发表机构
Donald P. Shiley School of Engr., Univ. of Portland（波特兰大学唐纳德·P·谢利工程学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出将颗粒介质准静态响应建模为线性互补问题，统一描述八种分岔与失稳病态，揭示破坏与软化对接触几何的敏感性及动态转变的必要性。
AI 中文摘要
本文研究了率无关耗散颗粒介质的离散准静态响应。颗粒系统通常使用本质上是动态的方法进行模拟，例如离散元法（DEM）和不连续变形法（DDA），其中颗粒的加速度和阻尼是关键方面。相比之下，准静态方法源于颗粒之间静态刚度关系。对于摩擦接触，集合体的刚度是增量非线性的，并取决于加载方向。本文通过将响应表述为线性互补问题（LCP）来解决这一困难。该方法受益于以往关于LCP解的存在性、唯一性和稳定性的研究基础，这些研究以一组简洁的规则加以阐述。推导了颗粒系统的LCP，考虑了颗粒在接触处曲率产生的几何效应、摩擦接触刚度以及颗粒上的位移约束。本文描述了颗粒系统的八种异常条件（病态），表现为各种分岔和不稳定性。当置于LCP的背景下时，这八种条件被明确地定义。这些病态包括三种类型的分岔：离散型、连续有界型（尚未在文献中报道）和连续无界型。文献中尚未报道的还有：当数据连续变化时，运动发生突然的不连续变化。方法和结果通过颗粒系统的示例加以说明。结果表明，不稳定性和分岔是接近破坏时的普遍现象；破坏和软化对颗粒在接触处的几何轮廓敏感；准静态系统可能遇到需要动态转变来解决与加载一致的路径缺失的状态。
英文摘要
The discrete quasi-static response of rate-independent dissipative granular media is addressed. Granular systems are conventionally simulated with methods that are intrinsically dynamic, such as the discrete element (DEM) and discontinuous deformation (DDA) methods, with the particles' accelerations and damping being essential aspects. In contrast, quasi-static methods derive from the static stiffness relationships among the particles. With frictional contacts, an assembly's stiffness is incrementally non-linear and dependent on the direction of loading. The paper resolves this difficulty by casting the response as a linear complementarity problem (LCP). The approach benefits from a foundation of past research on existence, uniqueness, and stability of LCP solutions, which are expounded in a concise set of rules. The LCP of a granular system is derived, accounting for geometric effects that arise from curvatures of particles at their contacts, frictional contact stiffnesses, and displacement constraints on the particles. The paper describes eight aberrant conditions (pathologies) of granular systems, in the forms of various bifurcations and instabilities. When placed in the context of an LCP, the eight conditions are unambiguously defined. These pathologies include three types of bifurcation: discrete, continuous-bounded (not yet reported in the literature), and continuous-unbounded. Not yet reported in the literature is an abrupt discontinuous change in movements upon a continuous change of the data. Methods and results are illustrated with examples of granular systems. Results show that instability and bifurcation are pervasive conditions near failure; that failure and softening are sensitive to the geometric contours of the particles at contacts; and that quasi-static systems can encounter states that require a dynamic transition to resolve a lack of paths consistent with loading.
Journal refComputer Methods in Applied Mechanics and Engineering, Vol. 444, 118117
