John C. Steuben

Inverse Characterization of Composite Materials Using Surrogate Models

In recent years, methods for the inverse characterization of mechanical properties of materials have seen significant growth, mainly because of the availability of enabling technologies like full-field measurement techniques, inexpensive high performance computing resources, and automated testing. Unfortunately, as the complexity of the material system increases even the most advanced methods for inverse characterization produce results in compute times that are not practical for real time applications. To overcome this limitation we present a method that uses Non-Uniform Rational B-spline (NURBs) based surrogate modeling to generate a very efficient representation of the material model and the associated objective function. In addition, we present a method for identifying the global minimum of this objective function that corresponds to the elastic properties that characterize the material. Validation of this methodology is achieved through synthetic numerical experiments that include both isotropic and orthotropic specimens defined both analytically and numerically. Statistical analyses on the effects of experimental noise supplement these results. We conclude with remarks regarding the use of this technique to recover the elastic properties from materials tested utilizing multiaxial robotic systems.Copyright

Robust Optimization of Mixed-Integer Problems Using NURBs-Based Metamodels

The optimization of mixed-integer problems is a classic problem with many industrial and design applications. A number of algorithms exist for the numerical optimization of these problems, but the robust optimization of mixed-integer problems has been explored to a far lesser extent. We present here a general methodology for the robust optimization of mixed-integer problems using Non Uniform Rational B-spline (NURBs)-based metamodels and graph theory concepts. The use of these techniques allows for a new and powerful definition of robustness along integer variables. In this work, we define robustness as an invariance in problem structure, as opposed to insensitivity in the dependent variables. The application of this approach is demonstrated on two test problems. We conclude with a performance analysis of our new approach, comparisons to existing approaches, and our views on the future development of this technique.Copyright

Robust Optimization and Analysis of NURBs-Based Metamodels Using Graph Theory

NURBs-based metamodels have been shown to accurately reproduce the behavior of computationally expensive models. These models in turn represent engineering problems of great complexity and importance. While the structure of NURBs-based metamodels has facilitated the development of discrete optimization algorithms, other analysis areas such as robust and multiobjective optimization have proven to be more difficult. We present here a new method for the analysis and optimization of these metamodels which is based on graph theory principles. The adoption of these principles allows the use of powerful existing algorithms for graph analysis. We have focused on the problem of robust optimization in this work, as the robust optimization of NURBs-based metamodels has been previously examined using more conventional techniques. We demonstrate that the graph-based analysis technique provides the design engineer a more comprehensive understanding of design problems and their behavior. We also demonstrate the new technique on a range of test functions in order to establish its validity and usefulness in the context of product and process optimization. We conclude with a discussion of the use of this new approach in addressing other analysis challenges such as multiobjective or mixed-integer optimization.Copyright

Robust Optimization Exploration Using NURBs-Based Metamodeling Techniques

Non-uniform rational B-splines (NURBs) demonstrate properties that are highly conductive to performing metamodeling for engineering design purposes. Previous research has resulted in the development of algorithms capable of fitting NURBs metamodels to design spaces of many input variables and performance indicies, and performing various discreet optimizations upon these metamodels. In the present research we expand upon this basis by illustrating the development of robust optimization algorithms that leverages the unique properties of NURBs metamodels. This optimization is conducted in a general fashion by considering both optimality and various robustness metrics as global or local model properties, and illustrates the tradeoffs between them using a novel graphical approach. The appeal of this approach is demonstrated by a series of test functions of one performance index and one or two performance indicies. A case study in designing composite structures of specific stiffness, of four and five design variables, follows. We proceed to discuss the future of NURBs metamodeling techniques and the potential for considering model properties besides optimality and robustness during optimization.Copyright

Towards Computational Synthesis of Microstructural Crystalline Morphologies for Additive Manufacturing Applications

Powder-based additive manufacturing technologies introduce severe variations in microstructure in terms of grain size and aspect ratio that, coupled with porosity, can result in dramatic effects on the functional (mechanical, thermal, fatigue, fracture etc.) performance of as-produced parts. In the context of Integrated Computational Materials Engineering (ICME), it is essential develop a computationally efficient approach for generating synthetic microstructural morphologies that reflect these process-induced features. In the present paper, we employ two methodologies for computing the evolution of metal solidification at the microstructural level as a function of process parameters associated with additive manufacturing. The first method is the Continuum Diffuse Interface Model (CDM) applied to an arbitrary material system, and the second, the Multi-Phase Field Model (MPFM) applied to pure nickel (Ni). We present examples of microstructures generated by these methods within the context of additive manufacturing.

