An Information-Theoretic Multiscale Framework with Applications to Polycrystalline Materials
Abstract
We considered the feasibility of utilizing High Dimensional Model Representation (HDMR) technique in the stochastic space to represent the model output as a finite hierarchical correlated function expansion in terms of the stochastic inputs starting from lower-order to higher-order component functions. HDMR is efficient at capturing the high-dimensional input-output relationship such that the behavior for many physical systems can be modeled only by the first few lower-order terms. An adaptive version of HDMR is developed to automatically detect the important dimensions and construct higher-order terms only as a function of the important dimensions. In this work, we also incorporate the newly developed adaptive sparse grid collocation (ASGC) method into HDMR to solve the resulting sub-problems. The efficiency of the proposed method is examined by comparing with Monte Carlo (MC) simulation. Finally, we developed a unique data-driven strategy to encode the limited information on initial texture in deformation processes and represent it in a finite-dimensional framework. We have developed the ability to produce the probabilistic distribution of the macro-scale properties of the material subjected to a specific process induced by the uncertainty in initial texture.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 20, 2009
- Accession Number
- ADA506164
Entities
People
- Nicholas Zabaras
Organizations
- Sibley School of Mechanical and Aerospace Engineering