The Meshless Local Petrov-Galerkin (MLPG) method has been employed to analyze the following linear and nonlinear solid mechanics problems: free and forced vibrations of a segmented bar and a cracked beam, pull-in instability of an electrostatically actuated microbeam, and plane strain deformations of incompressible hyperelastic materials. The Moving Least Squares (MLS) approximation is used to generate basis functions for the trial solution, and for the test functions. Local symmetric weak formulations are derived, and the displacement boundary conditions are enforced by the method of Lagrange multipliers. Three different techniques are employed to enforce continuity conditions at the material interfaces: Lagrange multipliers, jump functions, and MLS basis functions with discontinuous derivatives. For the electromechanical problem, the pull-in voltage and the corresponding deflection are extracted by combining the MLPG method with the displacement iteration pull-in extraction algorithm. The analysis of large deformations of incompressible hyperelastic materials is performed by using a mixed pressure-displacement formulation. For every problem studied, computed results are found to compare well with those obtained either analytically or by the Finite Element Method (FEM). For the same accuracy, the MLPG method requires fewer nodes but more CPU time than the FEM. / Ph. D.

Fiber-reinforced rubberlike materials (FRRM) commonly used in tires undergo large deformations, and exhibit different response in tension and compression along the fiber direction. Assuming that the response of a fiber-reinforced rubberlike material can be modeled as transversely isotropic with the fiber direction as the axis of transverse isotropy, we express the stored energy function, W, in terms of the five invariants of the right Cauchy-Green strain tensor and the fiber direction, and account for different response in tension and compression along the fiber direction. It has been shown in the literature that in shear-dominated deformations, the 5th invariant, I5, significantly contribution to the stress-strain curve. We have implemented the constitutive relation in the commercial software, LS-DYNA. The numerical solutions of several boundary value problems studied here agree with their analytical solutions derived by using Ericksen's inverse approach, in which a part of the solution is assumed and unknowns in the presumed solution are then found by analyzing the pertinent boundary value problem. However, computed results have not been compared with experimental findings. For W of the FRRMs an expression that is a complete quadratic function of the five invariants is also examined. Homogeneous deformations such as simple extension, simple shear, and biaxial loading problems are studied to delineate the mechanical behaviors of FRRMs. Consistency with the infinitesimal deformation theory requires that linear terms in the 4th and 5th invariants, I4 and I5, be included in the expression for W. Stability analysis of deformations reveals the qualitative changes triggered by the second order terms of the quadratic function. Analytical solutions for inflation, extension and twist deformations caused by internal pressure, end torque, and axial force for a pressurized cylindrical laminate are derived using Ericksen's inverse method. Effects of fiber orientations on the mechanical behaviors of a +/-α angle-ply cylindrical tube are investigated using the derived analytical solutions. The T-peel test, widely used for characterizing adhesion across a plethora of adhesives, adherends, and geometries, results in a range of responses that may complicate meaningful interpretation of the test data. This research effort, involving several specific specimen types, was undertaken to investigate concerns that commonly used configurations may not always result in plateaus in the force-displacement response. We experimentally and numerically study debonding of T-peel specimens having 75 mm bond length and 0.81 mm thick adherends made of either 6061 aluminum (Al) or one of the three steels (G70 70U hot dip galvanized, E60 elctrogalvanized (EGZ), 1010 cold-rolled steel (CRS) bonded with either LORD® 406 or Maxlok™ acrylic adhesive. For the EGZ and the Al adherends, specimens with a bond length of 250 mm and adherend thickness of 1.60 mm are also examined. Effects of adherend materials and thicknesses, bond lengths, and adhesives on test results are examined using three metrics to interpret the T-peel bond performance. We find a limited correlation between the commonly used "T-peel strength" and the energy dissipated per unit debond area. For those two metrics, the relative performances of the CRS and the Al specimens are quite different. Quasi-static plane strain deformations of the test specimens are analyzed by the finite element method (FEM) and a cohesive zone model using the commercial software, ABAQUS, to help interpret the test data. Numerical results provided energies required to elastically and plastically deform the adherends, and help determine the transition from non-self-similar to self-similar debonding. The FE simulations also facilitate determination of the fraction of the crosshead displacement at which self-similar debonding occurs. Results reported herein should help practitioners select appropriate specimen dimensions for extracting meaningful data for adhesive performance. / Ph. D. / Tire belts, seals, and impact absorbing cushions are usually made of fiber-reinforced rubberlike materials (FRRMs), but are difficult to analyze because their response to complex loading situations is strongly dependent on a variety of material properties. Many biological soft tissues, such as tendons, ligaments and arteries are also typically modeled as FRRMs. We assume that a fiber-reinforced rubberlike material can be modeled as nonlinear, incompressible and directionally dependent, with different response in tension and compression along the fiber direction. For such a material, the stored energy functions, W, depends upon five invariant metrics of the imposed strain state and the fiber direction. Explicit expressions for the stresses are derived for two polynomial functions of the five invariants for W. Homogeneous deformations such as simple extension, simple shear, and biaxial loading problems, nonhomogeneous deformations such as plane strain bending of a rectangle beam into a circular one, and inflation, twist and extension of a pressurized cylindrical laminate, are analyzed to reveal the mechanical behaviors descried by the developed material models. To enable the numerical solutions, the developed material models are incorporated in the commercial software, LS-DYNA, as user-defined subroutines. The implementations have been verified by ensuring that the computed solutions of several boundary value problems agree well with the derived analytical solutions or those available in the literature. The work provides theoretical guidelines for using quadratic polynomial functions for material models of FRRM, and delivers the software (user-defined material subroutines) capable of numerically analyzing large deformations of FRRM with different responses in tension and compressions. Large elasto-plastic deformations of T-peel joints have been analyzed using the commercial software, ABAQUS, to delineate conditions that result in self-similar debonding, enabling one to appropriately partition the energy involved in bending the adherends and propagating a debond. Using experimentally measured fracture energies from separate double cantilever beam (DCB) tests, implemented in a traction-separation law, accurate estimates of required peel force, crosshead displacements at break, and plastically deformed peel arm shapes are made. The demonstrated success of predicting load-displacement curves, deformed shape, and various energy metrics by using the traction-separation law in ABAQUS provides us with a framework to use in the future assessment of T-peel configurations being addressed in this study.

