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Variational regularization of damage models based on the emulated RVE
Continuum Mechanics and Thermodynamics ( IF 2.6 ) Pub Date : 2020-05-24 , DOI: 10.1007/s00161-020-00886-0
Stephan Schwarz , Philipp Junker , Klaus Hackl

Material models exhibiting softening effects due to damage or localization share the problem of leading to ill-posed boundary value problems that lead to physically meaningless, mesh-dependent finite element results. It is thus necessary to apply regularization techniques that couple local behavior, described, e.g., by internal variables, at a spatial level. The common way to do this is to take into account higher gradients of the field variables, thus introducing an internal length scale. In this paper, we suggest a different approach to regularization that does not make use of any nonlocal enhancement like the inclusion of higher gradients or integration over local sub-domains nor of any classical viscous effects. Instead we perform an appropriate relaxation of the (condensed) free energy in a time-incremental setting which leads to a modified energy that is coercive and satisfies quasiconvexity in an approximate way. Thus, in every time increment a regular boundary value problem is solved. The proposed approach holds the same advantage as other methods, but with less numerical effort. We start with the theoretical derivation, discuss a rate-independent version of the proposed model and present details of the numerical treatment. Finally, we give finite element results that demonstrate the efficiency of this new approach.



中文翻译:

基于仿真RVE的损伤模型的变分正则化

由于损坏或局部化而表现出软化效果的材料模型存在导致不适定的边值问题的问题,该问题会导致物理上无意义的,依赖于网格的有限元结果。因此,有必要应用将局部行为耦合的正则化技术,例如在空间级别上由内部变量描述。这样做的常见方法是考虑字段变量的较高梯度,从而引入内部长度标度。在本文中,我们提出了一种不同的正则化方法,该方法不利用任何非局部增强,例如不包括更高的梯度或在局部子域上的积分,也不利用任何经典的粘性效应。取而代之的是,我们在时间增量设置中适当地放松了(压缩的)自由能,从而产生了一种矫正的能量,并以近似的方式满足拟凸性。因此,每增加一个规则边界值问题就解决了。所提出的方法与其他方法具有相同的优点,但是所需的数值较少。我们从理论推导开始,讨论所提出模型的与速率无关的版本,并给出数值处理的细节。最后,我们给出有限元结果,以证明这种新方法的有效性。但用较少的数字努力。我们从理论推导开始,讨论所提出模型的与速率无关的版本,并给出数值处理的细节。最后,我们给出有限元结果,以证明这种新方法的有效性。但用较少的数字努力。我们从理论推导开始,讨论所提出模型的与速率无关的版本,并给出数值处理的细节。最后,我们给出有限元结果,以证明这种新方法的有效性。

更新日期:2020-05-24
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