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

Review and Perspectives: Shape Memory Alloy Composite Systems

Following their discovery in the early 60's, there has been a continuous quest for ways to take advantage of the extraordinary properties of shape memory alloys (SMAs). These intermetallic alloys can be extremely compliant while retaining the strength of metals and can convert thermal energy to mechanical work. The unique properties of SMAs result from a reversible difussionless solid-to-solid phase transformation from austenite to martensite. The integration of SMAs into composite structures has resulted in many benefits, which include actuation, vibration control, damping, sensing, and self-healing. However, despite substantial research in this area, a comparable adoption of SMA composites by industry has not yet been realized. This discrepancy between academic research and commercial interest is largely associated with the material complexity that includes strong thermomechanical coupling, large inelastic deformations, and variable thermoelastic properties. Nonetheless, as SMAs are becoming increasingly accepted in engineering applications, a similar trend for SMA composites is expected in aerospace, automotive, and energy conversion and storage related applications. In an effort to aid in this endeavor, a comprehensive overview of advances with regard to SMA composites and devices utilizing them is pursued in this paper. Emphasis is placed on identifying the characteristic responses and properties of these material systems as well as on comparing the various modeling methodologies for describing their response. Furthermore, the paper concludes with a discussion of future research efforts that may have the greatest impact on promoting the development of SMA composites and their implementation in multifunctional structures

Predicting Microstructural Pattern Formation Using Stabilized Spectral Homogenization

Instability-induced patterns are ubiquitous in nature, from phase transformations and ferroelectric switching to spinodal decomposition and cellular organization. While the mathematical basis for pattern formation has been well-established, autonomous numerical prediction of complex pattern formation has remained an open challenge. This work aims to simulate realistic pattern evolution in material systems exhibiting non-(quasi)convex energy landscapes. These simulations are performed using fast Fourier spectral techniques, developed for high-resolution numerical homogenization. In a departure from previous efforts, compositions of standard FFT-based spectral techniques with finite-difference schemes are used to overcome ringing artifacts while adding grid-dependent implicit regularization. The resulting spectral homogenization strategies are first validated using benchmark energy minimization examples involving non-convex energy landscapes. The first investigation involves the St. Venant-Kirchhoff model, and is followed by a novel phase transformation model and finally a finite-strain single-slip crystal plasticity model. In all these examples, numerical approximations of energy envelopes, computed through homogenization, are compared to laminate constructions and, where available, analytical quasiconvex hulls. Subsequently, as an extension of single-slip plasticity, a finite-strain viscoplastic formulation for hexagonal-closed-packed magnesium is presented. Microscale intragranular inelastic behavior is captured through high-fidelity simulations, providing insight into the micromechanical deformation and failure mechanisms in magnesium. Studies of numerical homogenization in polycrystals, with varying numbers of grains and textures, are also performed to quantify convergence statistics for the macroscopic viscoplastic response. In order to simulate the kinetics of pattern evolution, stabilized spectral techniques are utilized to solve phase-field equations. As an example of conservative gradient-flow kinetics, phase separation by anisotropic spinodal decomposition is shown to result in cellular structures with tunable elastic properties and promise for metamaterial design. Finally, as an example of nonconservative kinetics, the study of domain wall motion in polycrystalline ferroelectric ceramics predicts electromechanical hysteresis behavior under large bias fields. A first-principles approach using DFT-informed model constants is outlined for lead zirconate titanate, producing results showing convincing qualitative agreement with in-house experiments. Overall, these examples demonstrate the promise of the stabilized spectral scheme in predicting pattern evolution as well as effective homogenized response in systems with non-quasiconvex energy landscapes.</p

