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Microstructure-sensitive material design has become popular among materials engineering researchers in the last decade because it allows the control of material performance through the design of microstructures. In this study, the microstructure is defined by an orientation distribution function (ODF). A physics-informed machine learning approach is integrated into microstructure design to improve the accuracy, computational efficiency, and explainability of microstructure-sensitive design. When data generation is costly and numerical models need to follow certain physical laws, machine learning models that are domain-aware perform more efficiently than conventional machine learning models. Therefore, a new paradigm called Physics-Informed Neural Network (PINN) is introduced in the literature. This study applies the PINN to microstructure-sensitive modeling and inverse design to explore the material behavior under deformation processing. In particular, we demonstrate the application of PINN to small-data problems driven by a crystal plasticity model that needs to satisfy the physics-based design constraints of the microstructural orientation space. For the first problem, we predict the microstructural texture evolution of Copper during a tensile deformation process as a function of initial texturing and strain rate. The second problem aims to calibrate the crystal plasticity parameters of Ti-7Al alloy by solving an inverse design problem to match PINN-predicted final texture prediction and the experimental data. 

Protective coatings based on two dimensional materials such as graphene have gained traction for diverse applications. Their impermeability, inertness, excellent bonding with metals, and amenability to functionalization renders them as promising coatings for both abiotic and microbiologically influenced corrosion (MIC). Owing to the success of graphene coatings, the whole family of 2D materials, including hexagonal boron nitride and molybdenum disulphide are being screened to obtain other promising coatings. AI-based data-driven models can accelerate virtual screening of 2D coatings with desirable physical and chemical properties. However, lack of large experimental datasets renders training of classifiers difficult and often results in over-fitting. Generate large datasets for MIC resistance of 2D coatings is both complex and laborious. Deep learning data augmentation methods can alleviate this issue by generating synthetic electrochemical data that resembles the training data classes. Here, we investigated two different deep generative models, namely variation autoencoder (VAE) and generative adversarial network (GAN) for generating synthetic data for expanding small experimental datasets. Our model experimental system included few layered graphene over copper surfaces. The synthetic data generated using GAN displayed a greater neural network system performance (83-85% accuracy) than VAE generated synthetic data (78-80% accuracy). However, VAE data performed better (90% accuracy) than GAN data (84%-85% accuracy) when using XGBoost. Finally, we show that synthetic data based on VAE and GAN models can drive machine learning models for developing MIC resistant 2D coatings. 

The stiffness in the top surface of many biological entities like cornea or articular cartilage, as well as chemically cross-linked synthetic hydrogels, can be significantly lower or more compliant than the bulk. When such a heterogeneous surface comes into contact, the contacting load is distributed differently from typical contact models. The mechanical response under indentation loading of a surface with a gradient of stiffness is a complex, integrated response that necessarily includes the heterogeneity. In this work, we identify empirical contact models between a rigid indenter and gradient elastic surfaces by numerically simulating quasi-static indentation. Three key case studies revealed the specific ways in which (I) continuous gradients, (II) laminate-layer gradients, and (III) alternating gradients generate new contact mechanics at the shallow-depth limit. Validation of the simulation-generated models was done by micro- and nanoindentation experiments on polyacrylamide samples synthesized to have a softer gradient surface layer. The field of stress and stretch in the subsurface as visualized from the simulations also reveals that the gradient layers become confined, which pushes the stretch fields closer to the surface and radially outward. Thus, contact areas are larger than expected, and average contact pressures are lower than predicted by the Hertz model. The overall findings of this work are new contact models and the mechanisms by which they change. These models allow a more accurate interpretation of the plethora of indentation data on surface gradient soft matter (biological and synthetic) as well as a better prediction of the force response to gradient soft surfaces. This work provides examples of how gradient hydrogel surfaces control the subsurface stress distribution and loading response. 

In this article we study the stability of explicit finite difference discretization of advection–diffusion equations (ADE) with arbitrary order of accuracy in the context of method of lines. The analysis first focuses on the stability of the system of ordinary differential equations that is obtained by discretizing the ADE in space and then extends to fully discretized methods in combination with explicit Runge–Kutta methods. In particular, we prove that all stable semi‐discretization of the ADE leads to a conditionally stable fully discretized method as long as the time‐integrator is at least first‐order accurate, whereas high‐order spatial discretization of the advection equation cannot yield a stable method if the temporal order is too low. In the second half of the article, the analysis and the stability results are extended to a partially dissipative wave system, which serves as a model for common practice in many fluid mechanics applications that incorporate a viscous stress in the momentum equation but no heat dissipation in the energy equation. Finally, the major theoretical predictions are verified by numerical examples.