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Automatic analysis of the stress‐strain response of rheological models
Author(s) -
Schultz Timm,
Müller Ralf
Publication year - 2019
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201900232
Subject(s) - rheology , viscoelasticity , constitutive equation , laplace transform , hierarchy , computer science , domain (mathematical analysis) , stress (linguistics) , algorithm , mathematics , mathematical analysis , finite element method , materials science , structural engineering , engineering , linguistics , philosophy , economics , market economy , composite material
Viscoelastic material behaviour can be represented by rheological models combining elastic and viscous rheological elements. These combinations can be serial and parallel connections of such elements as well as combinations of both. A method based on transfer functions formulated in the Laplace domain allows the calculation of constitutive equations of serial and parallel connections by a simple summation. Furthermore the use of a breadth‐first search algorithm for the analysis of complex systems of rheological elements is explained. By using this search algorithm a hierarchy of nested connections in a system can be found. This hierarchy guarentees dependencies are satisfied during the calculation of constitutive equations and signal propagation through the system.