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Highlights • Physically perturbed variations of a bolted lap joint studied. • Modeling independent similarity metrics sought from parameter estimation studies. • The surrogate system hypothesis formulated and applied to the lap-jointed benchmarks. • Hypothesis tested in a multi-objective optimization framework. • Tuned whole-joint patch methods employed for the interfacial modeling. Abstract The main challenges in the design and analysis of jointed structures deal with the prediction of dissipation across bolted interfaces. Since friction is thought to be one of the main mechanisms for this, the current study investigates the utility of frictional parameter identification applied across different structures. Based on recent discoveries, a Surrogate System Hypothesis has been formulated to systematize this: the hypothesis states in brief, that the physical properties of a joint are independent of its structural context. The current work seeks to obtain a better understanding of the underlying systems by evaluating a confidence metric for the hypothesis for a relatively simple set of systems—physically perturbed configurations of the Brake-Reuß Beam. Interfacial friction is modeled using whole jointed patches with distributed hysteretic (Iwan) elements and simulations are conducted using the Quasi-Static Modal Analysis (QSMA) approach to estimate the modal characteristics of the system response (amplitude dependence of natural frequency and dissipation). Posing the estimation as a Multi-Objective Optimization Problem (MOOP) is shown to reveal important features of both the employed constitutive model as well as the structure that is modeled. Consequently, the approach is used to evaluate the epistemic uncertainty inherent in three different friction models. The studies reveal that a confidence metric for the hypothesis can be formulated in such a way that it is nearly independent of the friction constitutive model that is employed. [ABSTRACT FROM AUTHOR]

• Theoretic formulation for Nonlinear Modal Analysis (NMA). • Stationarity of Rayleigh Quotients (RQ) extended for nonliear systems. • Nonlinear modes about a static solution defined as non-trivial (finite) perturbations where the RQ's are stationary. • Special emphasis placed on hysteretic systems. • Computational implementation compared with frequency-domain techniques for a class of benchmarks. Non-linear Modal Analysis (NMA) refers to a class of analysis procedures that seek to characterize non-linear dynamical systems similar to how classical linear modal analysis characterizes the natural frequencies and mode shapes of linear systems. The current study proposes an extension to the stationarity of Rayleigh quotients, a classical technique for linear modal analysis, for non-linear, non-conservative, dynamical systems. The approach, termed Rayleigh Quotient-based Nonlinear Modal Analysis (RQNMA), formalizes each mode as a finite non-trivial perturbation about a static solution that is locally stationary in the work done. Apart from offering a theoretical basis for the concept of non-linear modes, this circumvents several limitations in previous methods (for example, Quasi-Static Modal Analysis (QSMA)), such as inconsistencies in handling static forces, assumptions on mode-shape change, etc. As with other NMA procedures, RQNMA is formulated for the characterization of the amplitude-dependent natural frequency (stiffness) and damping ratio (dissipation) near/at the resonances. The estimated stiffness and dissipation characteristics are compared with modal backbones generated from frequency-domain approaches, which typically are computationally more expensive than the presented approach. Comparisons are conducted using different benchmark models, placing special emphasis on structures with pre-stressed frictional contacts, in order to bring out the strengths and shortcomings of the presented approach to contextualize its applicability. [ABSTRACT FROM AUTHOR]

• Model form error is considered for different model strategies for jointed structures. • Twenty-six models (ten friction models and two representations) are considered. • The suitability of the Masing assumptions for joint dynamics are evaluated. • In addition to frictional damping, material damping is necessary for quality fits. • Fits based on the Masing assumptions have additional errors for transient analyses. Hysteretic models are widely used to model frictional interactions in joints to recreate experimental behavior. However, it is unclear which models are best suited for fitting or predicting the responses of structures. The present study evaluates 26 friction model/interface representation combinations to quantify the model form error. A Quasi-Static Modal Analysis approach (termed Rayleigh Quotient Nonlinear Modal Analysis) is adopted to calculate the nonlinear system response, and a Multi-Objective Optimization is solved to fit experimental data of the first mode of the Brake-Reuß Beam. Optimized parameters from the first mode are applied to the second and third bending modes to quantify the predictive ability of the models. Formulations for both tracing full hysteresis loops and recreating hysteresis loops from a single loading curve (Masing assumptions) are considered. Smoothly varying models applied to a five patch representation showed the highest flexibility (for fitting mode 1) and good predictive potential (for modes 2 and 3). For a second formulation, which uses 152 frictional elements to represent the interface, the physically motivated spring in series with a Coulomb slip model (elastic dry friction) has high error for fitting mode 1 and performs near the middle for predicting higher modes. For both interface representation, the best fit models are not the most physical, but rather the ones with the most parameters (as expected); however, the more physical models perform somewhat better for predicting the higher modes. [ABSTRACT FROM AUTHOR]

• Hyper-reduced whole-joint approach improving previous non-stiffening surface coupling. • Initial efforts at development of consistent whole-joint contact constitutive models. • Hyper-reduced remeshing approach consistent with a reference FE representation. • Explorations of possible approaches for constructing reduced order representations. • Comparisons of the applicability of two different types of interface reduction. One strategy to develop both accurate and computationally tractable models of jointed structures is reduced order modeling through hyper-reduced representations of the interfaces in contact. Hyper reduction refers to reduction techniques that result in a Reduced Order Model (ROM) that is complete by itself, i.e., all displacements and forces are fully described in the ROM coordinates directly. Focusing primarily on applications involving small relative displacement contacts, two fundamentally different approaches are formulated and compared for merits and limitations in applicability. The first is an adaptation of the stiffness-preserving RBE3 constraint elements, and the second is an interpolation approach based on remeshing the interface. Although RBE3 is extensively used in the literature, the current formulation derives stiffness preserving elements that are specifically useful for contact dynamics applications. Transformations are developed to express force–displacement relationships in the ROM coordinates that are congruent (in the sense of using the same contact models) as well as consistent (in the sense of being faithful to the quantities involved) with a high-fidelity model of the same structure. These approaches are applied to study a three-bolted lap-joint structure (the Brake-Reuß Beam (BRB) benchmark) that has been observed to demonstrate characteristic contact non-linearities. Multiple strategies for the hyper reduction are evaluated, including graph partitioning, finite element coarsening, and homogenization of field objectives, some of which involve an extra step of remeshing/choosing patches based on a field objective (e.g., contact pressure). The performances of the ROMs are assessed by conducting nonlinear modal analysis and computing a posteriori error metrics. [ABSTRACT FROM AUTHOR]