TY - JOUR

T1 - Efficient modeling of filled rubber assuming stress-induced microscopic restructurization

AU - Plagge, J.

AU - Ricker, A.

AU - Kröger, N. H.

AU - Wriggers, P.

AU - Klüppel, M.

N1 - Funding Information: This research was partially funded by the Arbeitsgemeinschaft industrieller Forschungsvereinigungen ”Otto von Guericke” e. V. (AiF) project ”Charakterisierung sowie Modellbildung zur Beschreibung von Kompressionsmoduli technischer Gummiwerkstoffe (19916 N). The authors thank Karsten Kruse, Hamburg Univerisity of Technology, Institute for Mathematics, for fruitful discussions related to the existence and uniqueness of Eq. (29).

PY - 2020/6

Y1 - 2020/6

N2 - The mechanical response of filled rubber depends on load history, strain rate and state, temperature and even direction of previous loading. Although there is a plurality of both physical and phenomenological models, only few are able to reproduce this rich spectrum of effects. Moreover, many of them suffer from physical or mathematical inconsistencies. We present a model, which is based on physical ideas and plausible assumptions about the material's microstructure, while being designed for high efficiency and robustness in finite element applications. It is shown by fits to extensive experimental data that it reproduces almost the full phenomenology of filled rubbers, both at low and high strains, for different deformation states and rates, holding times, and at different temperatures. The main modeling paradigm is the stress-induced breakdown and reorganization of microscopic structures which defines the time-dependent behavior of the material and allows to reproduce logarithmic relaxation effects. Moreover, its nine fit parameters evolve in a physically reasonable way under variation of filler and cross-linker content. A static limiting case of the model is derived, reducing the number of parameters and computational effort wherever necessary. Finally, a FE-implementation using computer-generated subroutines is presented and tested against experimental data of a simplified bushing under torsional, radial, cardanic and axial loading.

AB - The mechanical response of filled rubber depends on load history, strain rate and state, temperature and even direction of previous loading. Although there is a plurality of both physical and phenomenological models, only few are able to reproduce this rich spectrum of effects. Moreover, many of them suffer from physical or mathematical inconsistencies. We present a model, which is based on physical ideas and plausible assumptions about the material's microstructure, while being designed for high efficiency and robustness in finite element applications. It is shown by fits to extensive experimental data that it reproduces almost the full phenomenology of filled rubbers, both at low and high strains, for different deformation states and rates, holding times, and at different temperatures. The main modeling paradigm is the stress-induced breakdown and reorganization of microscopic structures which defines the time-dependent behavior of the material and allows to reproduce logarithmic relaxation effects. Moreover, its nine fit parameters evolve in a physically reasonable way under variation of filler and cross-linker content. A static limiting case of the model is derived, reducing the number of parameters and computational effort wherever necessary. Finally, a FE-implementation using computer-generated subroutines is presented and tested against experimental data of a simplified bushing under torsional, radial, cardanic and axial loading.

KW - Finite elements

KW - Finite strain

KW - Material softening

KW - Microstructures

KW - Rubber

KW - Viscoelasticity

UR - http://www.scopus.com/inward/record.url?scp=85087730543&partnerID=8YFLogxK

U2 - 10.1016/j.ijengsci.2020.103291

DO - 10.1016/j.ijengsci.2020.103291

M3 - Article

AN - SCOPUS:85087730543

VL - 151

JO - International Journal of Engineering Science

JF - International Journal of Engineering Science

SN - 0020-7225

M1 - 103291

ER -