Special Issue: Design of Heterogeneous Materials (original) (raw)
Related papers
Computer Methods in Applied Mechanics and Engineering, 2013
Recognizing that modern materials contain multiple phases with inherent random microstructure and in situ constituent material properties that are oft uncharacterizable with exactness, this research uses benchmark computational studies to unveil scenarios where uncertainties significantly affect macroscopic behavior. The benchmark studies, which serve as numerical experiments capturing the main features of a wide class of problems in solid mechanics, suggest a generalized uncertainty propagation criterion D whose assessment may be used to understand whether uncertainties may non-negligibly propagate to apparent system properties. The new D-criterion combines four features of a microstructured material system: the microstructure size (micro), material property correlation length (micro), structure size (macro), and global length scale of loading (macro). We compare the D-criterion with the familiar one from classical homogenization that relates a statistical volume element size to the size of the microstructure it contains. This work is motivated by the knowledge paucity of uncertainty's place in multiscale analysis and the great computational expense, either in runtime or implementation, of uncertainty propagation methods. The uncertainties considered are material property uncertainty of the separate phases comprising each problem's microstructure and the statistical description of the microstructure itself. The problems involve quasi-static elasto-plasticity, wave propagation in viscoelastic composite, and pattern transition in periodic voided elastomer. Besides the criterion, observed physical behavior for the benchmark problems is also presented in the context of input uncertainty. A close examination of the boundary condition effect on uncertainty propagation suggests that localization increases the characteristic microstructure length, which we represent with a simple deformationdependent microstructure evolution function and that increases uncertainty in apparent system properties. This work provides a systematic framework for modelers to understand when they may reliably waive the consideration of uncertainty for their application or when their application mandates it.
Systems Approaches to Materials Design: Past, Present, and Future
Annual Review of Materials Research, 2019
There is increasing awareness of the imperative to accelerate materials discovery, design, development, and deployment. Materials design is essentially a goal-oriented activity that views the material as a complex system of interacting subsystems with models and experiments at multiple scales of materials structure hierarchy. The goal of materials design is effectively to invert quantitative relationships between process path, structure, and materials properties or responses to identify feasible materials. We first briefly discuss challenges in framing process-structure-property relationships for materials and the critical role of quantifying uncertainty and tracking its propagation through analysis and design. A case study exploiting inductive design of ultrahigh-performance concrete is briefly presented. We focus on important recent directions and key scientific challenges regarding the highly collaborative intersections of materials design with systems engineering, uncertainty qu...
Robust multiscale simulation-based design of multifunctional materials
2005
ABSTRACT With the advances in understanding material behavior at atomic and higher length scales, multiscale modeling is gaining momentum in support of the field of materials design. Complex multiscale material models are shown to be useful in predicting the overall behavior of materials by accounting for phenomena at much smaller scales. However, we believe that multiscale modeling is just a means to an end.
Complexity science of multiscale materials via stochastic computations
2009
New technological advances today allow for a range of advanced composite materials, including multilayer materials and nanofiber-matrix composites. In this context, the key to developing advanced materials is the understanding of the interplay between the various physical scales present, from the atomic level interactions, to the microstructural composition and the macroscale behavior. Using the developing "Multiresolution Data Sets Mechanics", the "predictive science based governing laws of the materials microstructure evolutions" are derived and melted into a "Stochastic Multiresolution Design Framework." Under such a framework, the governing laws of the materials microstructure evolution will be essential to assess, across multiple scales, the impact of multiscale material design, geometry design of a structure, and the manufacturing process conditions, by following the cause-effect relationships from structure to property and then to performance.
Adaptive Strategies for Materials Design using Uncertainties
Scientific Reports, 2016
We compare several adaptive design strategies using a data set of 223 M 2 AX family of compounds for which the elastic properties [bulk (B), shear (G), and Young's (E) modulus] have been computed using density functional theory. The design strategies are decomposed into an iterative loop with two main steps: machine learning is used to train a regressor that predicts elastic properties in terms of elementary orbital radii of the individual components of the materials; and a selector uses these predictions and their uncertainties to choose the next material to investigate. The ultimate goal is to obtain a material with desired elastic properties in as few iterations as possible. We examine how the choice of data set size, regressor and selector impact the design. We find that selectors that use information about the prediction uncertainty outperform those that don't. Our work is a step in illustrating how adaptive design tools can guide the search for new materials with desired properties.
