An operator based notation of the Lagrange equations for systems with non‐material boundary conditions

Problems with non‐material boundary conditions are very important in many applications of continuum mechanics: for example rolling contact, calenders, breaking disks, band saws and belts. This paper deals with the LAGRANGE‐equation for non‐material boundary conditions. Such boundary conditions can be described by non‐material control volumes that cannot be assigned for one and only one set of particles over time. To define these volumes, a fictitious body is used. Within the scope of this paper several configurations are introduced for the definition of the location of the original and fictitious particles. With the help of the used operator notation it is possible to demonstrate a consistent representation of derivative operators and assign operators as well as entities to their configurations. On this basis, the LAGRANGE‐equation is derived for material and non‐material control volumes in the EULERIAN and LAGRANGIAN representation. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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