Nonconvex Models of Consolidation by Particle Rearrangement in Cohesive Aggregates

本研究的目的是了解细颗粒聚集体多相固结的物理特性，并开发和校准固结的预测模型。研究的重点是前30%到45%的固结过程，在这个阶段，固结主要是由颗粒重排主导的，这已经被证明是以相变的形式发生的。通过颗粒重排固结的张拉模型将制定使用均匀化方法和非凸分析。为了测试和校准不受模壁摩擦影响的模型，将在没有特征长度尺度的冲压实验中测量固结曲线，并开发一种从单个固结曲线中提取过渡应力值的方法。然后将模壁摩擦的影响包括在内，以预测圆柱形模具中的固结曲线，并将其与普通药物填料的固结曲线进行比较。对于更复杂几何形状的模具，将开发用于模拟内聚聚集的计算代码和用于模拟多相固结的离散粒子计算代码。作为本研究的一部分，开发的方法和计算程序将适用于陶瓷部件、粉末冶金部件和药片的成型，在这些领域，固结过程的设计仍然是一个反复试验的过程，并且考虑到颗粒重排的非均匀性可能会导致可靠的设计。这项研究可能有助于减少工业过程中的浪费，如造粒，其中20%的粉末由于不完全固化而必须回收。研究还涉及到沉积盆地沉降史的计算，对石油勘探具有重要意义。实验计划将为本科生提供参与的机会，研究生和本科生都将通过课堂教学受益。

The objective of this research is to understand the physics of multiphase consolidation of fine particulate aggregates and to develop and calibrate predictive models of consolidation. At the focus of the research is the first 30 to 45 percent of the consolidation stroke, where the consolidation is dominated by particle rearrangement, which has been shown to occur in the form of a phase transition. A tensorial model of consolidation by particle rearrangement will be formulated using homogeneization methods and nonconvex analysis. To test and calibrate the model independent of the effect of die-wall friction, consolidation curves will be measured in punching experiments devoid of a characteristic lengthscale, and a method to extract the value of the transition stress from a single consolidation curve will be developed. The effect of die-wall friction will then be included in order to predict consolidation curves in cylindrical dies, which will be compared with the consolidation curves of common pharmaceutical fillers. For dies of a more complicated geometry, a computational code will be developed for the simulation of cohesive aggregation and a discrete-particle computational code for the simulation of multiphase consolidation.The methods and computational programs developed as part of this research will be applicable to the forming of ceramic parts, powder metallurgical components, and pharmaceutical tablets, where the design of consolidation procedures has remained a trial-and-error process, and where accounting for the inhomogeneous nature of particle rearrangement may lead to reliable design. The research may help reduce waste in industrial processes such as granulation, in which 20 percent of the powders must be recycled due to incomplete consolidation. The research is also relevant to the computation of the subsidence history of sedimentary basins, of critical importance in oil prospecting. The experimental plan will provide opportunities for the participation of undergraduate students, and both graduate and undergraduate students will benefit through classroom instruction.