Comparison of various models for strain‐softening
Comparison of various models for strain‐softening
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各种应变软化模型的比较
DOI：
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发表时间：
1988
期刊：
影响因子：
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通讯作者：
M. Tabbara
中科院分区：
文献类型：
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作者：
G. Pijaudier;Z. Bažant;M. Tabbara
本文对最近文献中提出的裂纹或孔洞扩展等损伤引起的应变软化模型进行了比较。区分了以软化应力-应变关系表示的连续介质模型和以软化应力-位移关系表示的裂缝型模型。一维波传播计算表明，应变局部化不能实现到有限尺寸的区域。以前已有文献记载的伪收敛是用连续介质模型得到的，而应力-位移关系不能很好地模拟涂抹裂纹的情况。然而，如果实现了局部化限制器，则通常可以使用连续统模型。梯度型局部化限制器看起来相当复杂，它们需要求解带有附加边界条件的高阶平衡微分方程组。非局域局部化限制器，特别是具有局域应变的非局域连续体，其中只有能量耗散变量是非局域的，被发现是非常有效的，而且似乎也是物理上现实的。该公式可以正确地模拟均匀损伤状态和损伤局部化到可视为裂纹的小区域之间的转变。在拉伸或压缩试件的实验和数值响应中观察到的尺寸效应被证明是从连续型配方向断裂型配方逐渐转变的结果。
This paper presents a comparison of various models for strain‐softening due to damage such as cracking or void growth, as proposed recently in the literature. Continuum‐based models expressed in terms of softening stress—strain relations, and fracture‐type models expressed in terms of softening stress—displacement relations are distinguished. From one‐dimensional wave propagation calculations, it is shown that strain‐localization into regions of finite size cannot be achieved. The previously well‐documented spurious convergence is obtained with continuum models, while stress—displacement relations cannot model well smeared‐crack situations. Continuum models may, however, be used in general if a localization limiter is implemented. Gradient‐type localization limiters appear to be rather complicated; they require solving higher‐order differential equations of equilibrium with additional bourdary conditions. Non‐local localization limiters, especially the non‐local continuum with local strain, in which only the energy dissipating variables are non‐local, is found to be very effective, and also seems to be physically realistic. This formulation can correctly model the transition between homogeneous damage states and situations in which damage localizes into small regions that can be viewed as cracks. The size effect observed in the experimental and numerical response of specimens in tension or compression is shown to be a consequence of this progressive transition from continuum‐type to fracture‐type formulations.