Metals, 2022
Coupled process–microstructure–property modeling, and understanding the sources of uncertainty and their propagation toward error in part property prediction, are key steps toward full utilization of additive manufacturing (AM) for predictable quality part development. The OpenFOAM model for process conditions, the ExaCA model for as-solidified grain structure, and the ExaConstit model for constitutive mechanical properties are used as part of the ExaAM modeling framework to examine a few of the various sources of uncertainty in the modeling workflow. In addition to “random” uncertainty (due to random number generation in the orientations and locations of grains present), the heterogeneous nucleation density N0 and the mean substrate grain spacing S0 are varied to examine their impact of grain area development as a function of build height in the simulated microstructure. While mean grain area after 1 mm of build is found to be sensitive to N0 and S0, particularly at small N0 and la...
A Multiscale Design Approach with Random Field Representation of Material Uncertainty
2008
An integrated design framework that employs multiscale analysis to facilitate concurrent product, material, and manufacturing process design is presented in this work. To account for uncertainties associated with material structures and their impact on product performance across multiple scales, efficient computational techniques are developed for propagating material uncertainty with random field representation. Random field is employed to realistically model the uncertainty existing in material microstructure, which spatially varies in a product inherited from the manufacturing process. To reduce the dimensionality of random field representation, a reduced order Karhunen-Loeve expansion is used with a discretization scheme applied to finite-element meshes. The univariate dimension reduction method and the Gaussian quadrature formula are used to efficiently quantify the uncertainties in product performance in terms of its statistical moments, which are critical information for design under uncertainty. A control arm example is used to demonstrate the proposed approach. The impact of the initial microscale porosity random field produced during a casting process on the product damage is studied and a reliability-based design of the control arm is performed.
Computational materials design and engineering
Materials Science and Technology
Computational materials design integrates targeted materials process-structure and structureproperty models in systems frameworks to meet specific engineering needs. Design inherently consists of many competing requirements that require judicious decisions regarding key tradeoffs. The goal of computational materials design is to apply the best scientific understanding to facilitate decisions regarding the optimal tradeoffs that meet desired needs in the most time and resource efficient manner. Mechanistic materials design models require adequate fidelity to determine the favourability of one design solution over another but also the ability to be extrapolated over large parameter space to search for design optima in unexplored terrain. Design processes must not only efficiently find optimal solutions, but quickly identify failures. More broadly, materials design can only be as successful as the ability to identify the correct requirements for an application, and those requirements must address not only performance but also qualification hurdles including prediction of manufacturing variation.
Uncertainty quantification in homogenization of heterogeneous microstructures modeled by XFEM
International Journal for Numerical Methods in Engineering, 2011
An extended finite element method (XFEM) coupled with a Monte Carlo approach is proposed to quantify the uncertainty in the homogenized effective elastic properties of multiphase materials. The methodology allows for an arbitrary number, aspect ratio, location and orientation of elliptic inclusions within a matrix, without the need for fine meshes in the vicinity of tightly packed inclusions and especially without the need to remesh for every different generated realization of the microstructure. Moreover, the number of degrees of freedom in the enriched elements is dynamically reallocated for each Monte Carlo sample run based on the given volume fraction. The main advantage of the proposed XFEM-based methodology is a major reduction in the computational effort in extensive Monte Carlo simulations compared with the standard FEM approach. Monte Carlo and XFEM appear to work extremely efficiently together. The Monte Carlo approach allows for the modeling of the size, aspect ratios, orientations, and spatial distribution of the elliptical inclusions as random variables with any prescribed probability distributions. Numerical results are presented and the uncertainty of the homogenized elastic properties is discussed.