Online and real-time sensing and monitoring of the health state of complex structures, such as aircraft and critical components of power stations, are essential aspects of research in dynamics. Several types of sensors are used to capture dynamic responses and monitor changes during the operation of critical parts of complex systems. Piezoelectric (PZ) materials belong to a class of electroactive materials that convert mechanical deformation into an electrical response. For example, PZ ceramics or PVDF foils are employed for online sensing of the time history of mechanical deformation. This paper focuses on the dynamical response of a cantilever beam structure equipped with a glued PZ sensor and combines experimental and modelling approaches to achieve accurate and reliable results. The time history of the normal velocity at a point on the beam surface was recorded with a laser vibrometer during transient vibrations of the beam, triggered by the sudden removal of a mass load at the beam's free end. Simultaneously, the output voltage of the PZ sensor was measured with an electronic device. An elastodynamic model of a cantilever beam coupled with a piezoelectric sensor is introduced, along with its discretization using the finite element method. The mathematical model includes additional terms that enforce a floating-potential boundary condition to maintain a constant charge on one of the sensor's electrodes and is presented in an extended form suitable for sensitivity analysis or parameter identification. The model implementation is validated using a numerical example corresponding to the experimental setup. The computed results show good agreement with the experimental data. Furthermore, values of the Rayleigh damping parameters were identified based on the experimental measurements.

Detailed modelling of piezoelastic structures often includes also an external circuit.This is tied with the need for a weak imposition of electric potential Dirichlet boundary conditions and questions of simulation accuracy arise.Several methods allowing the weak imposition, namely the non-symmetric Nitsche's method, penalty method and their combinations, are evaluated and their numerical convergence w.r.t.uniform mesh refinement for various finite element approximation orders is reported.The numerical study is performed on a geometry corresponding to a piezoelectric sensor.

New methods are presented for the direct computation of higher-order inverse mass matrices (also called reciprocal mass matrices) that are used for explicit transient finite element analysis. The motivation of this work lies in the need of having appropriate sparse inverse mass matrices, which present the same structure as the consistent mass matrix, preserve the total mass, predict suitable frequency spectrum and dictate sufficiently large critical time step sizes. For an efficient evaluation of the reciprocal mass matrix, the projection matrix should be diagonal. This condition can be satisfied by adopting dual shape functions for the momentum field, generated from the same shape functions used for the displacement field. A theoretically consistent derivation of the inverse mass matrix is based on the three-field Hamilton principle and requires the projection matrix to be evaluated from the integral of these shape functions. Unfortunately, for higher-order FE shape functions and serendipity FE elements, the projection matrix is not positive definitive and can not be employed. Therefore, we study several lumping procedures for higher order reciprocal mass matrices considering their effect on total-mass preserving, frequency spectra and accuracy in explicit transient simulations. The article closes with several numerical examples showing suitability of the direct inverse mass matrix in dynamics.

An elastodynamical model of a cantilever beam coupled with a piezoelectric sensor is introduced and its discretization using the finite element method is presented.The mathematical model includes additional terms that enforce the floating potential boundary condition for keeping a constant charge on an electrode of the sensor.The behaviour of the model is illustrated using a numerical example corresponding to an experimental setup, where vibrations of the beam and the potential on the sensor are measured.

Different measuring techniques have been used to objectify the classification of hoof shape. The MicroScribe is a novel tool that might prove useful for measuring hooves without prior reconstruction or compensation of projection artefacts. The aim of this study was to compare biometric data of the equine hoof collected by the MicroScribe tool and measurements collected directly from hooves, scaled photographs and radiographs, from photogrammetry models and computed tomography datasets. The suitability of MicroScribe generated data to differentiate individual hoof conformations was tested. A total of 62 measures were recorded from 16 forehooves. 21 linear and nine angular measures were collected by at least four methods each, and evaluated further by analysis of variance (ANOVA) and multivariate analysis of variance (MANOVA). Ratios and differences of these measures were calculated as suitable for the definition of hoof shapes and analysed as well. Absolute equivalency of methods was detected for five linear and none of the angular measurements. The precision of the tested measurement methods was comparable. In some cases, different methods measure different structures. Radiographs tended to overestimate, while computed tomography slides to underestimate distances. Photogrammetry and scaled photographs were less suitable for measuring hoof angles. The MicroScribe tool can readily be used for hoof measurements. Its values for linear measures showed good equivalency with other methods based on real hooves. For angular measurements, the uneven hoof surface might introduce imprecision. Not all hoof conformations could be detected based on measuring results alone. Diagnosis by a skilled veterinarian is still essential.

