In this work, the dynamical behavior of a pantographic structure undergoing large deformations is analyzed. A harmonic force is applied on the structure, while its motion in time is recorded by means of a high-speed camera system. The resulting displacement field is obtained via the digital image correlation (DIC) method for the whole domain. A parametric study with respect to the amplitude of the imposed force exhibits the appearance of non-linear effects in the system response as well as the presence of a so-called boundary layer region. Such geometric nonlinearities are of paramount interest for studying the accuracy of a potential computational model. Boundary layers are known to be effected by the microstructure, but their roles in the system response are yet to be comprehended. The experimental results obtained in this work may be used as a benchmark case in modeling metamaterials.

The experimental and numerical analyses of the linear time-invariant dynamical behavior of the clamping region of a 2D pantographic material are presented. The experimental observations of the clamping area, obtained by means of a specialized stereo microscope, are compared with the results of a second gradient linear model enforcing the same symmetries as the system microstructure.

Pantographic structures are examples of metamaterials with such a microstructure that higher-gradient terms’ role is increased in the mechanical response. In this work, we aim for validating parameters of a reduced-order model for a pantographic structure. Experimental tests are carried out by applying forced oscillation to 3D-printed specimens for a range of frequencies. A second-gradient coarse-grained nonlinear model is utilized for obtaining a homogenized 2D description of the pantographic structure. By inverse analysis and through an automatized optimization algorithm, the parameters of the model are identified for the corresponding pantographic structure. By comparing the displacement plots, the performance of the model and the identified parameters are assessed for dynamic regime. Qualitative and quantitative analyses for different frequency ranges are performed. A good agreement is present far away from the eigenfrequencies. The discrepancies near the eigenfrequencies are a possible indication of the significance of higher-order inertia in the model. 

This paper proposes an experimental method for observing the anelastic anisotropic behaviour of poroelastic media. The setup relies on three-dimensional digital image correlation, enabling the acquisition of full-field displacement data from the visible faces of a vibrating cubic material sample. The latter is placed in a vacuum chamber, loaded with a seismic mass and excited uniaxially. The observability and relevance of the three-dimensional displacement field is assessed by means of a numerical simulation. A homogenised fully anisotropic model is used, implemented using the finite element method. Thus, a set of material properties obtained using single-point data is considered as the reference configuration for the numerical method. Selected experimental and numerical results are presented, highlighting the importance and the advantages that full-field observations yield over single-point measurements.

This thesis proposes an experimental method for observing and characterizing the viscoelastic properties of anisotropic media using high-speed white light stereo imaging. The method uses short-time video recordings of a specimen undergoing forced harmonic motion.The three-dimensional displacement field of the specimen is then resolved using digital image correlation.Measuring for a short time has multiple advantages: it minimizes the conditioning of the specimen, and gives meaningful results when true stationary conditions are inaccessible (e.g. because of relaxation processes, or changes in the environmental conditions that cannot be accounted for).Moreover, it enables a reduction of the data storage needs and the computational costs associated with the image acquisition and processing.To overcome the intrinsic limitations of a Fourier-based approach for short time records, an optimization algorithm is used to determine the point-wise amplitude, phase and frequency of the full-field harmonic motion.This approach maximizes signal-to-noise ratio, is suitable for the identification of non-linear behaviors and tolerates data records that are non-uniformly spaced in time (e.g. because of momentary data losses and failure of the image matching algorithms).The measurement accuracy is increased by proposing a method to extract the frame of reference of the specimen on a per-frame bases, and express the measured displacement field therein.A cube of melamine foam and a pantographic sheet have been observed using the proposed method, and the measured data compared with the outcome of linear viscoelastic numerical models.The added information obtained about the melamine is believed to improve the accuracy of the characterization of its viscoelastic behavior, and the observation of the pantographic sheet represents and absolute first in the experimental studies of its dynamics.

