A collaborative research institute was organized and held at Sandia Albuquerque for a period of six weeks. This research institute brought together researchers from around the world to work collaboratively on a set of research projects. These research projects included: developing experimental guidelines for studying variability and repeatability of nonlinear structures; decoupling aleatoric and epistemic uncertainty in measurements to improve dynamic predictions; a numerical round robin to assess the performance of five different numerical codes for modeling systems with strong nonlinearities; and an assessment of experimentally derived and numerically derived reduced order models. In addition to the technical collaborations, the institute also included a series of seminars given by both Sandians and external experts, as well as a series of tours and field trips to local places of scientific and engineering importance. This report details both the technical research and the programmatic organization of the 2014 Sandia Nonlinear Mechanics and Dynamics Summer Research Institute.
The following details the implementation of an analytical elastic plastic contact model with strain hardening for normal im pacts into the LAMMPS granular package. The model assumes that, upon impact, the co llision has a period of elastic loading followed by a period of mixed elastic plas tic loading, with contributions to each mechanism estimated by a hyperbolic seca nt weight function. This function is implemented in the LAMMPS source code as the pair style gran/ep/history. Preliminary tests, simulating the pouring of pure nickel spheres, showed the elastic/plastic model took 1.66x as long as similar runs using gran/hertz/history.
Impact between metallic surfaces is a phenomenon that is ubiquitous in the design and analysis of mechanical systems. We found that to model this phenomenon, a new formulation for frictional elastic–plastic contact between two surfaces is developed. The formulation is developed to consider both frictional, oblique contact (of which normal, frictionless contact is a limiting case) and strain hardening effects. The constitutive model for normal contact is developed as two contiguous loading domains: the elastic regime and a transitionary region in which the plastic response of the materials develops and the elastic response abates. For unloading, the constitutive model is based on an elastic process. Moreover, the normal contact model is assumed to only couple one-way with the frictional/tangential contact model, which results in the normal contact model being independent of the frictional effects. Frictional, tangential contact is modeled using a microslip model that is developed to consider the pressure distribution that develops from the elastic–plastic normal contact. This model is validated through comparisons with experimental results reported in the literature, and is demonstrated to be significantly more accurate than 10 other normal contact models and three other tangential contact models found in the literature.
The uncertainty of a system is usually quantified with the use of sampling methods such as Monte-Carlo or Latin hypercube sampling. These sampling methods require many computations of the model and may include re-meshing. The re-solving and re-meshing of the model is a very large computational burden. One way to greatly reduce this computational burden is to use a parameterized reduced order model. This is a model that contains the sensitivities of the desired results with respect to changing parameters such as Young's modulus. The typical method of computing these sensitivities is the use of finite difference technique that gives an approximation that is subject to truncation error and subtractive cancellation due to the precision of the computer. One way of eliminating this error is to use hyperdual numbers, which are able to generate exact sensitivities that are not subject to the precision of the computer. This paper uses the concept of hyper-dual numbers to parameterize a system that is composed of two substructures in the form of Craig-Bampton substructure representations, and combine them using component mode synthesis. The synthesis transformations using other techniques require the use of a nominal transformation while this approach allows for exact transformations when a perturbation is applied. This paper presents this technique for a planar motion frame and compares the use and accuracy of the approach against the true full system. This work lays the groundwork for performing component mode synthesis using hyper-dual numbers.
Quantifying uncertainty in model parameters is a challenging task for analysts. Soize has derived a method that is able to characterize both model and parameter uncertainty independently. This method is explained with the assumption that some experimental data is available, and is divided into seven steps. Monte Carlo analyses are performed to select the optimal dispersion variable to match the experimental data. Along with the nominal approach, an alternative distribution can be used along with corrections that can be utilized to expand the scope of this method. This method is one of a very few methods that can quantify uncertainty in the model form independently of the input parameters. Two examples are provided to illustrate the methodology, and example code is provided in the Appendix.
In 2012, a Matlab GUI for the prediction of the coefficient of restitution was developed in order to enable the formulation of more accurate Finite Element Analysis (FEA) models of components. This report details the development of a new Rebound Dynamics GUI, and how it differs from the previously developed program. The new GUI includes several new features, such as source and citation documentation for the material database, as well as a multiple materials impact modeler for use with LMS Virtual.Lab Motion (LMS VLM), and a rigid body dynamics modeling software. The Rebound Dynamics GUI has been designed to work with LMS VLM to enable straightforward incorporation of velocity-dependent coefficients of restitution in rigid body dynamics simulations.
In the process of model validation, models are often declared valid when the differences between model predictions and experimental data sets are satisfactorily small. However, little consideration is given to the effectiveness of a model using parameters that deviate slightly from those that were fitted to data, such as a higher load level. Furthermore, few means exist to compare and choose between two or more models that reproduce data equally well. These issues can be addressed by analyzing model form error, which is the error associated with the differences between the physical phenomena captured by models and that of the real system. This report presents a new quantitative method for model form error analysis and applies it to data taken from experiments on tape joint bending vibrations. Two models for the tape joint system are compared, and suggestions for future improvements to the method are given. As the available data set is too small to draw any statistical conclusions, the focus of this paper is the development of a methodology that can be applied to general problems.
It is often prohibitively expensive to integrate the response of a high order nonlinear system, such as a finite element model of a nonlinear structure, so a set of linear eigenvectors is often used as a basis in order to create a reduced order model (ROM). By augmenting the linear basis with a small set of discontinuous basis functions, ROMs of systems with local nonlinearities have been shown to compare well with the corresponding full order models.When evaluating the quality of a ROM, it is common to compare the time response of the model to that of the full order system, but the time response is a complicated function that depends on a predetermined set of initial conditions or external force. This is difficult to use as a metric to measure convergence of a ROM, particularly for systems with strong, non-smooth nonlinearities, for two reasons: (1) the accuracy of the response depends directly on the amplitude of the load/initial conditions, and (2) small differences between two signals can become large over time. Here, a validation metric is proposed that is based solely on the ROM’s equations of motion. The nonlinear normalmodes (NNMs) of the ROMs are computed and tracked as modes are added to the basis set. The NNMs are expected to converge to the true NNMs of the full order system with a sufficient set of basis vectors. This comparison captures the effect of the nonlinearity through a range of amplitudes of the system, and is akin to comparing natural frequencies and mode shapes for a linear structure. In this research, the convergencemetric is evaluated on a simply supported beam with a contacting nonlinearity modeled as a unilateral piecewise-linear function. Various time responses are compared to show that the NNMs provide a good measure of the accuracy of the ROM. The results suggest the feasibility of using NNMs as a convergencemetric for reduced order modeling of systems with various types of nonlinearities.
The goal of most computational simulations is to accurately predict the behavior of a real, physical system. Accurate predictions often require very computationally expensive analyses and so reduced order models (ROMs) are commonly used. ROMs aim to reduce the computational cost of the simulations while still providing accurate results by including all of the salient physics of the real system in the ROM. However, real, physical systems often deviate from the idealized models used in simulations due to variations in manufacturing or other factors. One approach to this issue is to create a parameterized model in order to characterize the effect of perturbations from the nominal model on the behavior of the system. This report presents a methodology for developing parameterized ROMs, which is based on Craig-Bampton component mode synthesis and the use of hyper-dual numbers to calculate the derivatives necessary for the parameterization.