In this work we present a simple and convenient method for handling tensors within computational mechanics frameworks based on the Kelvin decomposition. This methodology was set up within a crystal plasticity framework which permits, using the Kelvin base related to the crystal symmetries, to account for elastic anisotropy. The classical mixed velocity pressure finite element formulation has been modified in order to account for the elastic anisotropic behavior introduced into the crystal plasticity model. Moreover this modification of the mixed formulations allows to account for volume/pressure variations that can stream from constitutive models that could allow present compressible plasticity. Using this numerical framework, we explore the influence of elastic anisotropy onto the mechanical behavior of olivine. Our results suggest that at the polycrystal scale, the elastic anisotropy is not of first order importance. However the local changes on the stress state can be important for some physical phenomena such as recrystallization and damage.

在这项工作中，我们提出了一种基于开尔文分解的简单方便的方法来处理计算力学框架内的张量。该方法是在晶体可塑性框架内建立的，该框架允许使用与晶体对称性有关的开尔文碱来解释弹性各向异性。为了解决引入晶体可塑性模型中的弹性各向异性行为，对经典的混合速度压力有限元公式进行了修改。而且，混合制剂的这种改变允许考虑体积/压力变化，该体积/压力变化可以从本构模型流出，该本构模型可以允许存在可压缩的可塑性。使用此数值框架，我们探索了弹性各向异性对橄榄石力学行为的影响。我们的结果表明，在多晶尺度上，弹性各向异性并不重要。但是，应力状态的局部变化对于某些物理现象（例如重结晶和损坏）可能很重要。