Controlling the fracture response of structures via topology optimization: From delaying fracture nucleation to maximizing toughness
Controlling the fracture response of structures via topology optimization: From delaying fracture nucleation to maximizing toughness
复制标题
DOI：
10.1016/j.jmps.2023.105227
复制
发表时间：
2023-01
影响因子：
5.3
通讯作者：
Ying Jia;O. Lopez-Pamies;X. Zhang
中科院分区：
文献类型：
--
作者：
Ying Jia;O. Lopez-Pamies;X. Zhang
现在一个公认的事实是，即使是简单的拓扑变化也可以极大地改变结构的断裂响应。为了定量地了解这一现象，本文提出了一种基于密度的准静态力学载荷下结构断裂响应拓扑优化框架。所提出的框架的两个关键特征之一是，它利用了一个完整的相场断裂理论，该理论最近被证明能够准确地描述各种名义弹性材料在各种加载条件下的脆性断裂的成核和扩展。另一个关键特征是，该框架基于多目标函数，允许以加权方式进行优化：(i)结构的初始刚度，（i i）断裂成核的第一个实例，以及（i i i）一旦发生断裂成核，断裂扩展所消耗的能量。重点是由具有各向同性线弹性行为以及各向同性强度表面和韧性的单一均匀材料制成的结构的基本情况。针对这三种材料性质分别提出了新的插值规则。作为获得定量洞察力的第一次努力，该框架被部署来优化二维结构的断裂响应，其中裂缝必然在三种不同类型的区域成核：在体内，从几何奇点（预先存在的裂缝和尖角），以及从边界的光滑部分。与传统的刚度最大化优化结构相比，得到的优化结构具有显著增强的断裂行为。此外，结果有助于揭示各种强化和增韧机制。这些包括促进高多孔结构，形成拉压不对称区域，以及消除裂纹和尖角。一个给定的结构所偏爱的特殊机制，毫不奇怪，直接与所构成的材料的弹性、强度和韧性有关。
It is now a well-established fact that even simple topology variations can drastically change the fracture response of structures. With the objective of gaining quantitative insight into this phenomenon, this paper puts forth a density-based topology optimization framework for the fracture response of structures subjected to quasistatic mechanical loads. One of the two key features of the proposed framework is that it makes use of a complete phase-field fracture theory that has been recently shown capable of accurately describing the nucleation and propagation of brittle fracture in a wide range of nominally elastic materials under a wide range of loading conditions. The other key feature is that the framework is based on a multi-objective function that allows optimizing in a weighted manner:(i) the initial stiffness of the structure,(i i) the first instance at which fracture nucleates, and (i i i) the energy dissipated by fracture propagation once fracture nucleation has occurred. The focus is on the basic case of structures made of a single homogeneous material featuring an isotropic linear elastic behavior alongside an isotropic strength surface and toughness. Novel interpolation rules are proposed for each of these three types of material properties. As a first effort to gain quantitative insight, the framework is deployed to optimize the fracture response of 2D structures wherein the fracture is bound to nucleate in three different types of regions: within the bulk, from geometric singularities (pre-existing cracks and sharp corners), and from smooth parts of the boundary. The obtained optimized structures are shown to exhibit significantly enhanced fracture behaviors compared to those of structures that are optimized according to conventional stiffness maximization. Furthermore, the results serve to reveal a variety of strengthening and toughening mechanisms. These include the promotion of highly porous structures, the formation of tension-compression asymmetric regions, and the removal of cracks and sharp corners. The particular mechanism that is preferred by a given structure, not surprisingly, correlates directly to the elastic, strength, and toughness properties of the material that is made of.