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A first-order energy-dissipative momentum-conserving scheme for elasto-plasticity using the variational updates formulation

机译:使用变分更新公式的弹塑性一阶耗能动量守恒方案

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In a previous paper [L. Noels, L. Stainier, J.-P. Ponthot, An energy momentum conserving algorithm using the variational formulation of visco-plastic updates, Int. J. Numer. Methods Engrg. 65 (2006) 904-942] the authors demonstrated the efficiency of the variational formulation of elasto-plastic updates to develop energy-momentum conserving time integration algorithms. Indeed, within such a framework, the stress tensor always derives from an incremental potential, even when plastic behavior is considered. Therefore the verification of the conservation of energy in the non-linear range can easily be demonstrated: the sum of the reversible stored energy and irreversible dissipated energy exactly corresponds to the work of the external forces applied to the structure. Although this formulation was shown to be accurate and robust, the introduction of numerical dissipation for high-frequency numerical modes can be necessary to simulate complex phenomena. In this work, we propose a modification of the variational updates framework to introduce this numerical property, leading to a new energy-dissipative momentum-conserving time-integration algorithm for elasto-plasticity.
机译:在上一篇论文中[L. Noels,L.Stainier,J.-P. Ponthot,使用粘塑性更新的变分公式的能量动量守恒算法,Int。 J.纽默方法工程。 [J.Biol.Chem.65(2006)904-942]的作者证明了弹塑性更新的变分公式开发能量动量节约时间积分算法的效率。的确,即使在考虑塑性行为的情况下,在这样的框架内,应力张量也总是来自于增量电势。因此,可以很容易地证明在非线性范围内的能量守恒的验证:可逆存储能量和不可逆耗散能量的总和正好对应于施加在结构上的外力的功。尽管已证明此公式是准确且可靠的,但为模拟复杂现象可能需要为高频数值模式引入数值耗散。在这项工作中,我们提出了对变分更新框架的修改,以引入此数值属性,从而导致了一种用于弹塑性的新的耗能动量守恒时间积分算法。

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