published_or_final_version / Mechanical Engineering / Doctoral / Doctor of Philosophy

published_or_final_version / Mechanical Engineering / Master / Master of Philosophy

published_or_final_version / Mechanical Engineering / Master / Master of Philosophy

In the research undertaken a finite element formulation has been developed for an elastodynamic problem using a least squares approach. The special requirements of the problem demanded a study of suitability of various elements. The emergence of the final element is a result of both theoretical and numerical study of three different elements. The approximation function is assumed on the basis of the order of the governing differential equations. Then the square of the error resulting from the approximate solution is minimized over the entire domain as well as the boundaries in the same functional. The element equation emerging from the formulation does not yield a singular stiffness matrix, since the boundary conditions are already taken into account in the element equation. The formulation presented in this thesis is only for the normal propagation of phi-wave. A finite element code has been developed based on the new formulation.

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Orientador: José Luiz Antunes de Oliveira e Sousa / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Civil, Arquitetura e Urbanismo / Made available in DSpace on 2018-08-26T02:16:10Z (GMT). No. of bitstreams: 1 GeadosSantos_FabioLuis_M.pdf: 8564383 bytes, checksum: 72e9522142ccde293049d4563ab69368 (MD5) Previous issue date: 2014 / Resumo: Nos últimos anos, o aumento no número de construções mais altas e complexas fez com que o estudo das propriedades mecânicas do concreto na ruptura em tração fosse foco de muitas pesquisas. O concreto desenvolve, durante o carregamento, diferentes processos de coalescência e crescimento de micro-fissuras e, devido a sua natureza heterogênea, um enorme esforço ainda é requerido para o desenvolvimento de um modelo constitutivo capaz de descrever aspectos relevantes do seu comportamento. A essa premissa soma-se a discussão da validade dos procedimentos de ensaio em descrever o comportamento real do material, devido à influência estrutural (forma da geometria, condições de contorno e tamanho) do espécime de teste. O comportamento quase-frágil do concreto, caracterizado pelo desenvolvimento de uma zona de processos inelásticos e/ou zona de processos de fratura (ZPF) ao redor do fronte da trinca, quando na ruptura em tração, requer uma lei constitutiva ¿ chamada lei coesiva, curva tensão-abertura de fissura (? ¿ w), curva de amolecimento ou função coesiva (?=f(w)) ¿ que relaciona a tensão desenvolvida no fronte da fratura, isto é na ZPF, e a sua abertura como ingrediente para modelagem da nucleação e da propagação da fratura, seja esta representada de maneira implícita e/ou explícita. Desenvolveu-se um software para a determinação automática da lei constitutiva utilizando-se curvas da relação carga versus abertura da boca fratura (load versus crack mouth opening displecement ¿ P-CMOD) ou da relação carga versus deslocamento no ponto de aplicação (P-?) obtidas em ensaios com vigas prismáticas ranhuradas em flexão em três pontos (Three-Point-Bend Test), com taxas de carregamento variada. O objetivo desse trabalho é avaliar a lei coesiva-viscosa proposta por Rosa et al. (2012) utilizando o software desenvolvido para o ajuste de curvas P-? numéricas com curvas de vigas ranhuradas de concreto de alta resistência, ensaiadas com taxas de carregamento variando da ordem de ? ?=?10?^(-5) mm/s a ? ?=?10?^(+1) mm/s / Abstract: In recent years, the increase of high and more complex constructions, many researches focus on the study of the mechanical properties of concrete at failure. The concrete under loading develops different processes of coalescence and growth of micro-cracks, and due to its heterogeneous nature, a great effort is still required to develop a constitutive model capable of describing the relevant aspects of its behavior. In addition to this premise is the discussion of validity of tests that describe the real behavior of the material, due to the structural influence (shape of the geometry, boundary conditions and size) of the test specimen. The quasi-brittle behavior of concrete, characterized by the development of a zone of inelastic processes and/or fracture processes (ZPF) around the crack front at failure, requires a constitutive law ¿ called cohesive law curve stress-crack opening (? ¿ w), softening or cohesive function (?=f(w)) ¿ curve that relates the stress developed across the front of the fracture, i. e., the ZPF, and its opening displacement as an ingredient for modeling fracture nucleation and propagation, represented implicitly and/or explicitly. A software developed for automatic determination of a constitutive law using curves of load versus relative fracture mouth opening (P-CMOD) or the load versus displacement relationship at the application line (P-?) obtained in tests with notched prismatic beams in Three-point Bend Test, with varying loading rates. This study aims at the evaluation of the viscous-cohesive model proposed by Rosa et al. (2012), using a software developed for the curve fitting P-? numerical curve with notch beams of high strength concrete, tested with loading rate numerical in the order between ? ?=?10?^(-5) mm/s and ? ?=?10?^(+1) mm/s / Mestrado / Estruturas e Geotécnica / Mestre em Engenharia Civil

