Discontinuous Displacement Approximation for Capturing Plastic Localization
Discontinuous Displacement Approximation for Capturing Plastic Localization
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用于捕获塑性定位的不连续位移近似
DOI：
10.1002/nme.1620361209
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发表时间：
1993
影响因子：
2.9
通讯作者：
N. S. Ottosen
中科院分区：
文献类型：
--
作者：
R. Larsson;K. Runesson;N. S. Ottosen
建议通过在有限元细分的单元边界（界面）处包含正则化位移不连续性来捕获局部塑性变形。正则化基于界面的运动学假设，类似于与经典剪切带概念相关的界面。作为正则化的副产品，固有带宽被引入为“本构”属性，而不是有限元网格的几何特征。这样，可以避免当位移近似连续时获得的虚假网格灵敏度。另一个结果是元件之间的界面关系直接源自连续变形材料的传统本构特性。一个有趣的功能是，声学张量不仅可以用于诊断不连续分叉，而且还可以用作界面的切线刚度张量（最多在标量因子内）。对界面行为进行了分析研究，结果表明，对于一般塑性模型，膨胀确实可能伴随着“剪切”带内的滑移。对于平面应变和平面应力的简单问题，证明了正确网格对齐的重要性。结果表明，当塑性软化模量与带宽适当相关时，可以实现独特的结构峰后响应（根据非线性断裂力学）。本文最后对土坡中剪切带的逐渐发展进行了数值模拟。
It is proposed to capture localized plastic deformation via the inclusion of regularized displacement discontinuities at element boundaries (interfaces) of the finite element subdivision. The regularization is based on a kinematic assumption for an interface that resembles that which is pertinent to the classical shear band concept. As a by-product of the regularization, an intrinsic band width is introduced as a ‘constitutive’ property rather than a geometric feature of the finite element mesh. In this way the spurious mesh sensitivity, which is obtained when the displacement approximation is continuous, can be avoided. Another consequence is that the interfacial relation between the elements is derived directly from the conventional constitutive properties of the continuously deforming material. An interesting feature is that the acoustic tensor will not only play a role for diagnosing discontinuous bifurcation but will also serve as the tangent stiffness tensor of the interface (up to within a scalar factor). An analytical investigation of the behaviour of the interface is carried out and it is shown that dilatation may indeed accompany slip within a ‘shear’ band for a general plasticity model. The significance of proper mesh alignment is demonstrated for a simple problem in plane strain and plane stress. It is shown that a unique structural post-peak response (in accordance with non-linear fracture mechanics) can be achieved when the plastic softening modulus is properly related to the bandwidth. The paper concludes with a numerical simulation of the gradual development of a shear band in a soil slope.