Online and real-time sensing and monitoring of the health state of complex structures, such as aircraft and critical parts of power stations, is an essential part of the research in dynamics.Several types of sensors are used for sensing dynamic responses and monitoring response changes during the operation of critical parts of complex systems.The piezoelectric (PZ) materials belong to one group of electroactive materials, which transform mechanical deformation into an electrical response.For example, PZ ceramics or PVDF foils are employed for online sensing of the time history of mechanical deformation.Experimentally obtained response of a cantilever beam structure with a glued PZ sensor is the case of interest in this contribution.During the transient problem of the beam loaded by suddenly interrupted load due to the weight of a mass at the end of the beam, the time history of normal velocity at a point on the beam surface has been measured by a laser vibrometer and parallely, the output voltage on the PZ sensor has been measured by an electric device.The experimental data in the case of the first eigen-frequency is in good agreement with the value given by the formulae from the theoretical modeling of free vibration of a linear beam.

The paper deals with the problem of material identification for smooth muscle tissue in activated, or passive states. In [17] a composite type mathematical model has been proposed describing the complexity of the tissue reduced to the networks of muscle and collagen fibres. The computational model is based on the total Lagrangian formulation with incompressibility of the bulk material. The problem of inflating vessels is considered in order to allow simulation of real experimental conditions and, thus, to determine constitutive parameters of muscle in active state. These parameters are identified also from hysteresis, or relaxation curves. The direct differentiation, or the adjoint systems techniques are applied to the sensitivity analysis. Results of numerical tests are given.

Convergence rates of iterative algorithms for solving non-linear fixed-point (or root-finding) problems depend on the quality of the solution guess done in each iteration, which is used as the starting value in the next step. To avoid instabilities and oscillations, that guess is usually constructed (mixed) as a linear combination of the newly calculated value with values from the previous iterations. The mixing algorithm constitutes a crucial component for electronic structure calculation methods based on iterative seeking for a self-consistent state. This paper reviews several mixing algorithms for electronic structure calculations. The most important numerically confirmed finding is that the calculation speed depends more on the choice of the so-called “mixing coefficient” than on the choice of a particular algorithm. Then a new method allowing an automatic adaptation of this coefficient is proposed, implemented, and tested on various solid-state structures within three electronic structure calculation codes. In our testing cases, the newly designed Adaptive Anderson Algorithm exhibits better convergence for a broader range of initial mixing coefficients, and similar or better robustness, in comparison to the standard Anderson method. The Fortran implementation of the new algorithm and its Python wrapper are briefly described in the paper and made available for public use.

A new implementation of finite element matrix evaluation functions in the finite element code SfePy is introduced, leveraging several Python tensor contraction packages that implement a general function for evaluating expressions given using the Einstein summation convention.An example of the new weak form implementation is shown, and then results of a numerical study are presented comparing performance of the new implementation, the original implementation, and FEniCS suite.

Current industrial trends bring new challenges in energy absorbing systems. Polymer materials as the traditional packaging materials seem to be promising due to their low weight, structure, and production price. Based on the review, the linear low-density polyethylene (LLDPE) material was identified as the most promising material for absorbing impact energy. The current paper addresses the identification of the material parameters and the development of a constitutive material model to be used in future designs by virtual prototyping. The paper deals with the experimental measurement of the stress-strain relations of linear low-density polyethylene under static and dynamic loading. The quasi-static measurement was realized in two perpendicular principal directions and was supplemented by a test measurement in the 45° direction, i.e., exactly between the principal directions. The quasi-static stress-strain curves were analyzed as an initial step for dynamic strain rate-dependent material behavior. The dynamic response was tested in a drop tower using a spherical impactor hitting a flat material multi-layered specimen at two different energy levels. The strain rate-dependent material model was identified by optimizing the static material response obtained in the dynamic experiments. The material model was validated by the virtual reconstruction of the experiments and by comparing the numerical results to the experimental ones.

Acoustic waves in a poroelastic medium with periodic structure are studied with respect to permanent seepage flow which modifies the wave propagation. The effective medium model is obtained using the homogenization of the linearized fluid–structure interaction problem while respecting the advection phenomenon in the Navier–Stokes equations. For linearization of the micromodel, an acoustic approximation is introduced which yields a problem for the acoustic fluctuations of the solid displacements, the fluid velocity and pressure. An extended Darcy law of the macromodel involves the permeability and advection tensors which both depend on an assumed stationary perfusion of the porous structure. The monochromatic plane wave propagation is described in terms of two quasi-compressional and two quasi-shear modes. Two alternative problem formulations in the frequency domain are discussed. The one defined in terms of displacement and velocity fields leads to generalized eigenvalue problems involving non-Hermitean matrices whose entries are constituted by the homogenized coefficients depending on the incident wave frequencies, whereby degenerate permeabilities can be accounted for. The homogenization procedure and the wave dispersion analysis have been implemented to explore the influence of the advection flow and the microstructure geometry on the wave propagation properties, namely the phase velocity and attenuation. Numerical examples are reported.