Den här avhandlingen föreslår en experimentell metod för att observera och karakterisera de viskoelastiska egenskaperna i anisotropa material med hjälp av höghastighetsbildteknik baserad på vitt ljus och stereoinspelning. Metoden använder korttids inspelade videosekvenser av ett provobjekt som genomgår påtvingad harmonisk rörelse.Provets tredimensionella förskjutningsfält beräknas sedan med användning av digital bildkorrelation.Att mäta under en kort tid har flera fördelar: det minimerar påverkan (konditioneringen) av provet och ger därmed meningsfulla resultat när verkliga stationära förhållanden är otillgängliga (t.ex. på grund av relaxationsprocesser eller förändringar i miljöförhållandena som inte kan kontrolleras).Dessutom möjliggör det en minskning av datalagringsbehovet och de omfattande beräkningskostnaderna som tillkommer med videoinspelning och videobehandling.För att övervinna de inneboende begränsningarna i ett Fourier-baserat tillvägagångssätt för korta tidsinspelningar, används en optimeringsalgoritm för att bestämma den punktvisa amplituden, fasen och frekvensen för harmonisk rörelse i förskutningsfältet.Detta tillvägagångssätt maximerar signal-till-brusförhållandet, är lämplig för identifiering av icke-linjära beteenden och kan hantera dataposter som är ojämnt fördelade i tid (t.ex. på grund av kortvariga dataförluster och fel i bildmatchningsalgoritmerna).Mätnoggrannheten i metoden har dessutom förbättrats genom en metod för att extrahera en referens för provet för varje sekvens och däri uttrycka det uppmätta förskjutningsfältet.En kub av melaminskum och en pantografisk struktur har observerats med den föreslagna metoden och deras data har jämförts med resultat från linjära viskoelastiska numeriska modeller.Resultaten från mätningarna på melamin bidrar till att förbättra noggrannheten i karaktäriseringen av dess viskoelastiska beteende. För den pantografiska strukturen är de presenterade mätningarna de första observationerna som publicerats med avseende på dess dynamik.

In this paper, the results of numerical and experimental studies on the linear time-invariant dynamics of a 2D pantographic material are presented. The outcomes of a linear second gradient model enforcing the same symmetry of the microstructure is compared to experimental observations obtained via Digital Image Correlation (DIC). 

Preliminary results of the first experimental investigation of the spectral properties of a 2D pantographic material are presented and discussed. The observed eigenfrequencies and deflection shapes are compati-ble with the numerical predictions presented in previous numerical studies.

In the last decade, the exotic properties of pantographic metamaterials have been investigated and different mathematical models (both discrete or continuous) have been introduced. In a previous publication, a large part of the already existing literature about pantographic metamaterials has been presented. In this paper, we give some details about the next generation of research in this field. We present an organic scheme of the whole process of design, fabrication, experiments, models and image analyses.

In this paper, a setup for measuring the three-dimensional displacement field of a test object un-dergoing controlled dynamic excitation in a vacuum chamber is presented. The setup has beendesigned with porous materials in mind, yet is suitable for the measurement of anisotropic vis-coelastic solids in general. To achieve non-contact data acquisition, a stereo high-speed camerasystem measures the displacement of the foundation and of the test object. A laser Doppler vi-brometer is used before the actual measurement to choose an excitation level that maximizes thesignal-to-noise ratio while allowing to ensure that the test object is fully relaxed and stable at thebeginning of every measurement. The setup, comprising both commercial and in-house hardwareand software solutions, addresses the challenges of measuring in vacuum with non-contact tech-niques. All these aspects are discussed in the current paper, and preliminary results are presented.The ultimate objective is to estimate the dynamic properties of a material using inverse methodsand the data obtained.

One of the major challenges in accurately modeling poroelastic materials is the choice of the parametersrequired for their modeling, immediately followed by the practical difficulty in obtaining them. The direc-tional dependencies of the physical properties further complicate the task of designing experimental setupscapable of providing the macroscopic properties. In the work presented here, the focus has been set on theacquisition of high quality displacement data by means of two high-speed cameras and 3D Digital ImageCorrelation. The obtained displacement field, is fed into a general inverse formulation which is guided by anoptimization tool that minimizes the difference between the predicted and the measured data. As a minimumis found, the corresponding parameters are interpreted as material properties for a certain physical model.The solutions for each iteration are calculated with numerical prediction tools, in the cases discussed herethe finite element method, where it must be ascertained that the numerical errors are kept to a minimal level