A determinação das propriedades mecânicas em materiais hiperelásticos constitui uma atividade complexa, a qual requer a realização de ensaios mecânicos em laboratório, seleção de modelos matemáticos adequados a cada tipo de comportamento e ajuste de curva sobre os dados experimentais. O ensaio biaxial por inflação se caracteriza pela inflação de uma membrana fina após a aplicação de uma pressão uniforme agindo na direção normal a superfície e tem sido utilizado para obter a curva tensão versus deformação. O objetivo do presente trabalho é estudá-lo como um teste para a caracterização mecânicas de borrachas incompressíveis. É proposta uma metodologia e aspectos como a aplicabilidade da teoria de cascas finas, geometria esférica no topo da amostra, instabilidade e processo de deformação são investigados. Um código computacional foi desenvolvido para identificação de parâmetros da amostra deformada através de aquisição de imagem. A validação da metodologia foi realizada tanto através de análises numéricas por elementos finitos como através de ensaios experimentais realizados em laboratório. Um novo método analítico para a determincação da deformação no topo membrana inflada (ou bolha) foi proposto e testado. / The determination of mechanical properties of hyperelastic materials is a complex activity, which requires mechanical laboratory tests to obtain the stress-strain curve, selection of the appropriate mathematical model and curve fitting of the experimental data. The biaxial inflation test is characterized by the inflation of a thin membrane by applying uniform pressure acting on the normal direction of the surface. The purpose of this paper is to study it as a test for characterization of incompressible rubberlike materials. A methodology is proposed and aspects such as the applicability of the theory of thin shell, spherical geometry on top of the sample, instability and kinematic deformation process are investigated. A computer code was developed for identification of parameters of the deformed specimen by image acquisition. The validation of the methodology was carried out through both numerical analysis by finite elements and through experimental testing performed in laboratory. A new analytic method to determine the deformation of the apex of the inflated membrane (or bubble) is proposed and tested.

A determinação das propriedades mecânicas em materiais hiperelásticos constitui uma atividade complexa, a qual requer a realização de ensaios mecânicos em laboratório, seleção de modelos matemáticos adequados a cada tipo de comportamento e ajuste de curva sobre os dados experimentais. O ensaio biaxial por inflação se caracteriza pela inflação de uma membrana fina após a aplicação de uma pressão uniforme agindo na direção normal a superfície e tem sido utilizado para obter a curva tensão versus deformação. O objetivo do presente trabalho é estudá-lo como um teste para a caracterização mecânicas de borrachas incompressíveis. É proposta uma metodologia e aspectos como a aplicabilidade da teoria de cascas finas, geometria esférica no topo da amostra, instabilidade e processo de deformação são investigados. Um código computacional foi desenvolvido para identificação de parâmetros da amostra deformada através de aquisição de imagem. A validação da metodologia foi realizada tanto através de análises numéricas por elementos finitos como através de ensaios experimentais realizados em laboratório. Um novo método analítico para a determincação da deformação no topo membrana inflada (ou bolha) foi proposto e testado. / The determination of mechanical properties of hyperelastic materials is a complex activity, which requires mechanical laboratory tests to obtain the stress-strain curve, selection of the appropriate mathematical model and curve fitting of the experimental data. The biaxial inflation test is characterized by the inflation of a thin membrane by applying uniform pressure acting on the normal direction of the surface. The purpose of this paper is to study it as a test for characterization of incompressible rubberlike materials. A methodology is proposed and aspects such as the applicability of the theory of thin shell, spherical geometry on top of the sample, instability and kinematic deformation process are investigated. A computer code was developed for identification of parameters of the deformed specimen by image acquisition. The validation of the methodology was carried out through both numerical analysis by finite elements and through experimental testing performed in laboratory. A new analytic method to determine the deformation of the apex of the inflated membrane (or bubble) is proposed and tested.

