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Search results for: MICROPOLAR CONTINUUM
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Jacek Tejchman prof. dr hab. inż.
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Extended micropolar approach within the framework of 3M theories and variations thereof
PublicationAs part of his groundbreaking work on generalized continuum mechanics, Eringen proposed what he called 3M theories, namely the concept of micromorphic, microstretch, and micropolar materials modeling. The micromorphic approach provides the most general framework for a continuum with translational and (internal) rotational degrees of freedom (DOF), whilst the rotational DOFs of micromorphic and micropolar continua are subjected...
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On Non-holonomic Boundary Conditions within the Nonlinear Cosserat Continuum
PublicationWithin the framework of the nonlinear micropolar elastic continuum we discuss non-holonomic kinematic boundary conditions. By non-holonomic boundary conditions we mean linear relations between virtual displacements and virtual rotations given on the boundary. Such boundary conditions can be used for modelling of complex material interactions in the vicinity of the boundaries and interfaces.
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Two- and three-dimensional elastic networks with rigid junctions: modeling within the theory of micropolar shells and solids
PublicationFor two- and three-dimensional elastic structures made of families of flexible elastic fibers undergoing finite deformations, we propose homogenized models within the micropolar elasticity. Here we restrict ourselves to networks with rigid connections between fibers. In other words, we assume that the fibers keep their orthogonality during deformation. Starting from a fiber as the basic structured element modeled by the Cosserat...
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A Nonlinear Model of a Mesh Shell
PublicationFor a certain class of elastic lattice shells experiencing finite deformations, a continual model using the equations of the so-called six-parameter shell theory has been proposed. Within this model, the kinematics of the shell is described using six kinematically independent scalar degrees of freedom — the field of displacements and turns, as in the case of the Cosserat continuum, which gives reason to call the model under consideration...
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ON DYNAMICS OF ELASTIC NETWORKS WITH RIGID JUNCTIONS WITHIN NONLINEAR MICRO-POLAR ELASTICITY
PublicationWithin the nonlinear micropolar elasticity we discuss effective dynamic (kinetic) properties of elastic networks with rigid joints. The model of a hyperelastic micropolar continuum is based on two constitutive relations, i.e., static and kinetic ones. They introduce a strain energy density and a kinetic energy density, respectively. Here we consider a three-dimensional elastic network made of three families of elastic fibers connected...
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On rotational instability within the nonlinear six-parameter shell theory
PublicationWithin the six-parameter nonlinear shell theory we analyzed the in-plane rotational instability which oc- curs under in-plane tensile loading. For plane deformations the considered shell model coincides up to notations with the geometrically nonlinear Cosserat continuum under plane stress conditions. So we con- sidered here both large translations and rotations. The constitutive relations contain some additional mi- cropolar parameters...
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On Dynamic Extension of a Local Material Symmetry Group for Micropolar Media
PublicationFor micropolar media we present a new definition of the local material symmetry group considering invariant properties of the both kinetic energy and strain energy density under changes of a reference placement. Unlike simple (Cauchy) materials, micropolar media can be characterized through two kinematically independent fields, that are translation vector and orthogonal microrotation tensor. In other words, in micropolar continua...