Higher-order multi-scale deep Ritz method for multi-scale problems of authentic composite materials

The direct deep learning simulation for multi-scale problems remains a challenging issue. In this work, a novel higher-order multi-scale deep Ritz method (HOMS-DRM) is developed for thermal transfer equation of authentic composite materials with highly oscillatory and discontinuous coefficients. In this novel HOMS-DRM, higher-order multi-scale analysis and modeling are first employed to overcome limitations of prohibitive computation and Frequency Principle when direct deep learning simulation. Then, improved deep Ritz method are designed to high-accuracy and mesh-free simulation for macroscopic homogenized equation without multi-scale property and microscopic lower-order and higher-order cell problems with highly discontinuous coefficients. Moreover, the theoretical convergence of the proposed HOMS-DRM is rigorously demonstrated under appropriate assumptions. Finally, extensive numerical experiments are presented to show the computational accuracy of the proposed HOMS-DRM. This study offers a robust and high-accuracy multi-scale deep learning framework that enables the effective simulation and analysis of multi-scale problems of authentic composite materials

Roadmap on multiscale materials modeling

Modeling and simulation is transforming modern materials science, becoming an important tool for the discovery of new materials and material phenomena, for gaining insight into the processes that govern materials behavior, and, increasingly, for quantitative predictions that can be used as part of a design tool in full partnership with experimental synthesis and characterization. Modeling and simulation is the essential bridge from good science to good engineering, spanning from fundamental understanding of materials behavior to deliberate design of new materials technologies leveraging new properties and processes. This Roadmap presents a broad overview of the extensive impact computational modeling has had in materials science in the past few decades, and offers focused perspectives on where the path forward lies as this rapidly expanding field evolves to meet the challenges of the next few decades. The Roadmap offers perspectives on advances within disciplines as diverse as phase field methods to model mesoscale behavior and molecular dynamics methods to deduce the fundamental atomic-scale dynamical processes governing materials response, to the challenges involved in the interdisciplinary research that tackles complex materials problems where the governing phenomena span different scales of materials behavior requiring multiscale approaches. The shift from understanding fundamental materials behavior to development of quantitative approaches to explain and predict experimental observations requires advances in the methods and practice in simulations for reproducibility and reliability, and interacting with a computational ecosystem that integrates new theory development, innovative applications, and an increasingly integrated software and computational infrastructure that takes advantage of the increasingly powerful computational methods and computing hardware

A Finite Element Framework for Multiscale/Multiphysics Analysis of Structures with Complex Microstructures

This research work has contributed in various ways to help develop a better understanding of textile composites and materials with complex microstructures in general. An instrumental part of this work was the development of an object-oriented framework that made it convenient to perform multiscale/multiphysics analyses of advanced materials with complex microstructures such as textile composites. In addition to the studies conducted in this work, this framework lays the groundwork for continued research of these materials. This framework enabled a detailed multiscale stress analysis of a woven DCB specimen that revealed the effect of the complex microstructure on the stress and strain energy release rate distribution along the crack front. In addition to implementing an oxidation model, the framework was also used to implement strategies that expedited the simulation of oxidation in textile composites so that it would take only a few hours. The simulation showed that the tow architecture played a significant role in the oxidation behavior in textile composites. Finally, a coupled diffusion/oxidation and damage progression analysis was implemented that was used to study the mechanical behavior of textile composites under mechanical loading as well as oxidation. A parametric study was performed to determine the effect of material properties and the number of plies in the laminate on its mechanical behavior. The analyses indicated a significant effect of the tow architecture and other parameters on the damage progression in the laminates