Graph analysis of non-uniform rational B-spline-based metamodels

Over the past decade metamodels, also known as surrogate models, based on non-uniform rational B-splines (NURBs) have been developed. These metamodels exhibit unique properties that enable a wide range of computationally efficient analyses. Thus far, the analysis of these metamodels has been of a geometric nature, but in this article an approach based on graph theory is used. The properties of NURBs enable the interpretation of NURBs-based metamodels as graphs, and enable the demonstration of several analyses based on this structure. The general case of an analytically defined continuous-variable problem is given in the first example. A specific application in the field of robotic path planning constitutes the second example. Finally, an observation on the current state of this research, its merits and drawbacks, and an outline of future efforts that may increase its utility is provided.

Robust engineering design optimization with non-uniform rational B-splines-based metamodels

Non-uniform rational B-splines (NURBs) demonstrate properties that make them attractive as metamodels, or surrogate models, for engineering design purposes. Previous research has resulted in the development of algorithms capable of fitting NURBs-based metamodels to engineering design spaces, and optimizing these models. This article presents an approach to robust optimization that employs NURBs-based metamodels. This robust optimization technique exploits the unique structure of NURBs-based metamodels to derive a simple but effective robustness metric. An algorithm is demonstrated that uses this metric to weigh robustness against optimality, and visualizes the trade-offs between these metamodel properties. This approach is demonstrated with test problems of increasing dimensionality, including several practical design challenges.

NURBs for Robot Manipulator Trajectory Generation

Modern applications of automation and robotic technologies require increasingly sophisticated control systems. One of the areas in which the control of these robotic systems can be improved is the generation of motion trajectories. We demonstrate that Non-Uniform Rational B-splines (NURBs) can be successfully adapted for use in producing trajectories for 6-DOF manipulators. We also discuss a methodology for fitting such splines to arbitrary geometries allowing for the generation of paths in cases where it is difficult or impossible to do so using less sophisticated methods. We demonstrate these techniques in simulation, where they are applied to a pair of complex industrial tasks. Several important properties of NURBs which offer advantages not present in other methods are also discussed. We conclude by discussing the future research needed to bring this technique to maturity, and potential opportunities that may be realized in its adoption.Copyright

Enriched Analytical Solutions for Additive Manufacturing Modeling and Simulation

Abstract Recent developments in additive manufacturing (AM) technologies involving heat and mass deposition have exposed the need for computationally efficient modeling of thermal field histories. This is due to the effect of such histories on resulting morphologies and quantities of interest, such as micro- and meso-structure, residual strains and stresses, as well as on material and structural properties and associated functional performance at the macro-scale. Limiting undesirable manifestations of these phenomena has motivated the development of both feed-forward and feedback loop control methodologies. However, up to now the computational cost of existing methods for predicting thermal fields and associated aspects, have allowed only feed-forward control methods. Consequently, in this paper, analytic solutions are enriched and then used to model the thermal aspects of AM, in a manner that demonstrates both high computational performance and fidelity required to enable “in the loop” use for feedback control of AM processes. It is first shown that the utility of existing analytical solutions is limited due to their underlying assumptions, some of which are their derivation based on a homogeneous semi-infinite domain and temperature independent material properties among others. These solutions must therefore be enriched in order to capture the actual thermal physics associated with the relevant AM processes. Enrichments introduced herein include the handling of strong nonlinear variations in material properties due to their dependence on temperature, finite non-convex solution domains, behavior of heat sources very near domain boundaries, and mass accretion coupled to the thermal problem. The enriched analytic solution method (EASM) that implements these enrichments is shown to produce results equivalent to those of numerical methods (such as Finite Elements and Finite Differences) that require six orders of magnitude greater computational cost.

Oxygen-induced giant grain growth in Ag films

Thin film crystallites typically exhibit normal or abnormal growth with maximum grain size limited by energetic and geometric constraints. Although epitaxial methods have been used to produce large single crystal regions, they impose limitations that preclude some compelling applications. The generation of giant grain thin film materials has broad implications for fundamental property analysis and applications. This work details the production of giant grains in Ag films (2.5 μm-thick), ranging in size from ≈50 μm to 1 mm, on silicon nitride films upon silicon substrates. The presence of oxygen during film deposition plays a critical role in controlling grain size and orientation.