Xiaoyu Zhang, Ruize Hu and Xiang Zhang presented their research at USNCCM’14 in Montreal, Canada
The title of the Xiaoyu’s presentation was: “Material and Morphology Parameter Sensitivity Analysis in Particulate Composite Materials”.
Abstract:
We present a novel parameter sensitivity analysis framework for damage and failure modeling of particulate composite materials subjected to dynamic loading. The proposed framework is employed to quantify the sensitivity of the failure response of energetic materials (e.g., explosives, propellants) under dynamic loads to both material properties and morphological parameters that define the material microstructure. The proposed framework employs global sensitivity analysis (GSA) to study the decoupling of the uncertainty or variance in the failure response as a function of model parameter uncertainty. In view of the computational complexity of performing thousands of detailed microstructural simulations to characterize sensitivities, a Gaussian Process (GP) surrogate modeling is incorporated into the framework. The GP model is built on Gaussian kernels, and approximates the response surface generated by directly resolution finite element analysis with an extremely low cost mapping function. In order to capture the discontinuity in response surfaces, the GP models are integrated with a classification algorithm that identifies the discontinuities within response surfaces. A support vector machine (SVM) classifier is trained to obtain a separating hyperplane.
The proposed framework is employed to quantify variability and sensitivities in the failure response of particular energetic materials with a polymeric binder (PBX). The failure behavior is characterized with thermo-mechanical analyses at the scale of the material microstructure. Particular emphasis is placed on the identification of sensitivity to interfaces between the polymer binder and the energetic particles. The proposed framework has been demonstrated to identify the most consequential materials and morphological parameters under vibrational and impact loads.
The title of the Ruize’s presentation was: “Spatial-Temporal Nonlocal Homogenization Model for Transient Wave Propagation in Viscoelastic Composite”.
Abstract:
Heterogeneous materials exhibit complex response patterns when subjected to dynamic loading due to the intrinsic wave interactions induced by reflections and refractions at material constituent interfaces. Controlling these interactions offer tremendous opportunities in many engineering applications. For instance, acoustic metamaterials have received significant recent attention due to the unique and tailorable properties including negative effective density and bulk modulus, and wave attenuation within band gaps.
We present a spatial-temporal nonlocal homogenization model for transient wave propagation in elastic and viscoelastic composites. The homogenization model is particularly directed to capturing wave dispersion and attenuation induced by material heterogeneity. The proposed model is derived based on asymptotic homogenization with up to eighth order expansions. A momentum balance equation that is nonlocal in both space and time is consistently derived. Contributions from the high order terms in the momentum balance equation account for the heterogeneity induced wave dispersion and stop band formation. The coefficient tensors of the momentum balance equation are computed directly from microstructural material parameters and geometry. A Hybrid Laplace Transform/Isogeometric Analysis (HLT/IGA) is developed to solve the nonlocal momentum balance equation, which provides global C1 continuity as required by the spatial nonlocal term. The high order boundary conditions are also discussed. Response fields in time domain are obtained by applying discrete inverse Laplace transform method. The performance of the proposed model is assessed against direct finite element simulations and compared to classical homogenization models. The proposed model has demonstrated high level of computational efficiency over direct finite element simulation and accuracy over classical homogenization models. The key contributions of our work are: (1) the proposed model captures the wave dispersion in the first and second pass band and attenuation in the first stop band; (2) all the model parameters are computed directly from the microscale initial-boundary problem as an off-line process; (3) HLT/IGA provides an alternative to solve higher order problems (e.g. gradient elasticity).
The title of the Xiang’s presentation was: “Sparse and Scalable Eigenstrain-based Reduced Order Homogenization Models for Polycrystal Plasticity”.
Abstract:
We present an accelerated, sparse and scalable eigenstrain-based reduced order homogenization modeling approach for computationally efficient multiscale analysis of polycrystalline materials. The proposed approach is based on the eigenstrain-based reduced order homogenization model (EHM) for polycrystalline materials [1] that concurrently links the response of the structural scale to the response at the scale of the grains and provides significant efficiency in analysis of structures composed of complex polycrystalline microstructures.
EHM operates in a computational homogenization setting, and employs concepts from the transformation field theory to pre-compute certain microscale information (e.g. localization tensors, concentration tensors) by evaluating linear elastic microscale problems prior to a macroscale simulation. By this approach, a significant reduction in computational cost is achieved, compared with classical computational homogenization approaches that employ crystal plasticity finite element (CPFE) simulation to describe the microscale response. While EHM provides approximately two orders of magnitude efficiency compared with CPFE for middle-sized microstructures, its efficiency degrades as microstructure size increases. A grain-cluster accelerated, sparse and scalable reduced order homogenization model has been developed to address this issue. The acceleration is achieved by introducing sparsity into the linearized reduced order system through selectively considering the interactions between grains based on the idea of grain clustering. The proposed approach results in a hierarchy of reduced models that recovers eigenstrain-based homogenization, when full range of interactions are considered, and degrades to the Taylor model, when all inter-grain interactions are neglected. The resulting sparse system is solved efficiently using both direct and iterative sparse solvers, both of which show significant efficiency improvements compared to the full EHM. A layer-by-layer neighbor grain clustering scheme is proposed and implemented to define ranges of grain interactions. Performance of the proposed approach is evaluated by comparing the results against the full EHM and crystal plasticity finite element (CPFE) simulations.
[1] X. Zhang and C. Oskay. Eigenstrain based reduced order homogenization for polycrystalline materials. Comput. Methods Appl. Mech. Engrg., 297:408–436, 2015.