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Research Papers: Design for Manufacturing

# A Variable Fidelity Model Management Framework for Designing Multiphase Materials

[+] Author and Article Information
Gilberto Mejía-Rodríguez

Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN 46556gmejiaro@nd.edu

John E. Renaud1

Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN 46556renaud.2@nd.edu

Vikas Tomar

Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN 46556vikas.tomar@nd.edu

1

Corresponding author.

J. Mech. Des 130(9), 091702 (Aug 18, 2008) (13 pages) doi:10.1115/1.2965361 History: Received May 09, 2007; Revised March 12, 2008; Published August 18, 2008

## Abstract

Research applications involving design tool development for multi phase material design are at an early stage of development. The computational requirements of advanced numerical tools for simulating material behavior such as the finite element method (FEM) and the molecular dynamics (MD) method can prohibit direct integration of these tools in a design optimization procedure where multiple iterations are required. One, therefore, requires a design approach that can incorporate multiple simulations (multiphysics) of varying fidelity such as FEM and MD in an iterative model management framework that can significantly reduce design cycle times. In this research a material design tool based on a variable fidelity model management framework is presented. In the variable fidelity material design tool, complex “high-fidelity” FEM analyses are performed only to guide the analytic “low-fidelity” model toward the optimal material design. The tool is applied to obtain the optimal distribution of a second phase, consisting of silicon carbide (SiC) fibers, in a silicon-nitride $(Si3N4)$ matrix to obtain continuous fiber $SiC–Si3N4$ ceramic composites with optimal fracture toughness. Using the variable fidelity material design tool in application to two test problems, a reduction in design cycle times of between 40% and 80% is achieved as compared to using a conventional design optimization approach that exclusively calls the high-fidelity FEM. The optimal design obtained using the variable fidelity approach is the same as that obtained using the conventional procedure. The variable fidelity material design tool is extensible to multiscale multiphase material design by using MD based material performance analyses as the high-fidelity analyses in order to guide low-fidelity continuum level numerical tools such as the FEM or finite-difference method with significant savings in the computational time.

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## Figures

Figure 1

(a) The single edge notch specimen configuration with the second phase fibers’ (SiC) volume fraction Vf (stronger with lower fracture toughness KIC) making an angle θ with the vertical axis and (b) model of the same specimen in COMSOL (only half of the specimen is modeled assuming the symmetry in the geometry as well as in the phase distribution)

Figure 2

(a) Plot showing how the high-fidelity model for the fracture toughness is noisy for different values of the angle θ and (b) load-displacement graph showing different single-phase specimen behaviors used to find the bulk material’s critical load PQ, the critical crack length ac, and the maximum allowable stress σc

Figure 3

Variable fidelity model management framework (17)

Figure 4

Design domain showing first three iterations of the variable fidelity framework, and expansion of the trust region size as new better designs are obtained as result of good approximations to the high-fidelity model

Figure 5

Adjustment of the trust region size throughout the optimization process for the components Δθ (trust region size for the design variable θ) and ΔVf (trust region size for the design variable Vf). In order to know when the trust region adjustments take place with respect to the each iteration, the iteration numbers are shown inside circles.

Figure 6

(a) Von Mises stress distribution around the single edge crack tip of the optimal CFCC, showing that the stresses in the direction of the applied load are higher than the ones normal to the force and (b) mesh of the specimen modeled in COMSOL , showing finer mesh in the region of higher stresses, near the crack tip

Figure 7

Adjustment of the trust region size throughout the optimization process for the components Δθ (trust region size for the design variable θ) and ΔVf (trust region size for the design variable Vf). In order to know when the trust region adjustments take place with respect to the each iteration, iteration numbers are shown inside circles.

Figure 8

Von Mises stress distribution around the single edge crack tip of the optimal CFCC, showing that the stresses in the direction of the applied load are higher than the ones normal to the force

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