Mesoscale design involving control of material distribution pattern can create a statistically heterogeneous material system, which has shown increased adaptability to complex mechanical environments involving highly non-uniform stress fields. Advances in multi-material additive manufacturing can aid in this mesoscale design, providing voxel level control of material property. This vast freedom in design space also unlocks possibilities within optimization of the material distribution pattern. The optimization problem can be divided into a forward problem focusing on accurate predication and an inverse problem focusing on efficient search of the optimal design. In the forward problem, the physical behavior of the material can be modeled based on fundamental mechanics laws and simulated through finite element analysis (FEA). A major limitation in modeling is the unknown parameters in constitutive equations that describe the constituent materials; determining these parameters via conventional single material testing has been proven to be insufficient, which necessitates novel and effective approaches of calibration.
A calibration framework based in Bayesian inference, which integrates data from simulations and physical experiments, has been applied to a study involving a mesostructured material fabricated by fused deposition modeling. Calibration results provide insights on what values these parameters converge to as well as which material parameters the model output has the largest dependence on while accounting for sources of uncertainty introduced during the modeling process. Additionally, this statistical formulation is able to provide quick predictions of the physical system by implementing a surrogate and discrepancy model. The surrogate model is meant to be a statistical representation of the simulation results, circumventing issues arising from computational load, while the discrepancy is aimed to account for the difference between the simulation output and physical experiments. In this thesis, this Bayesian calibration framework is applied to a material bending problem, where in-situ mechanical characterization data and FEA simulations based on constitutive modeling are combined to produce updated values of the unknown material parameters with uncertainty. / Master of Science / A material system obtained by applying a pattern of multiple materials has proven its adaptability to complex practical conditions. The layer by layer manufacturing process of additive manufacturing can allow for this type of design because of its control over where material can be deposited. This possibility then raises the question of how a multi-material system can be optimized in its design for a given application. In this research, we focus mainly on the problem of accurately predicting the response of the material when subjected to stimuli. Conventionally, simulations aided by finite element analysis (FEA) were relied upon for prediction, however it also presents many issues such as long run times and uncertainty in context-specific inputs of the simulation. We instead have adopted a framework using advanced statistical methodology able to combine both experimental and simulation data to significantly reduce run times as well as quantify the various uncertainties associated with running simulations.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/85210 |
| Date | 01 October 2018 |
| Creators | Kim, Jee Yun |
| Contributors | Materials Science and Engineering, Yu, Hang, Kong, Zhenyu, Higdon, David |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Detected Language | English |
| Type | Thesis |
| Format | ETD, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
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