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Abstract: A nonlinear semi-numeric and finite element analysis of three-point bending tests of notched polymer fiber-reinforced concrete prisms was performed. The computational and experimental results were compared in terms of the load-displacement behavior. The vertical midspan displacement and the crack mouth opening displacement results were considered. The nonlinear semi-numeric computational procedure involved the moment-curvature relation, calculated by considering the constitutive material law from the fib Model Code for Concrete Structures 2010, and considered a plastic hinge mechanism to simulate the cracked region behavior. Two sets of tensile mechanical properties were considered for the constitutive material law: back-calculated (by an inverse analysis) tensile strength properties from the experimental results, and tensile strength properties calculated by simplified expressions from the fib Model Code for Concrete Structures 2010. Other mechanical properties were determined by additional compressive tests and standard relations for the dependency of various mechanical properties on the concrete compressive strength. The nonlinear finite element analysis incorporated the Menetrey-Willam material model to simulate the fiber-reinforced concrete behavior. The nonlinear semi-numeric analysis load-displacement results based on the back-calculated tensile strength properties relatively accurately matched with the experimental results, whereas the nonlinear semi-numeric analysis load-displacement results based on tensile strength properties calculated by simplified expressions from the fib Model Code for Concrete Structures 2010 and the nonlinear finite element analysis load-displacement results showed certain shortcomings.
Keywords: polymer fiber-reinforced concrete, moment-curvature relation, nonlinear plastic hinge, load-displacement relation, crack width, nonlinear analysis, finite element analysis, Menetrey-Willam material model, three-point bending test, compressive test
Published in DKUM: 19.02.2024; Views: 350; Downloads: 18
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Abstract: Topological defects (TDs) appear almost unavoidably in continuous symmetry breaking phase transitions. The topological origin makes their key features independent of systems' microscopic details; therefore TDs display many universalities. Because of their strong impact on numerous material properties and their significant role in several technological applications it is of strong interest to find simple and robust mechanisms controlling the positioning and local number of TDs. There are strong evidences that in physics the fields are fundamental entities of nature and not particles. If this is the case then topological defects (TDs) might play the role of fundamental particles. An adequate testing ground to study and gain fundamental understanding of TDs are nematic liquid crystals. We present a numerical study of TDs within effectively two dimensional closed soft films exhibiting in-plane orientational ordering. Popular examples of such class of systems are liquid crystalline shells and various biological membranes. We analyze the impact of extrinsic and intrinsic curvature on positions of topological defects (TDs) in two-dimensional (2D) nematic films. We demonstrate that both these curvature contributions are commonly present and are expected to be weighted by comparable elastic constants. A simple Landau-de Gennes approach in terms of tensor nematic order parameter is used to numerically demonstrate impact of the curvatures on position of TDs on 2D ellipsoidal nematic shells. We introduce the Effective Topological Charge Cancellation mechanism controlling localised positional assembling tendency of TDs and the formation of pairs (defect,antidefect) on curved surfaces. Furthermore, we estimate a critical depinning threshold to form pairs (defect,antidefect) using the electrostatic analogy. Finally, we show how one could efficiently switch among qualitatively different structures by using a relative volume of ordered shells, which represents a relatively simple naturally accessible control parameter. In doctoral thesis, we developed theoretical model of erythrocyte membrane by using a hybrid Helfrich-Landau type mesoscopic approach, taking into account in-plane membrane ordering. We demonstrate that the derived extrinsic membrane energy term, which strongly depends on the local orientations of the molecules, is essential for the predicted broadening of the range of the relative volumes corresponding to the stable discocyte shapes, which is otherwise very narrow if only intrinsic curvature energy term dominates.
Keywords: Topological defects, Continuum fields, Nematic liquid crystals, Biological membranes, Nematic shells, Landau-de Gennes formalism, Topological charge, Nanoparticles, Gaussian curvature, Electrostatic analogy, Intrinsic curvature, Extrinsic curvature, Crystal growth nucleation, Relative volume
Published in DKUM: 09.03.2018; Views: 2391; Downloads: 241
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Abstract: Effectively, two-dimensional (2D) closed films exhibiting in-plane orientational ordering (ordered shells) might be instrumental for the realization of scaled crystals. In them, ordered shells are expected to play the role of atoms. Furthermore, topological defects (TDs) within them would determine their valence. Namely, bonding among shells within an isotropic liquid matrix could be established via appropriate nano-binders (i.e., linkers) which tend to be attached to the cores of TDs exploiting the defect core replacement mechanism. Consequently, by varying configurations of TDs one could nucleate growth of scaled crystals displaying different symmetries. For this purpose, it is of interest to develop a simple and robust mechanism via which one could control the position and number of TDs in such atoms. In this paper, we use a minimal mesoscopic model, where variational parameters are the 2D curvature tensor and the 2D orientational tensor order parameter. We demonstrate numerically the efficiency of the effective topological defect cancellation mechanism to predict positional assembling of TDs in ordered films characterized by spatially nonhomogeneous Gaussian curvature. Furthermore, we show how one could efficiently switch among qualitatively different structures by using a relative volume v of ordered shells, which represents a relatively simple naturally accessible control parameter.
Keywords: topological defects, Gaussian curvature, self-assembling, crystal growth nucleation
Published in DKUM: 20.07.2017; Views: 1288; Downloads: 463
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Abstract: We studied biological membranes of spherical topology within the framework of the spontaneous curvature model. Both Monte Carlo simulations and the numerical minimization of the curvature energy were used to obtain the shapes of the vesicles. The shapes of the vesicles and their energy were calculated for different values of the reduced volume. The vesicles which exhibit inplane ordering were also studied. Minimal models have been developed in order to study the orientational ordering in colloids coated with a thin sheet of nematic liquid crystal (nematic shells).The topological defects are always present on the surfaces with the topology of a sphere.The location of the topological defects depends strongly on the curvature of the surface. We studied the nematic ordering and the formation of topological defects on vesicles obtained by the minimization of the spontaneous curvature energy.
Keywords: biological membranes, vesicles, spontaneous curvature model, Monte Carlo simulations, nematic shells, orientational ordering, topological defects
Published in DKUM: 14.06.2017; Views: 1285; Downloads: 396
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Abstract: In this thesis we introduce the problem of the ideal homogeneous hanging cable called the catenary. We observe the behaviour of the shape of the curve. Firstly, we solve the problem of the classical catenary on a flfat Earth, where the gravitational fifield is constant and perpendicular to the ground. Secondly, we focus on the true symmetric catenary in the central gravitational fifield, which comes from the -1/r potential. In both cases we use the method of calculus of variations for isoperimetric problems and in particular the Euler-Lagrange difffferential equation. Lastly, we explain the problem of the asymmetric case.
Keywords: Catenary, calculus of variations, Euler-Lagrange equation, curvature, potential energy, difffferential equation.
Published in DKUM: 25.09.2013; Views: 2336; Downloads: 184
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