标题： 分数弹塑性离散化的适定性 显示英文标题

标题： Well-Posedness of Discretizations for Fractional Elasto-Plasticity

摘要： 我们考虑一个基于线性各向同性和运动硬化以及标准的von-Mises屈服函数的分数塑性模型，其中流动法则被替换为Riesz--Caputo分数阶导数。 该产生的数学模型通常是非局部且非光滑的。 我们的数值算法基于众所周知的径向返回映射，并利用核函数具有有限支撑的特性。 我们提出了该模型的显式和隐式离散化方法，并展示了显式时间离散化与空间中标准有限元方法结合时的适定性。 我们在二维和三维中的数值结果说明了该算法的性能以及分数参数的影响。 显示英文摘要

摘要： We consider a fractional plasticity model based on linear isotropic and kinematic hardening as well as a standard von-Mises yield function, where the flow rule is replaced by a Riesz--Caputo fractional derivative. The resulting mathematical model is typically non-local and non-smooth. Our numerical algorithm is based on the well-known radial return mapping and exploits that the kernel is finitely supported. We propose explicit and implicit discretizations of the model and show the well-posedness of the explicit in time discretization in combination with a standard finite element approach in space. Our numerical results in 2D and 3D illustrate the performance of the algorithm and the influence of the fractional parameter.