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A one-dimensional computational model for hyperelastic string structures with Coulomb friction

: Shiryaev, Vladimir; Orlik, Julia


Mathematical Methods in the Applied Sciences 40 (2017), Nr.3, S.741-756
ISSN: 0170-4214
ISSN: 1099-1476
Deutsche Forschungsgemeinschaft DFG
DFG-Sachbeihilfe; OR 190/4-1
Mechanical multi-scale modeling and simulation of fiber structured materials
Fraunhofer ITWM ()

In this paper, we consider a new model for the simulation of textiles with frictional contact between fibers and no bending resistance. In the model, one-dimensional hyperelasticity and the Capstan equation are combined, and its connection with conventional hyperelasticity and Coulomb friction models is shown. Then, the model is formulated as a problem with the rate-independent dissipation, and we prove that the problem possesses proper convexity and continuity properties. The article concludes with a numerical algorithm and provides numerical experiments along with a comparison of the results with a real measurement.