论文标题
识别有关准静态弹性损伤演变的过程。第2部分 - 数值模拟
Identifying Processes Governing Damage Evolution in Quasi-Static Elasticity. Part 2 -- Numerical Simulations
论文作者
论文摘要
我们从数值上研究了卡塔诺夫型的准静态弹性系统。为此，我们提出了一个Euler时间离散化与合适的有限元方案（FEM）结合使用，以处理离散化是空间。我们使用ODE-Type参数来证明该方案的一致性及其收敛率。我们依靠计算平台Fenics在计算模型输出所需的空间中执行FEM离散化。模拟结果表明，与问题的物理学以及我们先前针对同一问题设定获得的定性数学分析结果既有良好的一致性。此外，我们的实施恢复了理论上预期的收敛速率。这是一项初步研究，为卡查诺夫型模型中的损害过程进行严格的数值识别准备了框架。
We investigate numerically a quasi-static elasticity system of Kachanov-type. To do so we propose an Euler time discretization combined with a suitable finite elements scheme (FEM) to handle the discretization is space. We use ODE-type arguments to prove the consistency of the scheme as well as its convergence rate. We rely on the computational platform FEniCS to perform the FEM discretizations in space needed to compute the model output. The simulation results show a good agreement with both the physics of the problem and with our previous qualitative mathematical analysis results obtained for precisely the same problem setting. Furthermore, our implementation recovers nicely the theoretically expected convergence rate. This is a preliminary study preparing the framework for the rigorous numerical identification of the damage process in Kachanov-type models.
