scholarly journals Solution of the Nonlinear High-Fidelity Generalized Method of Cells Micromechanics Relations via Order-Reduction Techniques

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Trenton M. Ricks ◽  
Thomas E. Lacy ◽  
Brett A. Bednarcyk ◽  
Annika Robens-Radermacher ◽  
Evan J. Pineda ◽  
...  
Keyword(s):  
Computational Efficiency ◽  
Order Reduction ◽  
Material Behavior ◽  
High Fidelity ◽  
Reduced Models ◽  
Reduction Techniques ◽  
Significant Difference ◽  
Generalized Method Of Cells ◽  
Unit Cells ◽  
Nylon 12

The High-Fidelity Generalized Method of Cells (HFGMC) is one technique, distinct from traditional finite-element approaches, for accurately simulating nonlinear composite material behavior. In this work, the HFGMC global system of equations for doubly periodic repeating unit cells with nonlinear constituents has been reduced in size through the novel application of a Petrov-Galerkin Proper Orthogonal Decomposition order-reduction scheme in order to improve its computational efficiency. Order-reduced models of an E-glass/Nylon 12 composite led to a 4.8–6.3x speedup in the equation assembly/solution runtime while maintaining model accuracy. This corresponded to a 21–38% reduction in total runtime. The significant difference in assembly/solution and total runtimes was attributed to the evaluation of integration point inelastic field quantities; this step was identical between the unreduced and order-reduced models. Nonetheless, order-reduced techniques offer the potential to significantly improve the computational efficiency of multiscale calculations.

Computationally efficient High-Fidelity Generalized Method of Cells micromechanics via order-reduction techniques

2016 ◽  
Vol 156 ◽  
pp. 2-9 ◽  
Author(s):  
Trenton M. Ricks ◽  
Thomas E. Lacy ◽  
Evan J. Pineda ◽  
Brett A. Bednarcyk ◽  
Steven M. Arnold
Keyword(s):  
Order Reduction ◽  
High Fidelity ◽  
Computationally Efficient ◽  
Reduction Techniques ◽  
Generalized Method Of Cells

Energy-Based Model Reduction Methodology for Automated Modeling

2010 ◽  
Vol 132 (6) ◽  
Author(s):  
Loucas S. Louca ◽  
Jeffrey L. Stein ◽  
Gregory M. Hulbert
Keyword(s):  
Model Reduction ◽  
Order Reduction ◽  
Process Models ◽  
Model Parameters ◽  
Automated Modeling ◽  
Reduced Models ◽  
System Models ◽  
Quarter Car Model ◽  
Reduction Techniques ◽  
Physical Phenomena

In recent years, algorithms have been developed to help automate the production of dynamic system models. Part of this effort has been the development of algorithms that use modeling metrics for generating minimum complexity models with realization preserving structure and parameters. Existing algorithms, add or remove ideal compliant elements from a model, and consequently do not equally emphasize the contribution of the other fundamental physical phenomena, i.e., ideal inertial or resistive elements, to the overall system behavior. Furthermore, these algorithms have only been developed for linear or linearized models, leaving the automated production of models of nonlinear systems unresolved. Other model reduction techniques suffer from similar limitations due to linearity or the requirement that the reduced models be realization preserving. This paper presents a new modeling metric, activity, which is based on energy. This metric is used to order the importance of all energy elements in a system model. The ranking of the energy elements provides the relative importance of the model parameters and this information is used as a basis to reduce the size of the model and as a type of parameter sensitivity information for system design. The metric is implemented in an automated modeling algorithm called model order reduction algorithm (MORA) that can automatically generate a hierarchical series of reduced models that are realization preserving based on choosing the energy threshold below which energy elements are not included in the model. Finally, MORA is applied to a nonlinear quarter car model to illustrate that energy elements with low activity can be eliminated from the model resulting in a reduced order model, with physically meaningful parameters, which also accurately predicts the behavior of the full model. The activity metric appears to be a valuable metric for automating the reduction of nonlinear system models—providing in the process models that provide better insight and may be more numerically efficient.

Material Behavior of 2D Steel Lattices with Different Unit-Cell Patterns

2021 ◽  
Vol 1046 ◽  
pp. 15-21
Author(s):  
Paiboon Limpitipanich ◽  
Pana Suttakul ◽  
Yuttana Mona ◽  
Thongchai Fongsamootr
Keyword(s):  
Elastic Modulus ◽  
Experimental Studies ◽  
Base Material ◽  
Unit Cell ◽  
Material Behavior ◽  
Closed Form Solutions ◽  
The Past ◽  
Weight Density ◽  
Unit Cells ◽  
Cell Patterns

Over the past years, two-dimensional lattices have attracted the attention of several researchers because they are lightweight compared with their full-solid counterparts, which can be used in various engineering applications. Nevertheless, since lattices are manufactured by reducing the base material, their stiffnesses then become lower. This study presents the weight efficiency of the lattices defined by relations between the elastic modulus and the weight density of the lattices. In this study, the mechanical behavior of 2D lattices is described by the in-plane elastic modulus. Experimental studies on the elastic modulus of the 2D lattices made of steel are performed. Three lattices having different unit cells, including square, body-centered, and triangular unit cells, are considered. The elastic modulus of each lattice is investigated by tensile testing. All specimens of the lattices are made of steel and manufactured by waterjet cutting. The experimental results of the elastic modulus of the lattices with the considered unit-cell patterns are validated with those obtained from finite element simulations. The results obtained in this study are also compared with the closed-form solutions founded in the literature. Moreover, the unit-cell pattern yielding the best elastic modulus for the lattice is discussed through weight efficiency.

Influence of Alloy Behavior on Multiaxial Fatigue Lifing Criteria for Turbine Disk Bores

2014 ◽  
Author(s):  
D. J. Greving ◽  
P. T. Kantzos ◽  
M. N. Menon
Keyword(s):  
Low Cycle Fatigue ◽  
Turbine Disk ◽  
Multiaxial Fatigue ◽  
Point Of View ◽  
Material Behavior ◽  
Tensile Yield Strength ◽  
Failure Initiation ◽  
Disk Alloy ◽  
Significant Difference ◽  
Nickel Base

In a previous paper, a criterion for multiaxial lifing of turbine disk bores made from a nickel base super alloy, DP-718, was substantiated using results from spin pit testing of mini disks. In this paper, another turbine and compressor disk alloy, Alloy 10, exhibiting a different material behavior than DP-718 is examined from multiaxial point of view. This new alloy manufactured by powder metallurgy processing, has a coarser grain size, lower tensile yield strength, contains a much finer distribution of brittle carbides in its microstructure and shows a significant difference in failure initiation behavior under low cycle fatigue when compared to DP-718. Under the multiaxiality conditions experienced by disk bores, Alloy-10 lives seem to correlate well using an effective stress based criterion, whereas DP-718 was found to follow principal stress based criterion. Interesting differences between DP-718 and Alloy-10 in alloy and fractographic behavior under uniaxial and multiaxial conditions are discussed.

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