乘法粘塑性的几何积分器：误差累积分析
Geometric integrators for multiplicative viscoplasticity: analysis of error accumulation
AI总结：
本文通过分析乘法粘塑性模型中几何积分器的指数稳定性和不可压缩性约束，揭示了精确保持几何性质的数值算法在精度和收敛性上的优势，并指出违反不可压缩性会导致收敛性能急剧恶化。
摘要：
不可压缩性是金属塑性/粘塑性的典型特征。在过去十年中，大量研究致力于构建精确保持这一几何性质的数值积分算法。本文从数值和数学角度考察了此类几何积分器的优异精度和收敛特性。 以有限粘塑性的经典模型为例，我们阐述了精确解的指数稳定性概念。我们证明，如果精确满足不可压缩性，这一性质使得构建有效且稳定的数值算法成为可能。另一方面，如果违反不可压缩性约束，则会引入虚假自由度，导致指数稳定性丧失和收敛行为急剧恶化。
英文摘要：
The inelastic incompressibility is a typical feature of metal plasticity/viscoplasticity. Over the last decade, there has been a great amount of research related to construction of numerical integration algorithms which exactly preserve this geometric property. In this paper we examine, both numerically and mathematically, the excellent accuracy and convergence characteristics of such geometric integrators. In terms of a classical model of finite viscoplasticity, we illustrate the notion of exponential stability of the exact solution. We show that this property enables the construction of effective and stable numerical algorithms, if incompressibility is exactly satisfied. On the other hand, if the incompressibility constraint is violated, spurious degrees of freedom are introduced. This results in the loss of the exponential stability and a dramatic deterioration of convergence behavior.
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