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Journal of Applied Mathematics
Volume 2013, Article ID 840936, 5 pages
Research Article

Semiholonomic Second Order Connections Associated with Material Bodies

Institute of Mathematics, Faculty of Mechanical Engineering, Brno University of Technology, Technická 2, 616 69 Brno, Czech Republic

Received 24 August 2012; Revised 12 November 2012; Accepted 13 November 2012

Academic Editor: Baolin Wang

Copyright © 2013 Jaroslav Hrdina and Petr Vašík. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The thermomechanical behavior of a material is expressed mathematically by means of one or more constitutive equations representing the response of the body to the history of its deformation and temperature. These settings induce a set of connections which can express local properties. We replace two of them by a second order connection and prove that the holonomity of this connection classifies our materials.