We study a parameter identification problem for the steady state diffusion equations. In this thesis, we transform this identification problem into a minimization problem by considering an appropriate cost functional and propose a finite element method for the identification of the parameter for the linear and nonlinear partial differential equation. The cost functional involves the classical output least square term, a term approximating the derivative of the piezometric head 𝑢(𝑥), an equation error term plus some regularization terms, which happen to be a norm or a semi-norm of the variables in the cost functional in an appropriate Sobolev space. The existence and uniqueness of the minimizer for the cost functional is proved. Error estimates in a weighted 𝐻⁻¹-norm, 𝐿²-norm and 𝐿¹-norm for the numerical solution are derived. Numerical examples will be given to show features of this numerical method. / Ph. D.

Thesis (MScEng)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: This thesis is concerned with the continued development of the Stellenbosch University joint-type knee wear simulator. Initially, information regarding simulators from the literature and commercial entities was collected to provide a knowledge base for current and future work. To further the design of the simulator itself, electronic hardware and software subsystems was developed and evaluated during experimental testing procedures. National Instruments’ cDAQ 9174 data acquisition unit was deemed inadequate for real-time inputoutput control, though proved sufficient for signal capturing purposes in conjunction with LabView software. Furthermore, the various servo-pneumatic sub-circuits’ individual ability to conform to the ISO 14243 series standards’ protocol led to the estimation of measurable performance criteria and the application to a single circuit for illustration. The anterior/posterior actuation circuit in question demonstrated adequate performance for the cases where the piston’s rod was respectively fixed and free to move. In-silico modelling and identification of the relevant servo-pneumatic components then commenced, with the valve and cylinder chamber models yielding adequate estimates of the recorded data. The identified quasi-static friction model proved sensitive to transient effects present within the system, resulting in performance deterioration of the integrated model. Sufficiently accounting for these effects would result in the emergence of the sub-circuit’s model as an invaluable tool in terms of control system development, prediction of the simulator’s behaviour and subsequent design recommendations. Future work therefore concerns improvement, identification and integration of the various sub-circuit models to fully exploit the aforementioned advantages. / AFRIKAANSE OPSOMMING: Hierdie tesis handel oor die voortgesette ontwikkeling van Universiteit Stellenbosch se gewrigstipe knie-afslytingsimulator. Aanvanklik is inligting versamel vanaf literatuur en kommersiële entiteite om sodoende ’n kennisbasis te verskaf vir huidige en toekomstige werk. Elektroniese hardeware en sagteware stelsels is ontwerp en geëvalueer tydens toetsprosedures om die ontwerp van die simuleerder self te verbeter. National Instruments se cDAQ 9174 dataversamelaarseenheid word onvoldoende geag vir intydse inset-uitset beheer, maar wel vir dataversamelingsdoeleindes tesame met LabView sagteware. Die nodigheid om die verskeie servo-pneumatiese sub-stroombane se individuele vermoë om aan te pas by die ISO 14243-reeks se protokol-standaarde te ondersoek, het gelei tot die beraming van meetbare werkverrigtingskriteria en die toepassing daarvan ter illustrasie. Die anterior/posterior stroombaan het voldoende werksverrigting getoon vir studies waar die suier se stang onderskeidelik vas en los was. In-silico modellering en die identifisering van servo-pneumatiese komponente het hierna begin. Die klep en silinderkamer modelle het voldoende skattings gelewer van die gemete data. Die geïdentifiseerde kwasistatiese wrywingsmodel het sensitiwiteit getoon teenoor die oorgangseffekte teenwoordig in die stelsel wat gelei het tot verminderde werksverrigting van die geïntegreerde model. Deur rekening te hou met sulke effekte kan die sub-stelsel se model waardevol wees sover dit beheerstelsel ontwikkeling aangaan, sowel as die voorspelling van die simuleerder se optrede en die daaropvolgende ontwerpsvoorstelle. Toekomstige navorsing kan fokus op die verbetering, identifikasie en integrasie van die verskeie sub-stroombaan modelle om die voorafgenoemde potensiaal ten volle ontgin.

