报告题目：Fracture & Complexity 断裂及复杂性
报告嘉宾：Alberto Carpinteri 院士（意大利都灵理工大学）
主持人：沈水龙院长
报告时间：2023年4月13日15:00
报告地点：图书馆报告厅
报告摘要：
The lecture deals with the opposite natural trends in composite systems: catastrophe and chaos arising from simple nonlinear rules, as well as order and structure emerging from heterogeneity and randomness.
本报告讨论组合系统中相反的自然规律: 由简单的非线性规则引起的突变和混沌，以及在非均匀和随机系统中秩序和结构。包含以下两个部分。
Part I deals with Nonlinear Fracture Mechanics models (in particular, the Cohesive Crack Model to describe strain-localization both in tension and in compression) and their peculiar consequences: fold catastrophes (post-peak strain-softening and snap-through instabilities) or cusp catastrophes (snap-back instabilities) in plain or reinforced structural elements. How can a relatively simple nonlinear constitutive law, which is scale-independent, generate a size-scale dependent ductile-to-brittle transition? Constant reference is made to Dimensional Analysis and to the definition of suitable nondimensional brittleness numbers that govern the transition. These numbers can be defined in different ways, according to the selected theoretical model. The simplest way is that of directly comparing critical LEFM conditions and plastic limit analysis results. This is an equivalent way --although more effective for finite-sized cracked plates-- to describe the ductile-to-brittle size-scale transition, if compared to the traditional evaluation of the crack tip plastic-zone extension in an infinite plate. In extremely brittle cases, the plastic zone or process zone tends to disappear and the cusp catastrophe conditions prevail over the strain-softening ones and tend to coincide with the LEFM critical conditions in the case of initially cracked plates.
第一部分讨论了非线性断裂力学模型(特别是描述拉伸和压缩中应变局部化的内聚裂纹模型)及其特殊后果: 素混凝土和钢筋混凝土结构的折叠的灾难性突变(峰值后应变软化和跳跃不稳定性)或尖点突降(回跳不稳定性)。一个相对简单的、与尺度无关的非线性本构关系如何产生尺度相关的延性-脆性转变？我们经常通过量纲分析和定义合适的无量纲脆性指数来控制延性-脆性的转变。根据所选择的理论模型不同，脆性指数可以用不同的方式来定义。最简单的方法是直接通过比较线弹性断裂力学的临界条件和塑性极限分析结果。与传统的无限大板内裂纹尖端塑性区扩展的评估方法相比，这种等效的方法来描述延性-脆性转变的尺寸效应，对描述带裂纹的有限大板来说更有效。在极端脆性的情况下，塑性区或过程区消失，应变软化将以尖点突降特征为主，其结果将与带初始裂纹的板的线弹性断裂力学临界条件相吻合。
Part II deals with the occurrence of self-similar and fractal patterns in the deformation, damage, fracture, and fragmentation of heterogeneous disordered materials, and with the consequent apparent scaling in the nominal mechanical properties of the same materials. Such a scaling is negative (lacunar fractality) for tensile strength and fatigue limit, whereas it is positive (invasive fractality) for fracture energy, fracture toughness, and fatigue threshold. At the same time, corresponding fractal (or renormalized) quantities emerge, which are the true scale-invariant properties of the material. They appear to be the constant factor (the universal property) in the power-law relating the nominal canonical quantity to the size-scale of observation. When the reference sets from self-similar become self-affine, we obtain Multi-fractal Scaling Laws, which are asymptotic and present a decreasing fractality for increasing structural sizes. They reproduce the experimental data very consistently. On the other hand, Critical Phenomena are always associated to the emergence of self-similar or self-affine patterns, to fractal (renormalized) or multi-fractal quantities, and to spontaneous self-organization. Typical examples are represented by: phase transformations, laminar-to-turbulent fluid flow transitions, avalanches in granular media, earthquakes, micro-cracking and fracture in structural materials. In a fractal framework, it is then possible to define a scale-invariant constitutive law: the so-called Fractal Cohesive Crack Model, in which stress and strain are defined over lacunar fractal sets and the fracture energy in an invasive fractal set, which is the Cartesian product of the two previous sets.
第二部分讨论了非均匀无序材料的变形、损伤、断裂和破碎过程中自相似和分形模式，以及由此导致的相同材料名义力学性能的明显尺度效应。这种尺寸效应对抗拉强度和疲劳极限是负影响(空隙分形) ，而对断裂能量、断裂韧性和疲劳阈值是正影响(侵入分形)。与此同时，获得相应的分形数(或重整化)。分形数是一个真正体现材料的尺度不变性的量。分形数似乎是幂律中的一个常数因子(具有普遍性质) 。幂律是一个将标称正则量与观测尺度联系起来的东西。当自相似参考集，变为自仿射时，我们得到多重分形律，多重分形律是渐近的，并且随着结构尺寸的增加呈递减分形。他们和实验数据非常吻合。另一方面，临界现象总是以自相似或自仿射模式的特征出现，而分形或多重分形与自发的自我组织有关。典型的例子有: 相变、层流-湍流流动转变、颗粒介质中的雪崩、地震、结构材料中的微裂纹和断裂。在一个分形框架中，可定义一个尺度不变的本构律，即所谓的分形内聚裂纹模型。在这个模型中，应力和应变定义在腔隙分形集上，而断裂能则定义在一个侵入分形集上。它们是前两个分形集的笛卡儿积。
报告人简介：
Alberto Carpinteri，先后于1976年和1981年获意大利博洛尼亚大学核工程专业博士学位和数学专业博士学位，现为意大利都灵理工大学教授，断裂力学实验室主任(1999至今)，欧洲科学院工程部主任(2016至今)，欧洲科学院、欧洲科学与艺术院、国际工程院等机构的院士，兼任国际断裂学会、国际混凝土结构断裂力学协会等多个协会主席、SCI期刊主编和编委。Alberto Carpinteri教授长期从事混凝土结构断裂力学、地震预测的研究，是国际知名结构工程专家，发表论文1000余篇，其中同行评审期刊论文490篇，被引超3万次，截止到目前谷歌H-index 86、Scopus H-index 64，获Inaugural Paul Paris金奖、Swedlow Memorial Lecture奖等奖项，此外，发行著作或主编期刊特刊共58本。
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