54 research outputs found

    On material-convective elasto-plasticity

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    A material-convective continuum formulation is presented which differs significantly from the finite elasto-plasticity descriptions of general-purpose finite element simulation tools like Dyna3D, Abaqus, Marc, etc. The material-convective continuum formulation offers physical significance in particular with respect to the geometrical interpretation of the (plastic) deformation tensors—in contrast to the so-called Updated Lagrangian Formulation of general-purpose finite element simulation tools which is unphysical due to its inaccurate (directional non-convective) integration of the (plastic) deformation increments: this inaccurately integrated (plastic) deformation does not obey the geometrical interpretation of proper (plastic) deformation tensors and may even lead to a violation of the first fundamental law of thermodynamics, the conservation of energy. The material-convective time integrals are the reverse of the material-convective time derivatives, and the only material-convective time derivative of a symmetric second-order Eulerian tensor is its Green-Naghdi rate which is rotationally and translationally convected with the material

    On the Multiplicative Logarithmic Strain Space Formulation

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    A new constitutive approach to finite-deformation formulations of elasto-plasticity (with isotropic thermal expansion) is presented, which is well-suited to a broad range of metals used for industrial applications. The constitutive equations are formulated within the logarithmic strain space. The coupling of elasticity, plasticity and thermal expansion is based on a multiplicative approach of commutative-symmetric stretch tensor products with symmetrizing rotation tensors in the middle of two symmetric stretch tensors. It is essential for finite-deformation formulations to refer to an appropriate reference configuration K0 in order to model material orthotropy correctly (and not to mix up material / physical anisotropy with deformation-induced / geometrical anisotropy). Furthermore, it is essential to define proper stretch and strain tensors which are geometrical interpretable, i.e. which only depend on a current  K and a reference K0 configuration (and not on the geometrical deformation path between these configurations). Therefore, all stretch and strain tensors are defined with respect to the same reference configuration K0, the total stretches and strains as well as the partial ones: the elastic, plastic and thermal stretches and strains. And these reference configurations should be the appropriate ones, where—in the case of fiber-reinforced (metal) bodies—the fibers are placed orthogonal to each other or where Walter Noll’s symmetry group considerations characterize the physical nature of materials with their most specificity as: orthotropic, transversal isotropic or fully isotropic

    Analytical assessment of the load carrying capacity of axially loaded wooden reinforced tubes

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    As a natural resource, an efficient use of wood should be also a requirement for structural timber design, but the usual structural solid sections do not achieve the required optimal behaviour. The performance of the structural elements (serviceability and strength) depends not only on the material properties, but mainly on the moment of inertia of the cross section. The Timber Construction Institute of Technische Universitát Dresden has developed a process for the manufacture of structural wood profiles. The resulting profiles combine economy, an efficient use of the material and optimal structural performance. They are externally reinforced with composite fibres, which improve the mechanical characteristics of the wood and protect it from weathering. The available experimental tests to axial loading show the outstanding properties of this new technology. Herein, the preliminary model developed to obtain the axial strength of longitudinally compressed tubes is presented. Two different analytical algorithms are discussed and applied. The model adequately predicts the axial strength of fibre reinforced wood profiles. The analytical results are within an error less than 10% to the available experimental results, with a mean error ratio less than 3%
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