Inflatable Aerodynamic Decelerators (IADs) are a candidate technology NASA began investigating in the late 1960’s. Compared to supersonic parachutes, IADs represent a decelerator option capable of operating at higher Mach numbers and dynamic pressures. IADs have seen a resurgence in interest from the Entry, Descent, and Landing (EDL) community in recent years. The NASA Space Technology Roadmap (STR) highlights EDL systems, as well as, Materials, Structures, Mechanical Systems, and Manufacturing (MSMM) as key Technology Areas for development in the future; recognizing deployable decelerators, flexible material systems, and computational design of materials as essential disciplines for development. This investigation develops a multi-scale flexible material modeling approach that enables efficient high-fidelity IAD design and a critical understanding of the new materials required for robust and cost effective qualification methods. The approach combines understanding of the fabric architecture, analytical modeling, numerical simulations, and experimental data. This work identifies an efficient method that is as simple and as fast as possible for determining IAD material characteristics while not utilizing complicated or expensive research equipment. This investigation also recontextualizes an existing mesomechanical model through validation for structures pertaining to the analysis of IADs. In addition, corroboration and elaboration of this model is carried out by evaluating the effects of varying input parameters. Finally, the present investigation presents a novel method for numerically determining mechanical properties. A sub-scale section that captures the periodic pattern in the material (unit cell) is built. With the unit cell, various numerical tests are performed. The effective nonlinear mechanical stiffness matrix is obtained as a function of elemental strains through correlating the unit cell force-displacement results with a four node membrane element of the same size. Numerically determined properties are validated for relevant structures. Optical microscopy is used to capture the undeformed geometry of the individual yarns.

Given the high and increasing social, health and economic costs of type 2 diabetes, early diagnosis and prevention are critical. Insulin sensitivity and insulin secretion are important etiological factors of type 2 diabetes and are used to define an individual’s risk or progression to the disease state. The dynamic insulin sensitivity and secretion test (DISST) concurrently measures insulin sensitivity and insulin secretion. The protocol uses glucose and insulin boluses as stimulus, and the participant response is observed during a relatively short protocol via glucose, insulin and C-peptide assays. In this research, the DISST insulin sensitivity value was successfully validated against the gold standard euglycaemic clamp with a high correlation (R=0.82), a high insulin resistance diagnostic equivalence (ROC c-unit=0.96), and low bias (-10.6%). Endogenous insulin secretion metrics obtained via the DISST were able to describe clinically important distinctions in participant physiology that were not observed with euglycaemic clamp, and are not available via most established insulin sensitivity tests. The quick dynamic insulin sensitivity test (DISTq) is a major extension of the DISST that uses the same protocol but uses only glucose assays. As glucose assays are usually available immediately, the DISTq is capable of providing insulin sensitivity results immediately after the final blood sample, creating a real-time clinical diagnostic. The DISTq correlated well with the euglycaemic clamp (R=0.76), had a high insulin resistance diagnostic equivalence (ROC c-unit=0.89), and limited bias (0.7%). These DISTq results meet or exceed the outcomes of most validation studies from established insulin sensitivity tests such as the IVGTT, HOMA and OGTT metrics. Furthermore, none of the established insulin sensitivity tests are capable of providing immediate or real-time results. Finally, and most of the established tests require considerably more intense clinical protocols than the DISTq. A range of DISST-based tests that used the DISST protocol and varying assay regimens were generated to provide optimum compromises for any given clinical or screening application. Eight DISST-based variants were postulated and assessed via their ability to replicate the fully sampled DISST results. The variants that utilised insulin assays correlated well to the fully sampled DISST insulin sensitivity values R~0.90 and the variants that assayed C-peptide produced endogenous insulin secretion metrics that correlated well to the fully-sampled DISST values (R~0.90 to 1). By taking advantage of the common clinical protocol, tests in the spectrum could be used in a hierarchical system. For example, if a DISTq result is close to a diagnostic threshold, stored samples could be re-assayed for insulin, and the insulin sensitivity value could be ‘upgraded’ without an additional protocol. Equally, adding C-peptide assays would provide additional insulin secretion information. Importantly, one clinical procedure thus yields potentially several test results. In-silico investigations were undertaken to evaluate the efficacy of two additional, specific DISTq protocol variations and to observe the pharmacokinetics of anti-diabetic drugs. The first variation combined the boluses