A determinação das propriedades mecânicas em materiais hiperelásticos constitui uma atividade complexa, a qual requer a realização de ensaios mecânicos em laboratório, seleção de modelos matemáticos adequados a cada tipo de comportamento e ajuste de curva sobre os dados experimentais. O ensaio biaxial por inflação se caracteriza pela inflação de uma membrana fina após a aplicação de uma pressão uniforme agindo na direção normal a superfície e tem sido utilizado para obter a curva tensão versus deformação. O objetivo do presente trabalho é estudá-lo como um teste para a caracterização mecânicas de borrachas incompressíveis. É proposta uma metodologia e aspectos como a aplicabilidade da teoria de cascas finas, geometria esférica no topo da amostra, instabilidade e processo de deformação são investigados. Um código computacional foi desenvolvido para identificação de parâmetros da amostra deformada através de aquisição de imagem. A validação da metodologia foi realizada tanto através de análises numéricas por elementos finitos como através de ensaios experimentais realizados em laboratório. Um novo método analítico para a determincação da deformação no topo membrana inflada (ou bolha) foi proposto e testado. / The determination of mechanical properties of hyperelastic materials is a complex activity, which requires mechanical laboratory tests to obtain the stress-strain curve, selection of the appropriate mathematical model and curve fitting of the experimental data. The biaxial inflation test is characterized by the inflation of a thin membrane by applying uniform pressure acting on the normal direction of the surface. The purpose of this paper is to study it as a test for characterization of incompressible rubberlike materials. A methodology is proposed and aspects such as the applicability of the theory of thin shell, spherical geometry on top of the sample, instability and kinematic deformation process are investigated. A computer code was developed for identification of parameters of the deformed specimen by image acquisition. The validation of the methodology was carried out through both numerical analysis by finite elements and through experimental testing performed in laboratory. A new analytic method to determine the deformation of the apex of the inflated membrane (or bubble) is proposed and tested.

En struktur analys på Ericssons MINILINK-6352 har utförts för att undersöka spänningar och deformationer på enheten, främst med fokus på de termiska gränskiktsmaterialen och buktningar av kretskortet. Dessa är viktiga aspekter när man överväger om enheten är termiska lämpad ur en mekanisk synvinkel, där god ytkontakt mellan de olika kropparna är avgörande för ordentlig kylning genom värmeledning. Analysen kräver tillräcklig materialdata till gränskiktsmaterialen och kretskortet för att kunna skapa lämpliga matematiska modeller. Enaxliga kompressionstester har genomförts för att karakterisera de hyperelastiska och viskoelastiska lagar för fyllda silikongummimaterial som används som termiska gränskiktsmaterial, som ibland kallas för gappad. Böjning av ett kretskort simulerades och jämfördes med ett tre--punkts böjtest för att verifiera om befintlig materialdata i beräkningsprogrammen var tillräcklig, jämförelsen visade god överensstämmelse. Kretskortet med dess komponenter, som modellerades som styva block, med gappads ovanpå som komprimeras av en platta simulerades och ett svagt område hittades. Detta område var sedan tidigare känt och har i ett senare skede eliminerats genom att tillsätta ytterligare en stödpelare. Därav visar denna studie en metod för att hitta intressanta regioner tidigt i konstruktionsfasen som lätt kan ändras för att uppfylla nödvändiga krav och undvika brister i konstruktionen. Arbetet har visat sig användbart genom att hitta detta svaga område i exempel produkten, arbetet ger även tillräckligt med information och exempeldata för att ytterligare utreda liknande produkter. Kombinationen av erfarenhet och simulering möjliggör smartare designval. / A structural analysis on Ericssons MINILINK-6352 has been performed in order to investigate stresses and deformations of the unit, mainly focusing on the thermal interface materials and warpage of the printed circuit boards. These are important aspects when considering if the unit is thermally adequate from a mechanical point of view, where good surface contact between various bodies are critical for proper cooling through heat conductivity. The analysis requires sufficient materal data for the interface material and the circuit board in order to create suitable mathematical models. Uniaxial compression tests have been conducted to characterise the hyperelastic and viscoelastic constitutive laws of a filled silicone rubber material used as a thermal interface material, commonly referred to as a thermal pad. Bending of a printed circuit board was simulated and compared to a three-point bend test on the circuit board in order to verify material data already available in the computational software, which showed good agreement. The entire radio unit was mechanically analysed during its sealing process. The circuit board with attached components modelled as stiff blocks with thermal pads on top compressed by plates was simulated and a weak area was found. This area in question was already known and has in a later stage been eliminated by adding an additional supporting pillar. Hence this study shows a methodology to find regions of interest at an early design phase which can easily be altered to fulfil necessary requirements and eliminate design flaws. This work has proven useful in finding weak regions in the example product, it also provides enough information and example data to further investigate similar products. The combination of experience and simulation allows for smarter design choices.