Free and forced propagation of Bloch waves in viscoelastic beam lattices

Beam lattice materials can be characterized by a periodic microstructure realizing a geometrically regular pattern of elementary cells. Within this framework, governing the free and forced wave propagation by means of spectral design techniques and/or energy dissipation mechanisms is a major issue of theoretical interest with applications in aerospace, chemical, naval, biomedical engineering. The first part of the Thesis addresses the free propagation of Bloch waves in non-dissipative microstructured cellular materials. Focus is on the alternative formulations suited to describe the wave propagation in the bidimensional infinite material domain, according to the classic canons of linear solid or structural mechanics. Adopting the centrosymmetric tetrachiral cell as prototypical periodic topology, the frequency dispersion spectrum is obtained by applying the Floquet-Bloch theory. The dispersion spectrum resulting from a synthetic Lagrangian beam lattice formulation is compared with its counterpart derived from different continuous models (high-fidelity first-order heterogeneous and equivalent homogenized micropolar continua). Asymptotic perturbation-based approximations and numerical spectral solutions are compared and cross-validated. Adopting the low-frequency band gaps of the dispersion spectrum as functional targets, parametric analyses are carried out to highlight the descriptive limits of the synthetic models and to explore the enlarged parameter space described by high-fidelity models. The microstructural design or tuning of the mechanical properties of the cellular microstructure is employed to successfully verify the wave filtering functionality of the tetrachiral material. Alternatively, band gaps in the material spectrum can be opened at target center frequencies by using metamaterials with inertial resonators. Based on these motivations, in the second part of the Thesis, a general dynamic formulation is presented for determining the dispersion properties of viscoelastic metamaterials, equipped with local dissipative resonators. The linear mechanism of local resonance is realized by tuning periodic auxiliary masses, viscoelastically coupled with the beam lattice microstructure. As peculiar aspect, the viscoelastic coupling is derived by a mechanical formulation based on the Boltzmann superposition integral, whose kernel is approximated by a Prony series. Consequently, the free propagation of damped Bloch waves is governed by a linear homogeneous system of integro-differential equations of motion. Therefore, differential equations of motion with frequency-dependent coefficients are obtained by applying the bilateral Laplace transform. The corresponding complex-valued branches characterizing the dispersion spectrum are determined and parametrically analyzed. Particularly, the spectra corresponding to Taylor series approximations of the equation coefficients are investigated. The standard dynamic equations with linear viscous damping are recovered at the first order approximation. Increasing approximation orders determine non-negligible spectral effects, including the occurrence of pure damping spectral branches. Finally, the forced response to harmonic single frequency external forces in the frequency and the time domains is investigated. The response in the time domain is obtained by applying the inverse bilateral Laplace transform. The metamaterial responses to non-resonant, resonant and quasi-resonant external forces are compared and discussed from a qualitative and quantitative viewpoint

The Mechanics and Multiphysics of Biomimetic Discrete Exoskeleton Substrates

Biological structures have inspired synthetic materials with unparalleled performances such as ultra-lightweight design, tunable elasticity, camouflaging, and antifouling. Among biological structures, exoskeletal scales that cover the exterior surfaces of fishes, fur, and many reptiles. These exoskeletal scales had appeared in the earliest stages of evolution of complex multicellular life and continued their existence in spite of millions of years of evolutionary pressures. This makes them an attractive candidate for biomimicry to produce high performance multifunctional materials with applications to soft robotics, wearables, energy efficient smart skins, antifouling surfaces and on-demand tunable materials. Canonically speaking, biomimetic samples can be fabricated by partially embedding stiffer plate-like segments on softer substrates to create a bi-material system, with overlapping scales. The bending behavior of this system has been carried out using assumption of periodic engagement even after scales contact. This is true only under the most ideal loading conditions or if the scales are extremely dense akin to a continuum assumption on the scales. Here, we develop a rigorous theory with computational validation of key parameters which relaxes these restrictions. We also present an analytical study to demonstrate a bioinspired mechanical pathway to tailor the elasticity of cantilevered beams as an alternative to traditional functional gradation. In addition, we explore for the first time the dynamic behavior of these scales during oscillatory motion using analytical models, supported by finite element (FE) computations. Finally, inspired by the hypothesis that fur surfaces, which consist of plate-like topography, significantly change the initial stages of biofouling, we shed light on the fundamentals of this process by reducing the fur to a scale-covered elastica under flow with biomass suspensions. A FE coupled nonlinear deposition-large deflection model of the system is developed

Advanced Mechanical Modeling of Nanomaterials and Nanostructures

This reprint presents a collection of contributions on the application of high-performing computational strategies and enhanced theoretical formulations to solve a wide variety of linear or nonlinear problems in a multiphysical sense, together with different experimental studies