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This paper analyzes the polyurethane material that can be used for the construction of seismic isolation devices based on rolling of elastomeric spheres. Such isolators could be used in low-income countries. Uniaxial tensile tests were performed on dumbbell-shaped polyurethane 95 ShA specimens under two different loading protocols. Protocol 1 consisted of applying a cyclic saw-tooth loading centered on a pre-imposed initial deformation, while Protocol 2 consisted of consecutive loadings followed by relaxation at three different deformation levels. Then, a material model comprising three-chains in parallel was calibrated against the tests. The model combined the Yeoh hyperelastic and Bergstrom-Boyce models. The results of the parameter calibration showed that different testing protocols could lead to different model parameter values. In terms of fitting errors, it is observed that fitting to Protocol 1 generates a good prediction on Protocol 2 with an error of 0.26%; however, when fitting to Protocol 2, the behavior observed on Protocol 1 could not be accurately predicted, resulting in an error of 9.10%. Moreover, when comparing fitting to match only Protocol 1 with considering both protocols simultaneously, the total error is only reduced from 0.32% to 0.20%, suggesting that Protocol 2 adds redundant information already contained in Protocol 1. Additional tests with different deformation rates and ranges need to be conducted to define an optimal protocol for material calibration., Proceedings of the Third European Conference on Earthquake Engineering and Seismology – 3ECEES, ISBN:978-973-100-533-1

As composite laminates have become essential to numerous modern industries, Structural Health Monitoring (SHM) strategies have to be implemented in order to manage the aging of structures made out of composite materials. In this paper, we present and compare two approaches involving solid and plate Spectral Elements (SE) in the time domain, with respect to their ability of modeling composite delamination: a task which lies in the context of modelbased data processing for non destructive evaluation techniques with Guided Waves (GWs). To this end, we review the multilayer flat shell delamination model [1], and propose a singlelayer alternative by extending the Layered Solid Spectral Element (LSSE) [2] method by means of partition of unity enrichment functions [3].These approaches are then compared in a numerical example with different damage scenarios. Finally, conclusions on the benefits and drawbacks of these two strategies are presented., Structural Health Monitoring 2021: Enabling Next Generation SHM for Cyber-Physical Systems, ISBN:978-1-60595-687-9

This contribution presents a hierarchical Bayesian filter for recursive input, state and parameter estimation using spatially incomplete and noisy output-only vibration measurements. The problem at hand is tailored to a dual-layered scheme, whereby the sought-after parameters are treated as random variables with a finite number of evolving states. For each one of these states an output-only Bayesian filter is employed for estimating the state and unknown input, creating thus a bank of filters, which are recursively weighted upon assimilation of the measurement data. The dynamics of parameter states are governed by an evolution strategy, which enables exploration of the parameter space and subsequent identification of the target values. The proposed scheme is numerically tested on crack identification problems using parametric reduced-order models (pROMs). The latter is a key element of the methodology in that it provides a generator of computationally efficient models, which can be evaluated at different parameter configurations, using mesh morphing. The performance of the algorithm is tested by means of simulated realistic components encountered in aerospace applications., Mechanical Systems and Signal Processing, 167 (B), ISSN:0888-3270, ISSN:1096-1216

A diverse variety of engineering and dynamic systems, ranging from control applications and solid mechanics to biology and economics, feature hysteretic phenomena. This commonly encountered nonlinear behavior can be captured and described via diverse numerical models, with the Bouc-Wen representation comprising a common choice within the nonlinear dynamics and vibration engineering community. In this benchmark, the Bouc-Wen model is employed to characterize the response of the nodal connections of a two-story frame structure. The resulting shear frame with hysteretic links is proposed as a multi-degree of freedom nonlinear response simulator. This case study can be seen as an extension to the single degree of freedom ’Hysteretic Benchmark with a Dynamic Nonlinearity’ problem already featured in the nonlinear benchmark website (http://www.nonlinearbenchmark.org/). Our simulator employs a similar parameterized representation of the Bouc-Wen model for each nonlinear link and builds upon it to also include strength deterioration and stiffness degradation effects in a structure with increased dimensionality. As a result, the featured parametric shear frame serves as a multi-degree of freedom nonlinear response simulator, able to model a wide range of nonlinear effects through the parametrized Bouc-Wen couplings. The provided simulator can be utilized as a benchmark problem to validate methods and tools in structural health monitoring, model reduction, or identification applications.

