Uniqueness, loss of ellipticity and localization for the time‐discretized, rate‐dependent boundary value problem with softening
Uniqueness, loss of ellipticity and localization for the time‐discretized, rate‐dependent boundary value problem with softening
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时间离散、速率相关的软化边值问题的唯一性、椭圆度损失和局部化
DOI：
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发表时间：
2010
期刊：
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通讯作者：
O. Hopperstad
中科院分区：
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作者：
A. Benallal;T. Berstad;T. Børvik;O. Hopperstad
本文研究了存在软化的速率相关（弹粘塑性）固体材料的初始边值问题的时间离散化。重点放在独特性、椭圆性损失和本地化上。研究发现，时间离散问题类似于速率无关材料的增量问题，如果时间步长大于临界值，软化可能会导致不适定性（椭圆率损失）。众所周知，空间离散化后数值模拟中椭圆率损失的含义是计算结果的病态网格依赖性。我们提供了一种计算关键时间步长的方法，并演示了其在简单示例问题中的用途。版权所有 © 2010 约翰威利父子有限公司
The discretization in time of the initial boundary value problem for rate‐dependent (elastic‐viscoplastic) solid materials in presence of softening is investigated in this paper. The emphasis is put on uniqueness, loss of ellipticity and localization. It is found that the time‐discretized problem resembles the incremental problem for rate‐independent materials and softening may lead to ill‐posedness (loss of ellipticity) if the time step is greater than a critical value. It is well established that the implication of loss of ellipticity for the numerical simulations after spatial discretization is the pathological mesh dependency of the computed results. We furnish a method to compute the critical time step and demonstrate its use for a simple example problem. Copyright © 2010 John Wiley & Sons, Ltd.