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

非局部理论和随机力学：结构建模的两个收敛方向？

基本信息

批准号：
EP/M004163/1
负责人：
Mariateresa Lombardo
金额：
$ 12.19万
依托单位：
Loughborough University
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2014
资助国家：
英国
起止时间：
2014 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FM004163%2F1
关键词：
Non local theories stochastic mechanics

项目摘要

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.

许多土木工程结构都是由非均质材料如混凝土、砌体和复合材料等组成，了解它们在不同荷载作用下的响应对于评估其在普通和极端事件下的性能至关重要。然而，许多问题仍未解决，包括人造材料的精确建模。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，这种方法非常耗时，并且需要复杂的计算机功能。一种有效的替代方法是用等效连续体代替复杂材料。这是在日常工程实践中，当经典的弹性模型采用有限元分析，在合理的时间内提供准确的解决方案，许多实际问题。然而，经典弹性学可能会忽视由底层微观结构引起的许多重要现象。非均质材料中的应力波传播就是其中的一种现象，这是一个值得关注的问题，因为许多用于结构健康监测、损伤检测和地震波分析的实验技术都需要对非均质结构中的应力波传播有深入的了解和可靠的模型。研究界面临的一个关键挑战是开发新的分析和数值模型，将微观结构信息纳入结构尺度模型。这个问题可以通过丰富的连续体成功解决，它具有非局部行为，即它们还包括微观结构长度尺度参数，以考虑相邻点的应力和应变的影响。此外，由于这些材料和结构的机械性能表现出很大的可变性，工程师们面临着一些问题，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特性的不确定性，以提高可靠性和安全性，并防止灾难性的结构故障。与非局部理论类似，随机材料由与非均匀性分布的“长度尺度”相关的一些函数来描述。基于非局部理论和随机力学是解决涉及非均匀性和不确定性的多尺度问题的替代策略的观察，本项目旨在揭示以下问题：材料特性的随机描述如何与动力学问题的非局部连续模型相互作用？对于某些工程问题，一种或另一种建模哲学会更好地工作吗？我们能否在这两种策略之间建立一种关系，然后利用专门用于其中一种策略的工具？本项目将通过调查混凝土梁的动力学来寻求这些问题的答案，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，并且可以用数码相机捕捉其微观结构。这是很重要的，因为这项研究还将开发一种新的方法，通过使用数字图像的微观结构的长度尺度参数的识别，和模型的参数的敏感性研究将在一个完整的随机力学设置进行。