Caglar Oskay delivered an invited lecture at Sandia National Laboratory
Lecture Title: A Reduced Order Multiscaling Paradigm for Predictive Simulation of Large-Scale Engineering Structures
Location: Solid Mechanics Group and Multiscale Science Group, Sandia National Laboratory.
Over the past couple of decades, tremendous effort has been devoted to the development of multiscale computational modeling and simulation strategies for physics-based prediction of structural response. Among these strategies, concurrent multiscaling (e.g., computational homogenization, FE2, heterogeneous multiscale method, etc.) holds great potential in effectively bridging the “material” response to that of the “structure”. Yet these approaches are so computationally intensive that they have remained within the academic realm, and have yet to make impact on realistic engineering problems.
We propose the Eigendeformation-based Reduced Order Homogenization Method (EHM) for computationally efficient and accurate concurrent multiscale analysis. We build and demonstrate this method to predict the response of structures made of polycrystalline materials, where crystal plasticity finite element (CPFE) simulations are concurrently coupled to a large scale structural analysis. EHM employs the idea of precomputing certain information on the material microstructure such as the influence functions, localization operators and coefficient tensors through RVE scale simulations, prior to the macroscale analysis. The reduced order fine scale model is achieved by: (1) constraining the kinematics of the inelastic response fields within the RVE; (2) selectively removing the long-range forces to achieve sparse linearized reduced-order systems; and (3) leveraging this sparsity to effectively evaluate the resulting systems. The scale bridging is ensured by the computational homogenization method.
We demonstrate the efficiency of the proposed approach in simulating the response of large structural problems (resolving each grain throughout the domain of the structure!) with modest computational resources. We also demonstrate the ability of the reduced order model to accurately capture the local, grain-scale features (grain level stress, strain, dislocation density evolution) and failure initiation mechanisms in the context of a high temperature titanium alloy (Ti-6242S) subjected to fatigue and dwell-fatigue cycles.