Non-local theories and stochastic mechanics: Two convergent directions for structural modelling?

许多土木工程结构是由混凝土、砖石和复合材料等非均匀材料组成的，了解它们对不同加载方式的响应对于评估在普通和极端情况下的性能至关重要。如今，随着计算技术的进步，结构和材料的计算机模拟得到了迅速发展。然而，许多问题仍然没有解决，包括人造材料的准确建模。人们可以选择将每一个细节都包括在分析中，但对于大型结构来说，这种方法很耗时，需要复杂的计算机能力。一种有效的替代方法是用等效的连续体代替复杂材料。这是在日常工程实践中采用经典弹性模型进行有限元分析时所做的，在合理的时间内为许多实际问题提供准确的解。然而，经典弹性理论可能忽略了由微观结构引起的许多重要现象。由于结构健康监测、损伤检测和地震波分析所使用的许多实验技术都需要对非均质结构中的波的传播有深入的了解和可靠的模型，所以这是一个非常值得关注的现象。对于研究界来说，一个关键的挑战是开发新的分析和数值模型，将微观结构信息引入结构尺度模型中。这个问题可以通过丰富的连续介质来成功地解决，这些连续介质具有非局部行为，即它们还包括微观结构长度尺度参数，以考虑邻近点处的应力和应变的影响。此外，由于这种材料和结构的机械性能表现出很大的变异性，工程师们面临着各种问题的挑战，其中不确定性也起着至关重要的作用。这表明，随机方法作为理论框架，可以成功地处理材料和几何性质的不确定性，以提高可靠性和安全性，并防止灾难性的结构失效。与非局域理论类似，随机材料被描述为与非局域分布的“长度尺度”有关的函数。由于观察到非局域理论和随机力学是处理涉及异质性和不确定性的多尺度问题的替代策略，本项目旨在阐明如下问题：材料性质的随机描述如何与动力学问题的非局域连续介质模型相互作用？对于某些工程问题，哪一种建模理念效果更好？我们能否在这两种策略之间建立关系，然后利用专门用于其中一种策略的工具？这个项目将通过研究混凝土梁的动力学来寻求这些问题的答案，之所以选择混凝土梁作为案例研究，是因为混凝土由于成分的不规则排列而具有固有的随机性，而且可以用数码相机捕捉其微观结构。这一点很重要，因为这项研究还将开发一种新的方法，利用微观结构的数字图像来识别长度尺度参数，并将在完全随机的力学环境下对模型参数进行灵敏度研究。

Many Civil Engineering structures are made of non-homogeneous materials such as concrete, masonry and composites, and understanding their response to different loading regimes is crucial to assess performance under ordinary and extreme events.Nowadays computer simulations of structures and materials have seen a rapid expansion as a result of the progress in computing technology. However, many issues are still unsolved, including the accurate modelling of man-made materials. One may choose to include every single detail into the analysis, but for large structures this approach is time consuming and requires sophisticated computer capabilities. An efficient alternative is to replace the complex material with an equivalent continuum. This is done in the everyday engineering practice when classical elasticity models are adopted for finite element analyses, delivering accurate solutions to many practical problems in a reasonable time. However, classical elasticity may overlook many important phenomena caused by the underlying microstructure. Stress wave propagation in heterogeneous materials due to dynamic/impact loading is one of such phenomena.This is of significant concern because many of the experimental techniques used in structural health monitoring, damage detection and seismic wave analysis require deep understanding and reliable models of wave propagation in heterogeneous structures. A key challenge for the research community is to develop new analytical and numerical models that bring microstructure information into the structural scale model.This issue can be successfully tackled by enriched continua, which enjoy non-local behaviour, i.e. they include also a microstructural length scale parameters to account for the influence of stress and strain at neighbouring points. Moreover, as mechanical properties of such materials and structures show great variability, engineers are challenged by problems where also uncertainties play a crucial role. This suggests stochastic methods as the theoretical framework where uncertainties in material and geometric properties can be successfully treated to improve reliability and safety and prevent catastrophic structural failure. In analogy to the non-local theories, random materials are described by some functions related to the "length scale" of the distribution of the heterogeneities.Motivated by the observation that non-local theory and stochastic mechanics are alternative strategies to tackle multiscale problems involving heterogeneity and uncertainties, this project aims to shed new light on questions such: How does stochastic description of material properties interact with non-local continuum models for dynamic problems? Would one or the other modelling philosophy work better for some engineering problems? Can we establish a relationship between the two strategies and then take advantage of the tools used exclusively for one or the other?This project will seek answers to these questions by investigating the dynamics of concrete beams, selected as a case study because concrete has an inherent randomness due to the irregular arrangement of the constituents and it is possible to capture its microstructure with a digital camera. This is important because the research will also develop a new approach for the identification of the length scale parameters by using digital images of the microstructure, and a sensitivity study of the model's parameters will be conducted in a full stochastic mechanics setting.