Data-driven and topological design of structural metamaterials for fracture resistance

Abstract

Data science as a promising paradigm provides novel and diverse opportunities for structural metamaterials attaining exceptional mechanical properties. It is demonstrated here that porous structures composed of brittle constitutive materials can be strong and tough through topological optimization and data-driven techniques. We show that brittle fracture properties can be tailored through the linear control of the homogenized stress and non-periodic microstructures from a multiscale perspective. These tough advanced structural metamaterials pave the way to multiscale components with exceptional fracture resistance.

Introduction

It is well-known that stress concentration will cause premature fracture of any bearing structural materials. Avoiding such a phenomenon is among the most important criteria to design a structure in engineering. However, controlling the stress distribution from a multi-scale perspective has not yet been explored. Besides, establishing inverse design optimization frameworks to support the creation of structural metamaterials with optimal architectures and fracture resistance is still in its infancy.

Topological optimization is an inverse design method that tailors the morphology of the structure by distributing materials inside a given domain under constraints like equilibrium and boundary conditions. Initially flourishing in stiffness optimization, it has been extended to tailor material microstructures to achieve prescribed or extreme constitutive properties [1], [2]. Recently, structural fracture resistance design has attracted some attention. In this direction, early works combine explicit crack initiation and propagation with structural design for fracture resistance [3], [4]. Later on, gradient-based topology optimization frameworks are proposed, where fracture simulation accounts for the entire failure process involving multiple crack types, while distributions of the constituent materials are tailored to enhance mechanical fracture properties [5], [6], [7], [8], [9]. For instance, designing the architecture of the soft constituent in biomimic composites [10] enables energy dissipation ahead of the crack tip to prevent crack propagation and toughen the composite.

On the other hand, fracture-related design of structural materials has also been addressed by introducing stress constraints to prevent material failure [11], [12]. Thereafter, the stress-based topological optimization for specific objectives (e.g. minimal mass, maximal stiffness or minimal overall stress) have been extensively investigated (see, e.g., [13]). This approach is similar to fracture resistance design from the perspective of alleviating the stress concentration around the crack tip such that the crack initiation is prevented, enhancing the fracture performance. Ref. [14] validated that the stress-based optimal structures achieve improved strength and toughness compared with other designs such as the stiffness-oriented solutions. However, both stress and failure process-based fracture resistance optimization have thus far been locked in a single-scale framework. Topological design of the material microstructures to enhance the fracture mechanical properties is, to our best knowledge, investigated here for the first time. Moreover, the ability of optimized non-periodic porous structures to achieve even further improvement in fracture properties is demonstrated.

Fracture resistance design from a multiscale perspective is a challenging topic, mainly due to the lack of robust multiscale methods for fracture simulation in the presence of complex heterogeneous media. In addition, numerical optimization is difficult with such a high-dimensional problem where heterogeneous materials and structures acting at different scales need to be optimized simultaneously. Under this stalemate, data-driven methods came into being, providing novel and prosperous ways for multi-scale design optimization, e.g. in reducing dimensionality [15] and accelerating the design of nanocomposites [16] and multiscale structures [17]. For the first time, this work combines data-driven and topology design methods to optimize the microstructure of materials by maximizing the uniform distribution of the macrostructural stress, thus toughening and strengthening the global (macroscopic) porous structure composed of brittle constituent materials.

Three steps are implemented to validate the enhancement of the fracture toughness of the porous structures. Firstly, a multiscale inverse optimization framework is established to precisely control the global stress by tailoring the distribution of the components of the homogenized stiffness tensor. Thereafter, the architecture of each unit cell is identified from a large database via data-driven techniques while guaranteeing the connectivity between neighboring cells. Finally, the fracture resistance performance of the assembled structure is validated through the phase field method [18], [19], [20], [21].