Introducing the concept of directly connected rheological elements by reviewing rheological models at large strains. (15th October 2016)

• Record Type: Journal Article
• Authors: Kießling, R.; Landgraf, R.; Scherzer, R.; Ihlemann, J.
• Is Part Of: International journal of solids and structures. Volume 97/98(2016)
• Page Start: 650
• Page End: 667
• Publication Date: 2016-10-15
• Subjects: Material modelling -- Rheological models -- Large strains -- Multiplicative viscoplasticity; Mechanics, Applied -- Periodicals; Structural analysis (Engineering) -- Periodicals; Elastic solids -- Periodicals; Mécanique appliquée -- Périodiques; Constructions, Théorie des -- Périodiques; Solides élastiques -- Périodiques; Elastic solids; Mechanics, Applied; Structural analysis (Engineering); Periodicals; 624.18
• DOI: 10.1016/j.ijsolstr.2016.04.023
• Languages: English
• ISSNs: 0020-7683

Abstract

Abstract: Rheological models are often used to exemplify the structure of phenomenological material models. For this purpose, different elements, representing elastic, viscous or plastic material behaviour, are combined in parallel and series connections. This article introduces a concept to material modelling within the framework of multiplicative decomposition of the deformation gradient. Thereby, the basic idea of rheological connections is directly applied. Assuming the additive decomposition of the stress power, relations for parallel as well as series connections are derived and the thermodynamic consistency of the concept is proved. To exemplify the modelling concept, an existing viscoplastic model of overstress type, which is motivated by a rheological model, is reviewed and reproduced. To this end, specific nonlinear material models representing elastic, viscous and plastic material behaviour are applied in a thermodynamically consistent manner and the connection relations are evaluated. Finally, a numerical procedure is proposed, which implements the connection relations directly rather than solving the evolution equations for inelastic strains. Both the analytical derivation and the numerical procedure based on the connection relations yield equal results compared to standard methods, which highlights the applicability of the presented concept for the development of models of multiplicative inelasticity at large strains.