Application-Specific Computational Materials Design via Multiscale Modeling and the Inductive Design Exploration Method (IDEM)

Abstract

The development of materials is a laborious, iterative, expensive, and intuitive process, often requiring decades to transition from early laboratory studies to commercial applications. This research seeks to address this issue by demonstrating a systematic process for linking process-structure-propertyperformance (PSPP) relations. We argue that the limitations on time for the material development process arise in large part due to lack of effective approaches for exploring the material design space that anticipates application requirements, objectives, and constraints. The material design process employed here utilizes hierarchical multiscale modeling, analytical models, and associated metamodels to construct a set of bottom-up deductive mappings, along with the inductive design exploration method (IDEM) to account for uncertainty in pursuing top-down inductive decision support problems that address application-specific design objectives. The demonstrated problem considers the simultaneous design of ultra-highperformance concrete material and a structural panel able to withstand a 1.5-MPa-ms reflected blast wave impulse. A set of PSPP mappings were constructed across micro-, meso-, and macro-length-scales using analytical expressions and a hierarchical multiscale finite element model at the single fiber, multiple fiber, and structural length scales. The set of PSPP deductive mappings considered seven design variables-panel thickness, fiber pitch, ratio of water to cementitious materials, curing temperature, and volume fractions of fibers, cement, and silica fume-across four hierarchical levels. After the set of deductive PSPP mappings were constructed and validated, ranged sets of feasible values for each design variable were determined via IDEM. Starting with the highest and next-tohigher hierarchical levels as the output and input spaces, respectively, IDEM was implemented via application of three steps-discretization of input variables, projection of discretized sets of input variables with account of uncertainty to a range in the output space, and determination of which sets of discrete input values satisfy the output space requirement(s). By recursively applying these three steps, the PSPP relations were robustly searched for properties, structures, and processes that satisfy the performance requirement(s). The advantages of this approach are the identification of ranged sets of values of design variables and the ability to account for propagated uncertainty. By defining additional mass and cost objectives, the feasible input space was then searched to find the preferred combination of values of design variables that minimized mass and minimized cost while maintaining a robust material and structural design.

Inductive Design Exploration Method with Active Learning for Complex Design Problems

“…As mentioned, the number of design points to be evaluated has a direct influence on the accuracy of feasible solution spaces. Many existing studies, which utilized the traditional IDEM [6][7][8][9][10][11][12], also appear to show that the sample size is predetermined owing to computational cost. However, it is very difficult to choose the appropriate sample size beforehand and this difficulty is compounded when high cost computational models are involved.…”

“…The detailed process in IDEM can be found in the literature for solving many complex engineering problems, including blast-resistant sandwich panels [9], vehicle-mounted antenna-supporting structures [10], ultra-high-performance concrete (UHPC) panels, etc. [11,12].…”

Microstructure-sensitive uncertainty quantification for crystal plasticity finite element constitutive models using stochastic collocation methods

“…Tallman et al Tallman et al (2019Tallman et al ( , 2020 applied Gaussian process regression and the Materials Knowledge System framework to predict a set of homogenized materials properties with uncertainty from a distribution function for crystallography orientations and textures. Inductive design exploration method (IDEM) Ellis and McDowell (2017);McDowell et al (2009); Choi et al (2008) has been introduced as a materials design methodology to identify feasible and robust design for microstructure features, which has been broadly applied to many practical problems. From a methodological perspective, numerous applied mathematical UQ techniques have been developed over a few decades.…”

Solving stochastic inverse problems for property-structure linkages using data-consistent inversion and machine learning

“…The problem we considered in this paper is somewhat similar to the work of Acar et al [2], even though we do not assume a parametric representation, e g., a Gaussian distribution, for the target or inverse distributions and we not pursue a deterministic optimization approach. Inductive design exploration method (IDEM) [17,34,12] has been introduced as a materials design methodology to identify feasible and robust design for microstructure features, which has been applied to many problems in practice. The framework also formulates as a deterministic optimization problem, which finds a unique and optimal microstructure features, but currently does not allow incorporation of prior and posterior density function.…”