：剪切带不适定性和颤振不适定性。这些不适定模式的特点是模式在无限精细尺度上不受控制的增长，这最终违反了连续统假设。在之前的工作中[L. An 和 A. Peirce，SIAM J. Appl。 Math., 54(1994), pp. 708–730]，建立了一个考虑微尺度变形的连续体模型。线性分析证明了微观结构的规整效应，并提供了局部不稳定性的宽度与微观长度尺度之间的关系。在本文中，使用弱非线性分析来探索解的直接后临界行为。对于一维和反平面剪切模型，塑性区域中的后临界变形受 Boussinesq 方程控制（完全可积的偏微分方程之一，具有如此...
At certain critical values of the hardening modulus, the governing equations of elasto-plastic flow may lose their hyperbolicity and exhibit two modes of ill-posedness: shear-band and flutter ill-posedness. These modes of ill-posedness are characterized by the uncontrolled growth of modes at infinitely fine scales, which ultimately violates the continuum assumption. In previous work [L. An and A. Peirce, SIAM J. Appl. Math., 54(1994), pp. 708–730], a continuum model accounting for microscale deformations was built. Linear analysis demonstrated the regularizing effect of the microstructure and provided a relationship between the width of the localized instabilities and the microlength scale. In this paper a weakly nonlinear analysis is used to explore the immediate post-critical behavior of the solutions. For both one-dimensional and anti-plane shear models, post-critical deformations in the plastic regions are shown to be governed by the Boussinesq equation (one of the completely integrable PDEs having so...