This thesis addresses normal axisymmetric contact of dissimilar elastic solids at finite interfacial friction. It is shown that in the case of smooth and convex but otherwise arbitrary contact profiles and monotonically increasing loading a single stick-slip contour evolves being independent of loading and profile geometry. This allows developing an incremental procedure based on a reduced problem corresponding to frictional rigid flat punch indentation of an elastic half-space. The reduced problem, being independent of loading and contact region, was solved by a finite element method based on a stationary contact contour and characterized by high accuracy. Subsequently, a tailored cumulative superposition procedure was developed to resolve the original problem to determine global and local field values for two practically important geometries: flat and conical profiles with rounded edges and apices. Results are given for relations between force, depth and contact contours together with surface stress distributions and maximum von Mises effective stress, in particular to predict initiation of fracture and plastic flow. It is also observed that the presence of friction radically reduces the magnitude of the maximum surface tensile stress, thus retarding brittle fracture initiation. Hertzian fracture through indentation of flat float glass specimens by steel balls has been examined experimentally for a full load cycle. It has been observed that if the specimen survived during loading to a maximum level it frequently failed at decreasing load. It has been proposed by Johnson et al. (1973) that the underlying physical cause of Hertzian fracture initiation during load removal is that at unloading frictional tractions reverse their sign over part of the contact region. Guided by these considerations a robust computational procedure has been developed to determine global and local field values in particular at unloading at finite friction. In contrast to the situation at monotonically increasing loading, at unloading invariance properties are lost and stick-slip regions proved to be severely history dependent and in particular with an opposed frictional shear stress at the contact boundary region. This causes an increase of the maximum tensile stress at the contour under progressive unloading. It is shown that the experimental observations concerning Hertzian fracture initiation at unloading are at least in qualitative correlation with the effect friction has on the maximum surface tensile stress. A contact cycle between two dissimilar elastic bodies at finite Coulomb friction has been further investigated analytically and numerically for a wider range of material parameters and contact geometries. With the issue of Hertzian fracture initiation in mind, results concerning the influence of the friction coefficient and compliance parameters on the absolute maximum surface tensile stress during a frictional contact cycle are reported along with the magnitudes of the relative increase of maximum tensile stresses at unloading. Based on a critical stress fracture criterion it is discussed how the predicted increases will influence the critical loads required for crack initiation. Fracture loads are measured with steel and tungsten carbide spherical indenters in contact with float glass specimens at monotonically increasing loading and during a load cycle. Computational predictions concerning the fracture loads are given based on Hertz and frictional contact theories combined with a critical stress fracture criterion. The computational results obtained for frictional contact are shown to be in better agreement with experimental findings as compared to the predictions based on the Hertz theory. The remaining quantitative discrepancy was attributed to the well-known fact that a Hertzian macro-crack initiates from pre-existing defects on the specimen’s surface. In order to account for the influence of the random distribution of these defects on the fracture loads at monotonic loading, Weibull statistics was introduced. The predicted critical loads corresponding to 50% failure probability were found to be in close agreement with experimentally observed ones. / QC 20100729

Electro-active polymers (EAPs) have emerged as a new class of active materials, which produce large deformations in response to an electric stimulus. EAPs have attractive characteristics of being lightweight, inexpensive, stretchable, and flexible. Additionally, EAPs are conformable, and their properties can be tailored to satisfy a broad range of requirements. These advantages have enabled many target applications in actuation and sensing. A general constitutive formulation for isotropic and anisotropic electro-active materials is developed using continuum mechanics framework and invariant theory. Based on the constitutive law, electromechanical stability of the electro-elastic materials is investigated using convexity and polyconvexity conditions. Implementation of the electro-active material model into a commercial finite element software (ABAQUS 6.9.1, PAWTUCKET, RI, USA) is presented. Several boundary and initial value problems are solved to investigate the actuation and sensing response of isotropic and anisotropic dielectric elastomers (DEs) subject to combined mechanical and electrical loads. The numerical response is compared with experimental results to validate the theoretical model. For the constitutive formulation of the electro-elastic materials, invariants for the coupling between two families of electro-active fibers (or particles) and the applied electric field are introduced. The effect of the orientation of the electro-active fibers and the electric field on the electromechanical coupling is investigated under equibiaxial extension. Advantage of the constitutive formulation derived in this research is that the electromechanical coupling can be illustrated easily by choosing invariants for the deformation gradient tensor, the electro-active fibers, and the electric field. For the electromechanical stability, it is shown that the stability can be controlled by tuning the material properties and the orientation of the electro-active fibers. The electromechanical stability condition is useful to build a stable free energy function and prevent the instabilities (wrinkling and electric breakdown) for the electro-elastic materials. The invariant-based constitutive formulation for the electro-elastic materials including the isotropic and anisotropic DEs is implemented into a user subroutine (UMAT in ABAQUS: user defined material) by using multiplicative decomposition of the deformation gradient and the applicability of the UMAT is shown by simulating a complicated electromechanical coupling problem in ABAQUS/CAE. Additionally, the static and dynamic sensing and actuation response of tubular DE transducers (silicone and polyacrylate materials) with respect to combined electrical and mechanical stimuli is obtained experimentally. It is shown that the silicone samples have better dynamic and static sensing characteristics than the polyacrylate. The theoretical modeling accords well with the experimental results. / Ph. D.

[pt] Simula-se numericamente o fenômeno de estricção em um bloco sob tração. Supõe-se que o material seja hiperelástico, isotrópico e que tenha uma lei de comportamento descrita pelo modelo de Blatz e Ko para espuma de borracha de poliuretano. Discretiza-se o problema de problema de equilíbio utilizando o Método dos Elementos Finitos clássico. A pesquisa das soluções é realizada por meio da implementação de uma Técnica de Continuação de Euler-Newton, que permite abordar situações onde instabilidades mecânicas, tais como a localização de deformações e o amolecimento, estejam presentes. Finalmente, identifica-se as regiões do material onde estas instabilidades ocorrem. / [en] The phenomenon of necking is numerically simulated for a block under traction tensile test. A hyperelastic, isotropic constitutive model, developed by Blatz and Ko for the description of some foamed polyurethane elastomers, is considered. An Euler-Newton Continuation Algorithm is employed in the search for solutions of the equilibrium problem, which is discretized by means of a classical Finite Element Method. This algorithm makes possible tha treatment of situations where mechanical instabilities, such as localization and strain-softening behaviors, are present. Finally, the regions of material, where these instabilities appear, are identified.