A meshfree numerical approach for soils at rest and in flow

颗粒材料是固体，因为它们可以永久地承受剪应力。另一方面，它们可能会发生大变形(如液体)。从内部应力随应变增加的小应变到进一步变形(流动)时应力保持不变的大应变的转变可视为相变。最明显的相似之处是图案的形成，在颗粒体中表现为剪切定位。颗粒物质在流体和固体之间的特殊位置表征了它们的许多科学和技术应用。它们可以被放置在填充物、斜坡和筒仓中，但也可以在山谷和管道中顺流而下。船只可以在沙子上移动，但也可能沉入沙子。建筑物是安全地建立在沙子上的，但它们也可能在液化过程中下沉到沙子里。隐含的大变形通常是非拓扑的，即不保留邻域关系。因此，无网格方法似乎是进行模拟的合适的数值工具。与离散元方法相比，无网格方法不仅可以使用精细的本构模型，而且可以使用变初始密度和连续介质力学的全谱。在我们的研究项目的第一阶段，我们开发了一种特殊的无网格方法，其特点是非常简单。它是点运动的一种特殊实现，其密度、速度和应力可以通过邻域构形的内插来获得。控制平衡方程采用强形式。开发了两个程序：显式和线性化隐式变形程序(FPM)和非线性变形程序(SPARC)。在延续阶段，所获得的见解和成果将不仅用于模拟准静态(慢)变形，还将用于模拟动态(快速)变形，并将它们相互耦合。耦合问题的特征是固体/准流体/固体类型的相变。为了模拟这种转变，必须加强迄今应用的每一种方法，并必须利用协同效应。耦合过程的清单很长，涉及岩土结构的破坏(山体滑坡)、筒仓泄洪、隧道坍塌等。最大的挑战是数学/物理性质的：在相变(岩土工程中的极限状态)附近发生的颗粒材料的力学行为失去可控性。这种损失以各种方式表现出来：计算不稳定、矩阵病态、收敛问题等等，并且需要特殊的正则化方法。

Granular materials are solids as they can permanently sustain shear stress. On the other hand, they can undergo large deformations (like fluids). The transition from small strain, where the inner stresses increases with strain, to large strain, where the stresses remain constant at further deformation (flow), can be considered as phase transition. The most striking similarity is pattern formation, which in granular bodies appears as shear localization.The particular position of granular materials between fluids and solids characterizes many of their scientific and technical applications. They can be placed in fills, slopes and silos, but they can also flow downhill in valleys and pipes. Vessels can move upon sand, but they also can sink into it. Buildings are safely founded on sand but they can also subside into it during liquefaction. The implied large deformations are usually non-topological, i.e. neighborhood relations are not preserved. Therefore, meshfree methods appear to be the appropriate numerical tool for simulations. As compared with the Discrete Element Method, meshfree methods open the possibility to use not only refined constitutive models but also variable initial densities as well as the whole spectrum of continuum mechanics.In the first phase of our research project, we developed a special meshfree method that is characterized by outstanding simplicity. It is a particular implementation of the motion of points whose density, velocity, and stress can be obtained by interpolation of neighborhood configuration. The governing balance equations are used in the strong form. Two codes have been developed, FPM (explicit and linearized implicit) and SPARC (nonlinear).In the continuation phase, applied herewith, the gained insights and achievements will be used to simulate not only quasi-static (slow) deformations but also dynamic (fast) ones, and also to couple them to each other. Coupled problems are characterized by phase transitions of the type solid / quasi-fluid / solid. To model such transitions each method applied so far has to be enhanced, and synergy effects have to be exploited. The list of coupled processes is long and involves e.g. failures of geotechnical structures (landslides), discharge from silos, tunnel collapse, etc.The biggest challenge is of mathematical/physical nature: the loss of controllability of the mechanical behavior of granular materials that occurs in the vicinity of phase transitions (limit states in geotechnical engineering). This loss manifests in various ways: computation instabilities, ill-conditioned matrices, problems of convergence, and the like, and requires special regularization methods.