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Biaxial Loading of Continuously Graded Thermoviscoplastic Materials

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Abstract

In this paper we study the problem of biaxial loading of a sheet made of a continuously graded thermoviscoplastic material. The material phases are supposed to exhibit thermal softening, strain-rate sensitivity and strain hardening, continuously varying along all directions. First we formulate the plane stress problem of a non-homogeneous material and study the behavior of temperature, strain and strain-rate related to inhomogeneities of thermomechanical parameters and geometrical defects. Next we present the “effective” instability analysis of Dudzinski and Molinari (Int J Solids Struc 1991), adapted to the non-homogeneous case, to define the critical conditions and select the localization modes by studying the overall strains for which a certain level of instability growth is developed. Finally, we present the numerical simulation of the fully non-linear dynamical problem. Several aspects of the deformation process and the related role of non-homogeneities are analyzed onset of strain and temperature localization, ductility, contours of temperature increase as detectors of instability, interplay with initial defects, multiple necking, decrease of thinning-rate, variation of the multiple necking due to boundary conditions.

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Authors and Affiliations

  1. Department of Civil Engineering, Aristotle University of Thessaloniki, 541 24, Thessaloniki, Greece

    George Chatzigeorgiou & Nicolas Charalambakis

  2. Department of Mathematics, Division of Applied Mathematics and Mechanics, University of Ioannina, 45110, Ioannina, Greece

    Vassilios Kalpakides

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  1. George Chatzigeorgiou
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  2. Nicolas Charalambakis
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  3. Vassilios Kalpakides
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Correspondence to Nicolas Charalambakis.

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Chatzigeorgiou, G., Charalambakis, N. & Kalpakides, V. Biaxial Loading of Continuously Graded Thermoviscoplastic Materials. Comput Mech 39, 335–355 (2007). https://doi.org/10.1007/s00466-006-0030-4

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