Multiscale Modeling Of The Hierarchical Structure Of Cellulose Nanocrystals

Cellulose constitutes the most abundant renewable polymeric resource available today. It considered an almost inexhaustible source of raw material, and holds great promise in meeting increasing demands for environmentally friendly and biocompatible products. Key future applications are currently under development for the automotive, aerospace and textile industries. When cellulose fibers are subjected to acid hydrolysis, the fibers yield rod-like, highly crystalline residues called cellulose nanocrystals (CNCs). These particles show remarkable mechanical and chemical properties (e.g. Young Modulus ~200 GPa) within the range of other synthetically-developed reinforcement materials. Critical to the design of these materials are fundamental material properties, many of which are unavailable in the existing literature. A multiscale framework has been developed to predict and describe the thermo-mechanical characteristics of cellulose nanocrystals using state-of-the-art computational tools capable of connecting atomistic based simulations to experiments through continuum based modeling techniques. First-principle density functional theory and molecular dynamic simulations were utilized at the atomistic level. Longstanding issues regarding the elastic and thermal expansion anisotropies for crystalline cellulose have been studied in terms of the single-crystal elasticity tensor and the thermal expansion tensor components. First-principles phonon calculations via van der Waals density functionals as well as reverse non-equilibrium molecular dynamics simulations were used to gain a fundamental understanding of defect-free, crystalline cellulose thermo-mechanical properties. Entropy, enthalpy, constant pressure heat capacity, thermal expansion tensor, thermal conductivity, Young\u27s modulus, and Poisson\u27s ratio, were computed over a wide range of temperatures (0 to 500 K). A comprehensive study of the hydrogen bond structure that characterizes crystalline cellulose has been conducted in an attempt to ascertain the roles that inter- and intra- molecular hydrogen bonds play in determining the mechanical properties of CNCs. Five different force fields/parameter sets were compared with experimental results and first-principles simulations in terms of their ability to predict the following properties: lattice parameters and angles, linear elasticity tensor and linear thermal expansion tensor. Continuum based modeling techniques were used to answer fundamental questions regarding the role of hydrogen bonding in the mechanical response of CNCs. A variety of finite element-based continuum models were specifically developed for cellulose chains and non-bonding interactions (van der Waals, Coulomb and hydrogen bonds). As a result, a complete multiscale framework capable of reproducing the mechanical behavior of cellulose nanocrystals has been developed

Numerical modelling of additive manufacturing process for stainless steel tension testing samples

Nowadays additive manufacturing (AM) technologies including 3D printing grow rapidly and they are expected to replace conventional subtractive manufacturing technologies to some extents. During a selective laser melting (SLM) process as one of popular AM technologies for metals, large amount of heats is required to melt metal powders, and this leads to distortions and/or shrinkages of additively manufactured parts. It is useful to predict the 3D printed parts to control unwanted distortions and shrinkages before their 3D printing. This study develops a two-phase numerical modelling and simulation process of AM process for 17-4PH stainless steel and it considers the importance of post-processing and the need for calibration to achieve a high-quality printing at the end. By using this proposed AM modelling and simulation process, optimal process parameters, material properties, and topology can be obtained to ensure a part 3D printed successfully

Variational Foundations and Generalized Unified Theory of RVE-Based Multiscale Models

A unified variational theory is proposed for a general class of multiscale models based on the concept of Representative Volume Element. The entire theory lies on three fundamental principles: (1) kinematical admissibility, whereby the macro- and micro-scale kinematics are defined and linked in a physically meaningful way; (2) duality, through which the natures of the force- and stress-like quantities are uniquely identified as the duals (power-conjugates) of the adopted kinematical variables; and (3) the Principle of Multiscale Virtual Power, a generalization of the well-known Hill-Mandel Principle of Macrohomogeneity, from which equilibrium equations and homogenization relations for the force- and stress-like quantities are unequivocally obtained by straightforward variational arguments. The proposed theory provides a clear, logically-structured framework within which existing formulations can be rationally justified and new, more general multiscale models can be rigorously derived in well-defined steps. Its generality allows the treatment of problems involving phenomena as diverse as dynamics, higher order strain effects, material failure with kinematical discontinuities, fluid mechanics and coupled multi-physics. This is illustrated in a number of examples where a range of models is systematically derived by following the same steps. Due to the variational basis of the theory, the format in which derived models are presented is naturally well suited for discretization by finite element-based or related methods of numerical approximation. Numerical examples illustrate the use of resulting models, including a non-conventional failure-oriented model with discontinuous kinematics, in practical computations