The aims of this thesis are to study the fracture behaviour in unreinforced masonry, to carry out a limited experimental program on three-point bending (TPB) masonry panels and to develop a time-dependent fracture formulation for the study of mode I fracture in quasi-brittle materials. A micro-model for fracture in unreinforced masonry is developed using the concept of the discrete crack approach. All basic masonry failure modes are taken into account. To capture brick diagonal tensile cracking and masonry crushing, a linear compression cap is proposed with a criterion for defining the compression cap. The failure surface for brick and brick-mortar interfaces are modelled using a Mohr-Coulomb failure surface with a tension cut-off and a linear compression cap. The fracture formulation, in nonholonomic rate form within a quasi-prescribed displacement approach, is based on a piecewise-linear constitutive law and is in the form of a so-called ?linear complementarity problem? (LCP). The proposed model has been applied to simulating fracture in masonry shear walls and masonry TPB panels. An experimental program was undertaken to investigate the failure behaviour of masonry panels under TPB with relatively low strength mortar. The basic material parameters were obtained from compression, TPB and shear tests on bricks, mortar and brick-mortar interfaces. The experimental results showed that the failure of masonry TPB panels is governed by both tensile and shear failure rather than just tensile failure. The simulation of the masonry TPB tests compared well with the experimental results. In addition, the LCP fracture formulation is enhanced to study the time-dependent mode I fracture in quasi-brittle materials. Two main time-dependent sources, the viscoelasticity of the bulk material and the crack rate dependent opening, are taken into account. A simplified crack rate model is proposed to include the rate-dependent crack opening. The model is applied to predicting time-dependent crack growth in plain concrete beams under sustained loading. The model captures the essential features including the observed strength increase with loading rate, the load-deflection and load-CMOD responses, the deflection-time and CMOD-time curves, the predicted time to failure and the stress distributions in the fracture zone.

The aims of this thesis are to study the fracture behaviour in unreinforced masonry, to carry out a limited experimental program on three-point bending (TPB) masonry panels and to develop a time-dependent fracture formulation for the study of mode I fracture in quasi-brittle materials. A micro-model for fracture in unreinforced masonry is developed using the concept of the discrete crack approach. All basic masonry failure modes are taken into account. To capture brick diagonal tensile cracking and masonry crushing, a linear compression cap is proposed with a criterion for defining the compression cap. The failure surface for brick and brick-mortar interfaces are modelled using a Mohr-Coulomb failure surface with a tension cut-off and a linear compression cap. The fracture formulation, in nonholonomic rate form within a quasi-prescribed displacement approach, is based on a piecewise-linear constitutive law and is in the form of a so-called ?linear complementarity problem? (LCP). The proposed model has been applied to simulating fracture in masonry shear walls and masonry TPB panels. An experimental program was undertaken to investigate the failure behaviour of masonry panels under TPB with relatively low strength mortar. The basic material parameters were obtained from compression, TPB and shear tests on bricks, mortar and brick-mortar interfaces. The experimental results showed that the failure of masonry TPB panels is governed by both tensile and shear failure rather than just tensile failure. The simulation of the masonry TPB tests compared well with the experimental results. In addition, the LCP fracture formulation is enhanced to study the time-dependent mode I fracture in quasi-brittle materials. Two main time-dependent sources, the viscoelasticity of the bulk material and the crack rate dependent opening, are taken into account. A simplified crack rate model is proposed to include the rate-dependent crack opening. The model is applied to predicting time-dependent crack growth in plain concrete beams under sustained loading. The model captures the essential features including the observed strength increase with loading rate, the load-deflection and load-CMOD responses, the deflection-time and CMOD-time curves, the predicted time to failure and the stress distributions in the fracture zone.