In finite element calculations, the integral forms are usually evaluated using nested loops over elements, and over quadrature points. Many such forms (e.g. linear or multi-linear) can be expressed in a compact way, without the explicit loops, using a single tensor contraction expression by employing the Einstein summation convention. To automate this process and leverage existing high performance codes, we first introduce a notation allowing trivial differentiation of multi-linear finite element forms. Based on that we propose and describe a new transpiler from Einstein summation based expressions, augmented to allow defining multi-linear finite element weak forms, to regular tensor contraction expressions. The resulting expressions are compatible with a number of Python scientific computing packages, that implement, optimize and in some cases parallelize the general tensor contractions. We assess the performance of those packages, as well as the influence of operand memory layouts and tensor contraction paths optimizations on the elapsed time and memory requirements of the finite element form evaluations. We also compare the efficiency of the transpiled weak form implementations to the C-based functions available in the finite element package SfePy.

Acoustic waves in a slightly compressible fluid saturating porous periodic structure are studied using two complementary approaches: 1) the periodic homogenization (PH) method provides effective model equations for a general dynamic problem imposed in a bounded medium, 2) harmonic acoustic waves are studied in an infinite medium using the Floquet-Bloch (FB) wave decomposition. In contrast with usual simplifications, the advection phenomenon of the Navier-Stokes equations is accounted for. For this, an acoustic approximation is applied to linearize the advection term. The homogenization results are based the periodic unfolding method combined with the asymptotic expansion technique providing a straight upscaling procedure which leads to the macroscopic model defined in terms of the effective model parameters. These are computed using the characteristic responses of the porous microstructure. Using the FB theory, we derive dispersion equations for the scaffolds saturated by the inviscid, or the viscous, barotropic fluids, whereby the advection due to a permanent flow in the porous structures is respected. A computational study is performed for the numerical models obtained using the finite element discretization. For the FB methods-based dispersion analysis, quadratic eigenvalue problems must be solved. The numerical examples show influences of the microstructure size and of the advection generating an anisotropy of the acoustic waves dispersion. (c) 2021 Elsevier Inc. All rights reserved.

n amendment to this paper has been published and can be accessed via a link at the top of the paper.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Despite the wide choice of commercial heart valve prostheses, cryopreserved semilunar allograft heart valves (C-AHV) are required, and successfully transplanted in selected groups of patients. The expiration limit (EL) criteria have not been defined yet. Most Tissue Establishments (TE) use the EL of 5 years. From physiological, functional, and surgical point of view, the morphology and mechanical properties of aortic and pulmonary roots represent basic features limiting the EL of C-AHV. The aim of this work was to review methods of AHV tissue structural analysis and mechanical testing from the perspective of suitability for EL validation studies. Microscopic structure analysis of great arterial wall and semilunar leaflets tissue should clearly demonstrate cells as well as the extracellular matrix components by highly reproducible and specific histological staining procedures. Quantitative morphometry using stereological grids has proved to be effective, as the exact statistics was feasible. From mechanical testing methods, tensile test was the most suitable. Young’s moduli of elasticity, ultimate stress and strain were shown to represent most important AHV tissue mechanical characteristics, suitable for exact statistical analysis. C-AHV are prepared by many different protocols, so as each TE has to work out own EL for C-AHV.

In the paper, we present a direct inverse mass matrix in the higher-order finite element method for solid mechanics. The direct inverse mass matrix is sparse, has the same structure as the consistent mass matrix and preserves the total mass. The core of derivation of the semi-discrete mixed form is based on the Hamilton's principle of least action. The cardinal issue is finding the relationship between discretized velocities and discretized linear momentum. Finally, the simple formula for the direct inverse mass matrix is presented as well as the choice of density-weighted dual shape functions for linear momentum with respect to the displacement shape function with a choice of the lumping mass method for obtaining the correct and positive definitive velocity-linear momentum operator. The application of Dirichlet boundary conditions into the direct inverse mass matrix for a floating system is achieved using the projection operator. The suggested methodology is tested on a free-vibration problem of heterogeneous bar for different orders of shape functions.