At the dawn of Industry 4.0, it has become apparent that assessment of engineered systems should be informed from the state of the system “as-is”. To this end, data needs to be fused with adequate and efficient system models. Such system models should account for the underlying physics and the possibly nonlinear dynamic processes involved. This paper introduces a physics-based parametric formulation for nonlinear structural systems. A Reduced Order Model (ROM) of the high fidelity system is developed, retaining the dependencies on system properties and on temporal and spectral characteristics of the excitation. The ROM formulation relies on i) Proper Orthogonal Decomposition applied to snapshots of the nonlinear response, and ii) manifold interpolation of the resulting projection bases. Its performance is evaluated on a 3D earthquake-excited shear frame with nonlinear couplings. The developed ROM can be exploited for a number of tasks including monitoring, diagnostics and residual life estimation of critical components.

In finite element analysis for solid mechanics, the solution of the linear system of equations represents the performance bottleneck in terms of both computation time and memory storage. For this task, direct solvers are a common choice due to their simplicity and robustness, however the very large amount of memory required to factorize the stiffness matrix precludes the solution of medium to large-sized problems. For this reason, substantial research effort in the field of iterative solvers has resulted in the adoption of the Conjugate Gradient (CG) method. In this procedure, explicit factorization and thus large quantities of additional memory are not necessary, due to the use of a gradient-descent optimization process. Among many available improvements of the CG, the Deflated Conjugate Gradient (DCG) solver includes information from approximate eigenvectors (known as the deflation space) to achieve a faster convergence. In this contribution, we present an application of the DCG for fracture mechanics with the eXtended Finite Element Method (XFEM). Among other features, such as holes and inclusions, cracks can be effectively modeled with this method, due to the addition of degrees of freedom and functions that enable the representation of discontinuous displacements and singular stresses within the solution space. In addition to the perspective of accelerated numerical analysis, the motivation to employ an iterative solver lies in the fact that no explicit assembly of the entire stiffness matrix is required, which has positive implications in crack propagation and large scale analyses. With this approach, the main challenge lies in the construction of the deflation space in the presence of additional displacement patterns provided by the enrichment functions. Different methods to achieve this feature are studied and tested. With respect to the CG, the decrease in the number of necessary iterations provided by the optimal method should be comparable to the one delivered in a setup without enrichment. Finally, one can observe that, especially for large simulations, such acceleration justifies the higher implementation effort required.

ISSN:1097-0207 ISSN:0029-5981

A three-dimensional (3D) version of the vector level set method [1] is combined to a well conditioned and optimally convergent XFEM variant in order to deal with non-planar three dimensional crack propagation problems. The proposed computational fracture method achieves optimal convergence rates by using tip enriched elements in a fixed volume around the crack front (geometrical enrichment) while keeping conditioning of the resulting system matrices in acceptable levels. Conditioning is controlled by using a three dimensional extension of the degree of freedom gathering technique [2]. Moreover, blending errors are minimized and conditioning is further improved by employing weight function blending and enrichment function shifting [3,4]. As far as crack representation is concerned, crack surfaces are represented by linear quadrilateral elements and the corresponding crack fronts by ordered series of linear segments. Level set values are obtained by projecting points at the crack surface and front respectively. Different criteria are employed in order to assess the quality of the crack representation. References [1] Ventura G., Budyn E. and Belytschko T. Vector level sets for description of propagating cracks in finite elements. Int. J. Numer. Meth. Engng. 58:1571-1592 (2003). [2] Laborde P., Pommier J., Renard Y. and Salaün M. High-order extended finite element method for cracked domains. Int. J. Numer. Meth. Engng. 64:354-381 (2005). [3] Fries T.P. A corrected XFEM approximation without problems in blending elements. Int. J. Numer. Meth. Engng. 75:503-532 (2008). [4] Ventura G., Gracie R. and Belytschko T. Fast integration and weight function blending in the extended finite element method. Int. J. Numer. Meth. Engng. 77:1-29 (2009).