used in the DISTq and reduced the overall test time to 20 minutes with only two glucose assays. The results of this investigation implied no significant degradation of insulin sensitivity values is caused by the change in protocol and suggested that clinical trials of this protocol are warranted. The second protocol variant added glucose content to the insulin bolus to enable observation of first phase insulin secretion concurrently with insulin sensitivity from glucose data alone. Although concurrent observation was possible without simulated assay noise, when clinically realistic noise was added, model identifiability was lost. Hence, this protocol is not recommended for clinical investigation. Similar analyses are used to apply the overall dynamic, model-based clinical test approach to other therapeutics. In-silico analysis showed that although the pharmacokinetics of insulin sensitizers drugs were described well by the dynamic protocol. However, the pharmacokinetics of insulin secretion enhancement drugs were less observable. The overall thesis is supported by a common model parameter identification method. The iterative integral parameter identification method is a development of a single, simple integral method. The iterative method was compared to the established non-linear Levenberg-Marquardt parameter identification method. Although the iterative integral method is limited in the type of models it can be used with, it is more robust, accurate and less computationally intense than the Levenberg-Marquardt method. Finally, a novel, integral-based method for the evaluation of a-priori structural model identifiability is also presented. This method differs significantly from established, derivative based approaches as it accounts for sample placement, measurement error, and probable system responses. Hence, it is capable of defining the true nature of identifiability, which is analogous, not binary as assumed by the established methods. The investigations described in this thesis were centred on model-based insulin sensitivity and secretion identification from dynamic insulin sensitivity tests with a strong focus on maximising clinical efficacy. The low intensity and informative DISST was successfully validated against the euglycaemic clamp. DISTq further reduces the clinical cost and burden, and was also validated against the euglycaemic clamp. DISTq represents a new paradigm in the field of low-cost insulin sensitivity testing as it does not require insulin assays. A number of in-silico investigations were undertaken and provided insight regarding the suitability of the methods for clinical trials. Finally, two novel mathematical methods were developed to identify model parameters and asses their identifiability, respectively.

Cardiovascular disease is a large problem in the intensive care unit (ICU) due to its high prevalence in modern society. In the ICU, intensive monitoring is required to help diagnose cardiac and circulatory dysfunction. However, complex interactions between the patient, disease, and treatment can hide the underlying disorder. As a result, clinical staff must often rely on their skill, intuition, and experience to choose therapy, increasing variability in care and patient outcome. To simplify this clinical scenario, model-based methods have been created to track subject-specific disease and treatment dependent changes in patient condition, using only clinically available measurements. The approach has been tested in two pig studies on acute pulmonary embolism and septic shock and in a human study on surgical recovery from mitral valve replacement. The model-based method was able to track known pathophysiological changes in the subjects and identified key determinants of cardiovascular health such as cardiac preload, afterload, and contractility. These metrics, which can be otherwise difficult to determine clinically, can be used to help provide targets for goal-directed therapies to help provide deliver the optimal level of therapy to the patient. Hence, this model-based approach provides a feasible and potentially practical means of improving patient care in the ICU.

Type 2 diabetes has reached epidemic proportions worldwide. The resulting increase in chronic and costly diabetes related complications has potentially catastrophic implications for healthcare systems, and economics and societies as a whole. One of the key pathological factors leading to type 2 diabetes is insulin resistance (IR), which is the reduced or impaired ability of the body to make use of available insulin to maintain safe glucose concentrations in the bloodstream. It is essential to understand the physiology of glucose and insulin when investigating the underlying factors contributing to chronic diseases such as diabetes and cardiovascular disease. For many years, clinicians and researchers have been working to develop and use model-based methods to increase understanding and aid therapeutic decision support. However, the majority of practicable tests cannot yield more than basic metrics that allow only a threshold-based assessment of the underlying disorder. This thesis gives an overview on several dynamic model-based methodologies with different clinical applications in assessing glycaemia via measuring effects of treatment or medication on insulin sensitivity. Other tests are clinically focused, designed to screen populations and diagnose or detect the risk