Making peridynamic models fit for real-world multiphysics applications

周期动力学是近年来兴起的一种非局域理论，受到越来越多的关注。它已被广泛用于模拟断裂分析中具有挑战性的现象，如固体中裂纹的形核、扩展和扩展。最近，钯在腐蚀问题上的应用也引起了相当大的关注。然而，与经典的局部理论和相关的计算方法(如有限元方法)相比，局部放电建模仍处于起步阶段。因此，尽管PD在过去几年里在学术界蓬勃发展，但它在复杂的现实世界问题中的应用仍然很少。其中一个主要原因是，PD模型目前的计算成本比有限元等现有方法高得多，因为几十年来为后者开发的工具和有效的实现方案目前仍然缺乏PD。在这个项目中，我们将通过开发新的高效和健壮的实现方案以及辅助工具来解决PD建模的这个关键问题，从而提高PD模型的计算效率。具体地说，我们的目标是开发(1)显著改进的自适应离散化和积分格式，以及(2)新的非局部边界条件，以处理具有PD模型的无界区域。预计这些发展将使PD首次适合于处理广泛的复杂现实世界多物理问题。这一点将在项目的最后阶段通过开发可腐蚀降解的生物医用镁(MG)植入物的PD多物理模型来证明。

Peridynamics (PD) is a recent nonlocal theory receiving increasing attention. It has been widely exploited as a promising tool to model challenging phenomena in fracture analysis such as nucleation, growth and propagation of cracks in solids. More recently, also application of PD to corrosion problems has attracted considerable attention. However, PD modeling is still in its infancy compared to classical local theories and associated computational methods such as the finite element method. As a consequence, while PD has been thriving in the academic community over the last years, its application to complex real-world problems still remains sparse. One of the main reasons for this is that PD models are suffering at the moment from a considerably higher computational cost than established approaches like the finite element method because the tools and efficient implementation schemes that have been developed for the latter over several decades are at the moment still lacking for PD. In this project, we will address this key problem of PD modeling by developing novel efficient and robust implementation schemes as well as supplementary tools making PD models computationally more efficient. Specifically, we aim at the development of (1) substantially improved adaptive discretization and integration schemes and (2) of new nonlocal boundary conditions to handle unbounded domains with PD models. These developments are expected to make PD for the first time fit for tackling a broad range of complex real-world multiphysics problems. This will be demonstrated in the last stage of the project, by the development of a PD multiphysics model of the corrosion degradable biomedical magnesium (Mg) implants.