Qinghua Wei | Searcharxiv

arXiv2026

The direct-line method for forward and inverse linear elasticity problems of composite materials in general domains with multiple singularities

In this work, a combined strategy of domain decomposition and the direct-line method is implemented to solve the forward and inverse linear elasticity problems of composite materials in general domains with multiple singularities. Domain decomposition technology treats the general domain as the union of some star-shaped subdomains, which can be handled using the direct-line method. The direct-line method demonstrates rapid convergence of the semi-discrete eigenvalues towards the exact eigenvalues of the elliptic operator, thereby naturally capturing the singularities. We also establish optimal error estimates for the proposed method. Especially, our method can handle multiple singular point problems in general regions, which are difficult to deal with by most methods. On the other hand, the inverse elasticity problem is constructed as a energy functional minimization problem with total variational regularization, we use the aforementioned method as a forward solver to reconstruct the lamé coefficient of multiple singular points in general regions. Our method can simultaneously deduce heterogeneous $μ$ and $λ$ between different materials. Through numerical experiments on three forward and inverse problems, we systematically verified the accuracy and reliability of this method to solve forward and inverse elastic problems in general domains with multiple singularities.

math.NA↗

arXiv2021

Accelerated design of linear-superelastic Ti-Nb nanocomposite alloys with ultralow modulus via high-throughput phase-field simulations and machine learning

The controlled design of martensitic transformation (MT) to achieve specific properties is crucial for the innovative application of shape memory alloys (SMAs) in advanced technologies. Herein, we explore and design the MT behaviors and the mechanical properties of Ti-Nb nanocomposites by combining high-throughput phase-field simulations and machine learning (ML) approaches. Based on the systematic phase-field simulations, we obtain data sets of the mechanical properties for various nanocomposites constructed by four macroscopic degrees of freedom, which can be employed to design and optimize the microstructures for different applications. To accelerate the phase-field screening of the desired metallic biomaterials, a ML assisted strategy is adopted to perform multi-objective optimization of the mechanical properties, through which promising nanocomposite configurations are pre-screened for the next set of phase-field simulations. With the ML guided simulations, an optimized candidate composed of Nb-rich matrix and Nb-lean nanofillers that exhibits a combination of unprecedented mechanical properties, including ultra-low modulus, linear super-elasticity, and near-hysteresis-free is designed. The exceptional mechanical properties in the nanocomposite originate from optimized continuous MT rather than a sharp first-order transition, which is common in typical SMAs. This work provides a new computational approach and design concept for developing novel functional materials with extraordinary properties.

cond-mat.mtrl-sci↗