of developing diabetes. Thus, it is very important to observe sensitivity metrics in various clinical and research settings. Interstitial insulin kinetics and their influence on model-based insulin sensitivity observation was analysed using data from the clinical pilot study of the dynamic insulin sensitivity and secretion (DISST) test and the glucose-insulin PK-PD models. From these inputs, a model of interstitial insulin dose-response that best links insulin action in plasma to response in blood glucose levels was developed. The critical parameters influencing interstitial insulin pharmacokinetics (PKs) are saturation in insulin receptor binding (αG) and the plasma-interstitium diffusion rate (nI). Population values for these parameters are found to be [αG, nI]=[0.05,0.055]. Critically ill patients are regularly fed via constant enteral (EN) nutrition infusions. The impact of incretin effects on endogenous insulin secretion in this cohort remains unclear. It is hypothesised that the identified SI would decrease during interruptions of EN and would increase when EN is resumed, where, for short periods around transition, the true patient SI would be assumed constant. The model-based analysis was able to elucidate incretin effects by tracking the identified model-based insulin sensitivity (SI) in a cohort of critically ill patients. Thus, changes in model-based SI given the fixed assumed endogenous secretion by the model would support the presence of an EN-related incretin effect in the population of non-diabetic, critically ill patients studied. The PD feedback-control model of Uen was designed to investigate endogenous insulin secretion amongst subjects with different metabolic states and levels of insulin resistance. The underlying effects that influence insulin secretion i.e. incretin effects were also defined by tracking the control model gain/response and the identified insulin sensitivity (SI) using intravenous (IV) bolus and oral glucose responses of insulin sensitivity tests. This new PD control model allowed the characterisation of both static (basal) and dynamic insulin responses, which defined the pancreatic β-cell glucose sensitivity parameters. However, incretin effects were unobserved during oral glucose responses as the PD control gains failed to simulate the true endogenous insulin secretion due to potentially inaccurate glucose appearance rates and low data resolution of glucose concentrations. The net effect of haemodialysis (HD) treatment on glycaemic regulation and insulin sensitivity in a critically ill cohort was investigated. It was hypothesized that the observed SI would decrease during HD due to enhanced insulin clearance compared to the model, and would be recaptured again when HD is stopped. The changes in model-based SI metric at HD transitions in a cohort of critically ill patients were evaluated. Significant changes of -29% in model-based SI was observed during HD therapy. However, there were insignificant changes when HD treatment was ended. Thus, the changes in model-based SI would thus offer a unique observation on insulin kinetics and action in this population of critically ill patients with ARF that would better inform metabolic care.

The principal objective of this investigation is to develop a constitutive model to simulate the hysteresis behaviour of unbonded flexible risers. A new constitutive model for flexible risers is proposed and a procedure for the identification of the related input parameters is developed using a multi-scale approach. The constitutive model is formulated in the framework of an Euler-Bernoulli beam model, with the addition of suitable pressure terms to the generalised stresses to account for the internal and external pressures, and therefore can be efficiently used for large-scale analyses. The developed non-linear relationship between generalised stresses and strains in the beam is based on the analogy between frictional slipping between different layers of a flexible riser and frictional slipping between micro-planes of a continuum medium in nonassociative elasto-plasticity. Hence, a linear elastic relationship is used for the initial response in which no-slip occurs; an onset-slip function is introduced to define the ‘noslip’ domain, i.e. the set of generalised stresses for which no slip occurs; a nonassociative rule with linear kinematic hardening is used to model the full-slip phase. The results of several numerical simulations for a riser of small-length, obtained with a very detailed (small-scale) non-linear finite-element model, are used to identify the parameters of the constitutive law, bridging in this way the small scale of the detailed finite-element simulations with the large scale of the beam model. The effectiveness of the proposed method is validated by the satisfactory agreement between the results of various detailed finite-element simulations for a short riser, subject to internal and external uniform pressures and cyclic bending and tensile loadings, with those given by the proposed constitutive law. The merit of the present constitutive law lies in the capturing of many important aspects of risers structural response, including the energy dissipation due to frictional slip between layers and the hysteretic response. This privilege allows one to accurately study the cyclic behavior of unbonded flexible risers subject to axial tension, bending moment, internal and external pressures.

