Complexity science of multiscale materials via stochastic computations

Abstract

SUMMARYNew 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.The future integrated multiscale analysis system will be constructed based on a probabilistic complexity science-based mathematical framework. Its verification, validation and uncertainty quantification are done through carefully designed experiments, and the life-cycled materials design for products design and manufacturing is performed through the use of petascale computing. The various techniques of microstructure reconstruction result in the generation of model microstructures that, at some level, has the same statistical properties as the real heterogeneous media. Having reconstructed the heterogeneous medium, one can then evaluate its effective properties via direct numerical simulation and compare these values with experimentally measured properties of the actual medium. The proposed analysis will be dynamic in nature to capture the multi-stage historical evolvement of material/structure performance over the life span of a product. In addition to providing more accurate assessment of structure performance with stochastic multiscale analysis, our development will provide the capability of predicting structure failures and system reliability to enable more reliable design and manufacturing decisions in product development.

Possibility and Evidence-Based Reliability Analysis and Design Optimization

“…There are rich studies that compare probability theory with possibility theory, or with fuzzy sets theory and evidence theory (Liu et al, 2009;2012;Greene et al, 2011;Klir and Yuan, 1995;Misra and Soman, 1995;Utkin et al, 1995;Cai, 1996;Cayrac et al, 1996;Ferson and Ginzburg, 1996;Huang, 1996;Utkin and Gurov, 1996). Discussions mainly focus on the aspect of axiom, from which we conclude that a principal difference between these theories is that the probability theory's additivity axiom (about the probability of the disjointed events uniting) is replaced with less restrictive axioms.…”

“…He defined possibility, in 1961, as the degree to which it is likely for an event to occur. Moreover, he stated that possibility should be used instead of probability when the conditions under which we have to make a decision under uncertainty cannot be reproduced (Liu et al, 2009).…”

“…Following Dempster's work, it was his student, Shafer (1976) and Liu et al (2009) who extended Dempster's probability to the theory of evidence in 1976, including a more thorough explanation of belief functions. The name "Dempster-Shafer theory" was coined by Barnett in a paper which marked the entry of the belief functions into the field of artificial intelligence (Aughenbaugh and Paredis, 2005).…”

“…In the DempsterShafer theory, evidence is represented by the basic probability assignment and the combination rule of evidence is discussed. Liu et al (2009); and Shafer (1976) let U denote a finite, nonempty universal set that represents the entire collection of elements having the same characteristics, which is usually called a Frame of Discernment (FD) in DS theory. Let ℘(U) denote the power set of U, set A is a collection of some elements of U.…”

“…Over the past two decades, there has been an ever-increasing tendency to take uncertainty analysis into account. Various uncertainties can be observed in engineering practices across multiple spatial and temporal scales, as well as phases of product design (Liu et al, 2009;2012;Greene et al, 2011); these Science Publications AJEAS must be carefully dealt with in engineering design activity. In fact, uncertainty is associated with both the qualitative and quantitative characteristics of design problems, hence, we first present classifications, theories and design considerations to provide a better understanding of uncertainty.…”