On a consistent hourglass stabilization technique to treat large inelastic deformations and thermo‐mechanical coupling in plane strain problems
On a consistent hourglass stabilization technique to treat large inelastic deformations and thermo‐mechanical coupling in plane strain problems
复制标题
采用一致的沙漏稳定技术来处理平面应变问题中的大非弹性变形和热力耦合
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发表时间：
2003
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通讯作者：
S. Reese
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作者：
S. Reese
在线性弹性中，如果做了一定的假设，可以直接从混合方法中推导出减少积分与沙漏稳定化相结合的概念。当应力和应变之间的关系是高度非线性的时，这样的推导要困难得多。早期的工作使用经典多场泛函的线性化形式，以便解析地推导沙漏稳定性。在目前的贡献中，它显示了如何在弱形式的水平上直接推导出这种稳定技术。新概念的关键是本构相关量相对于元素中心的泰勒展开式。该方法适用于各种非弹性材料模型和热-力耦合。新单元技术的一个重要特点是它的计算效率，这在单元级的数值计算量很高时尤为明显。版权所有©2003 John Wiley & Sons， Ltd
In linear elasticity, the concept of reduced integration combined with hourglass stabilization can be directly derived from a mixed method, if certain assumptions are made. Such a derivation is much more difficult when the relation between stress and strain is highly non‐linear. Earlier works use the linearized form of a classical multi‐field functional in order to derive the hourglass stabilization analytically. In the present contribution, it is shown how such stabilization techniques can be directly derived at the level of the weak form. Crucial to the new concept is a Taylor expansion of the constitutively dependent quantities with respect to the centre of the element. The approach is suitable for various kinds of inelastic material models and thermo‐mechanical coupling. One of the important features of the new element technology is its computational efficiency which is especially visible when the numerical effort at the element level is very high. Copyright © 2003 John Wiley & Sons, Ltd.