Esta tese apresenta um procedimento de identificação experimental de coeficientes hidrodinâmicos de veículos submarinos não tripulados. Apresenta-se o desenvolvimento de uma plataforma experimental para pesquisas em dinâmica, controle e navegação de veículos submarinos. A plataforma experimental inclui: 1) um veículo submarino não tripulado semi-autônomo do tipo estrutura-aberta chamado de LAURS, 2) um sistema multissensorial e multipropulsores para o controle de movimento, e 3) software e arquitetura de controle para a aquisição de dados dos sensores e o controle de movimento. A fim de deduzir as equações do movimento dinâmico do LAURS, apresenta-se a formulação geral das equações hidrodinâmicas não lineares de um veículo submarino com seis graus de liberdade. A partir destas equações gerais acopladas, são deduzidos modelos mais simples para um grau de liberdade (movimento unidirecional) e três graus de liberdade (movimento planar) do veículo. O método de estimação de parâmetros utilizado neste trabalho não requer medidas de aceleração e é baseado na aplicação da técnica dos mínimos quadrados à forma integral das equações dinâmicas do sistema. O procedimento de identificação proposto é baseado na informação dos sensores embarcados. Primeiramente, os coeficientes de arrasto são obtidos a partir de testes de velocidade constante e depois, fixando os coeficientes de arrasto do modelo matemático com estes valores obtidos, são identificados a inércia virtual e os coeficientes de acoplamento a partir de testes de velocidade variável. Nos testes de velocidade variável são aplicadas entradas de força do tipo senoidal. Apresentam-se os valores dos coeficientes hidrodinâmicos para os movimentos de avanço, deriva, arfagem, guinada e caturro do veículo, os quais foram obtidos usando o procedimento de identificação proposto. O desempenho dos modelos dinâmicos identificados é quantitativamente comparado ao movimento do veículo observado experimentalmente. Para o caso dos testes de velocidade constante em avanço e arfagem, foi feita uma comparação dos valores dos coeficientes obtidos usando a abordagem de identificação de sistemas com os dados obtidos a partir dos ensaios de reboque em tanque de provas. Os resultados obtidos validam o procedimento de identificação proposto. Além disso, são apresentados os resultados experimentais obtidos a partir de manobras do tipo zig-zag e é feita uma discussão da identificabilidade de coeficientes de modelos acoplados. Conclui-se que o procedimento de identificação proposto é eficaz na obtenção de valores reais (consistentes com a concepção física do veículo) para os coeficientes hidrodinâmicos de veículos submarinos. A fim de modelar a força hidrodinâmica que atua no veículo em avanço com movimento oscilatório e amplitudes menores do que um comprimento característico, são apresentados os resultados dos ensaios de oscilação forçada usando um mecanismo de movimento planar (MMP). Apresentam-se os valores dos coeficientes de arrasto e de inércia obtidos a partir dos ensaios em avanço no MMP para diferentes números de Keulegan-Carpenter. Os resultados mostram que os coeficientes de arrasto e de inércia para a faixa de velocidades de 0,1 até 0,8m/s dependem fortemente do número de Keulegan-Carpenter e não do número de Reynolds. A partir destes resultados, conclui-se que a amplitude da oscilação do veículo é o principal fator que causa a variação dos coeficientes hidrodinâmicos e não a velocidade do veículo. / In this work, a procedure for experimental identification of hydrodynamic coefficients of unmanned underwater vehicles is presented. At first, the development of a testbed for research on dynamics, control, and navigation of underwater vehicles is presented. This experimental platform includes: 1) a open-frame semi-autonomous unmanned underwater vehicle named LAURS, 2) a multi-sensorial and multi-thruster system for motion control, and 3) software and control architecture for sensor data logging and motion control. In order to derive the LAURS dynamic motion equations, the general formulation of the nonlinear hydrodynamic equations of motion of an underwater vehicle with six degree of freedom is initially presented. From these general coupled equations, simpler formulations with one (unidirectional movement) and three degrees of freedom (planar movement) are derived. The parameter estimation method does not require acceleration measurements and is based on the application of the least squares technique to the integral form of the system dynamic equations. The identification procedure is based on on-board sensor data. First the drag coefficients are obtained from constant velocity tests and afterwards, fixing the drag coefficients in the mathematical model with the obtained values, virtual inertia and coupling coefficients of the vehicle are identified from variable velocity tests. In the tests of variable velocity, sinusoidal force inputs are applied. Values of hydrodynamic coefficients for surge, sway, heave, yaw, and pitch motions are estimated using the proposed identification procedure. Performance of the identified dynamic models is quantitatively compared to the experimentally observed vehicle motion. In the case of constant velocity tests, for the surge and heave motions, comparisons of the hydrodynamic drag coefficient values obtained using the system identification method with data obtained from towing tank tests are presented. Obtained results corroborate for the feasibility of the proposed identification method. Moreover, experimental results obtained from zig-zag maneuvers are presented and the identifiability of coupled dynamic models is discussed. It is possible to conclude that using the proposed method actual hydrodynamic parameters might be estimated. In order to model the hydrodynamic force that acts on the vehicle, in surge motion, with oscillatory movements and with amplitudes that are smaller than or equal to the characteristic length of the LAURS, results of forced oscillation tests in a planar motion mechanism (PMM) are presented. The drag and inertia coefficient values obtained from surge motion tests in the PMM for different Keulegan-Carpenter numbers are presented and discussed. Results illustrates that drag and inertia coefficients, when the vehicle velocity is in the range of 0,1 and 0,8m/s, do not strongly depend on the Reynolds number, however, they are strongly dependent on the Keulegan-Carpenter number. In this context, we can conclude that the oscillation amplitude is the main factor that causes the variation of hydrodynamic coefficients and not the vehicle velocity.

