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Justification of Homogenized Models for Viscoplastic Bodies with Microstructure

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Deformation and Failure in Metallic Materials

Part of the book series: Lecture Notes in Applied and Computational Mechanics ((LNACM,volume 10))

Abstract

We justify the formal homogenization of the quasistatic initial boundary value problem with internal variables, called the microscopic problem, which models the deformation behavior of viscoplastic bodies. To this end it is first shown that the formally derived homogenized initial-boundary value problem has a solution. From this solution an asymptotic solution of the microscopic problem is constructed, and it is shown that the difference of the exact solution and the asymptotic solution tends to zero if the length scale of the microstructure converges to zero. Our results are proved for viscoplastic material behavior that can be modeled by constitutive equations of monotone type with linear hardening terms. For technical reasons we are only able to prove the convergence result locally in time and for smooth data.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Darmstadt University of Technology, Schlossgartenstr. 7, D-64289, Darmstadt, Germany

    Hans-Dieter Alber

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  1. Hans-Dieter Alber
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Editors and Affiliations

  1. Department of Mechanics, Technical University of Darmstadt, Hochschulstr. 1, D-64289, Darmstadt, Germany

    Kolumban Hutter  & Herbert Baaser  & 

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Alber, HD. (2003). Justification of Homogenized Models for Viscoplastic Bodies with Microstructure. In: Hutter, K., Baaser, H. (eds) Deformation and Failure in Metallic Materials. Lecture Notes in Applied and Computational Mechanics, vol 10. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-36564-8_12

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  • DOI: https://doi.org/10.1007/978-3-540-36564-8_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-05649-9

  • Online ISBN: 978-3-540-36564-8

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