Adaptive Multiscale Computational Framework for Transient Problems

摘要 拟议的研究计划的目标是开发一个自适应的多尺度计算框架的瞬态问题，旨在预测工程部件和结构的动态响应，包括复杂的故障机制在多个时间和空间尺度上运行。多尺度计算框架强调结构系统的动力学行为是从比目前模拟中解决的更小的空间和时间尺度上运行的基本物理过程来评估的。技术挑战是开发新的多尺度分析和设计概念，其中材料和结构被视为一个单一的系统，并使分析师能够更详细地考虑问题的物理性质，以确保计算的可靠性。 智力优点：所提出的框架将在以下两个方面扩展基本的计算和材料力学知识：统一的离散到连续和连续到连续的尺度桥接，同时考虑多个时间和空间尺度，以及分层数学模型的适应性。 更广泛的影响：如果成功，这一努力将极大地影响科学和工业界以准确及时的方式建模、分析和理解大量多尺度系统的能力。这些技术的验证将在三个功能应用上进行：（a）压电陶瓷的冲击波响应;（B）蜂窝的能量吸收;（c）聚合物基复合结构系统的碰撞预测。这三个功能的应用程序已被精心挑选，不仅因为它们体现了典型的复杂性与建模多个空间和时间尺度，但更重要的是，由于其国家经济的影响（能量吸收材料系统的重要性），和实验数据的可用性的计算能力的验证至关重要。除了选定的三个功能应用程序，其他应用程序需要大规模，高保真，预测性数值模拟的自然异质材料和工程复合材料将受益于这项工作。 这项工作所涉及的技术正在实现与机械工程、材料科学、物理学、高级建模和软件开发相关的自适应多尺度计算技术。教育材料，包括一个新的研究生课程，题为自适应多尺度工程原理以及教程和多尺度模拟工具将开发。

ABSTRACT The goal of the proposed research program is to develop an adaptive multiscale computational framework for transient problems aimed at predicting dynamic response of engineered components and structures including complex failure mechanisms operating at multiple temporal and spatial scales. The term multiscale computational framework is coined to emphasize that the dynamic behavior of structural systems is assessed from the fundamental physical processes operating at smaller spatial and temporal scales than currently resolved in simulations. The technical challenge is to develop new multiscale analysis and design concepts where material and structure are viewed as a single system and to enable the analyst to account in much more detail for the physics of the problem to ensure reliability of computations. Intellectual merit: The proposed framework will expand the fundamental computational and material mechanics knowledge in the following two respects: unified discrete-to-continuum and continuum-to-continuum scale bridging with concurrent consideration of multiple temporal and spatial scales, and adaptivity of hierarchical mathematical models. Broader impact: If successful, this effort will greatly impact science and industry's ability to model, analyze, and understand a vast array of multiscale systems in an accurate timely manner. Validation of these technologies will be performed on three feature applications: (a) Shock wave response of piezoelectric ceramics; (b) Energy absorption of honeycombs; (c) Crash prediction of polymer-based composite structural systems. These three feature applications have been carefully selected not only because they embody typical complexities associated with modeling multiple spatial and temporal scales, but more so due to their national economical impact (importance of energy absorbing material systems), and availability of experimental data critical for validation of computational capabilities. In addition to the three feature applications selected, other applications requiring large-scale, high-fidelity, predictive numerical simulation of naturally heterogeneous materials and engineered composites will benefit from this work. The technologies involved with this effort are enabling adaptive multiscale computational technologies associated with mechanical engineering, material science, physics, advanced modeling and software development. Educational materials including a new graduate course entitled Adaptive Multiscale Engineering Principles as well as tutorials and multiscale simulation tools will be developed.