The da Vinci Surgical System is one of the most established robot-assisted surgery device commended for its dexterity and ergonomics in minimally invasive surgery. Conversely, it inherits disadvantages which are lack of autonomy and haptic feedback. In order to address these issues, this work proposes an industry-inspired solution to the field of force control in medical robotics. This approach contributes to shared autonomy by developing a controller for cooperative object manipulation with force tracking utilizing available manipulators and force feedback. To achieve simultaneous position and force tracking of the object, master and slave manipulators were assigned then controlled with Cartesian position control and impedance control respectively. Because impedance control requires a model-based feedforward compensation, we identified the lumped base parameters of mass, inertias, and frictions of a three degree-of-freedom double four-bar linkage mechanism with least squares and weighted least squares regression methods. Additionally, semidefinite programming was used to constrain the parameters to a feasible physical solution in standard parameter space. Robust stick-slip static friction compensation was applied where linear Viscous and Coulomb friction was inadequate in modeling the prismatic third joint. The Robot Operating System based controller was tested in RViz to check the cooperative kinematics of up to three manipulators. Additionally, simulation with the dynamic engine Gazebo verified the cooperative controller applying a constant tension force on a massless spring-damper virtual object. With adequate model feedback linearization, the cooperative impedance controller tested on the da Vinci Research Kit yielded stable tension force tracking while simultaneously moving in Cartesian space. The maximum force tracking error was +/- 0.5 N for both a compliant and stiff manipulated object.

A simulação numérica de componentes estmturais necessita de dados do material que são obtidos por ensaios mecânicos. Materiais não-lineares, como termoplásticos, podem apresentar em ensaios de tração estricção quando submetidos à deformações firútas. Este fenômeno normalmente ainda está associado a campos de deformações heterogêneos que possuem uma cinemática particular, se propagando ao longo do corpo. A formação e propagação da estricção podem mascarar o real comportamento mecârúco do material quando obtido por um ensaio de tração, levando o processo de caracterização da curva tensão-deformação real do material a um procedimento não-trivial. Através de um ensaio de tração de um termoplástico, dados experimentais de força e do campo de deslocamentos da região de estricção, obtido através de métodos ópticos, são utilizados em um procedimento numérico-experimental de otimização para a deternúnação dos parâmetros (FEMU) de alguns modelos constitutivos capazes de representar a tendência do comportamento de termoplásticos. De modo a estudar a capacidade representativa da resposta mecânica do ensaio, um modelo constitutivo multi linear e um modelo constitutivo variacional, são estudados. Uma função objetivo conveniente que utiliza dados experimentais e numéricos é usada para considerar a cinemática da estricção, responsável pela mudança geométrica que diferencia as respostas nonúnais e reais da curva tensão-deformação. Por meio dos resultados obtidos neste trabalho verificou-se que a caracterização dos modelos constitutivos utilizando somente a resposta de força, não garante uma caracterização constitutiva adequada, sendo necessária a resposta de deslocamento para garantir a representação da cinemática da região de estricção. / Numerical simulation of structural components requires material data obtained from mechanical testing. Nonlinear materials, like thermoplastics, submitted to tensile testing presents necking undergoing finite strain. This phenomenon is still typically associated to heterogeneous strain fields which possess a particular kinematic, propagating through the body. Necking and colddrawing may mask the actual mechanical behavior measured by a tensile testing machine, turning the real stress-strain curve characterization process into a non-trivial procedure. Through a thermoplastic tensile testing, force experimental data and displacement experimental data from the necking region, obtained by optical methods, are used in a numerical-experimental optimization procedure in order to determine the constitutive parameters (FEMU) from some constitutive models which are able to represent the thermoplastic behavior tendency. In order to study the representative capacity of the mechanical testing response, a multilinear constitutive model and a variational constitutive model, are studied. A suitable objective function which uses experimental and numerical data is used to consider the necking kinematics, responsible for geometric change that distinguishes the nominal and real responses of the stress-strain curve. Through the obtained results, it can be seen that the model parameters determination using, in addition to force, the displacement field in the objective function is necessary to represent the kinematic behavior in the necking region.