On finite bending of visco-hyperelastic materials: a novel analytical solution and FEM

In this paper, an analytical approach is proposed to examine the finite strain time-dependent behavior of incompressible, isotropic visco-hyperelastic elastomeric material under bending. Phenomenological hyperelastic invariant-based strain energy density function, Yeoh model, and N-termed Prony seri...

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Bibliographic Details
Published in:Acta mechanica 2020-08, Vol.231 (8), p.3435-3450
Main Authors: Shojaeifard, Mohammad, Sheikhi, Sara, Baniassadi, Majid, Baghani, Mostafa
Format: Article
Language:English
Subjects:
Bending moments
Classical and Continuum Physics
Computational fluid dynamics
Computer simulation
Constitutive models
Control
Creep recovery
Creep tests
Dynamical Systems
Elastomers
Engineering
Engineering Fluid Dynamics
Engineering Thermodynamics
Exact solutions
Finite element method
Flux density
Heat and Mass Transfer
Isotropic material
Mathematical models
Optimization
Original Paper
Polyamides
Prony series
Solid Mechanics
Strain
Stress concentration
Stress relaxation
Stress relaxation tests
Theoretical and Applied Mechanics
Three dimensional models
Time dependence
Vibration
Viscoelastic materials
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Summary:In this paper, an analytical approach is proposed to examine the finite strain time-dependent behavior of incompressible, isotropic visco-hyperelastic elastomeric material under bending. Phenomenological hyperelastic invariant-based strain energy density function, Yeoh model, and N-termed Prony series are utilized to define the strain-dependent and time-dependent parts of the visco-hyperelastic constitutive model, respectively. 3D finite element analysis of the problem is carried out using ABAQUS/Visco to verify the analytical solution results. Material parameters of polyurea are calibrated using an optimization framework for experimental results under five different strain rates, simultaneously. Two well-known tests of viscoelastic materials, stress relaxation and creep tests, are investigated both analytically and numerically. Distribution of the Cauchy stress components and the resultant bending moment versus time, and the variation of the mentioned results with different rise times and ultimate bent angles are provided for the stress relaxation test. Moreover, the strain and bending angle results are plotted in a creep test for different rise times and applied moments. Besides, a multi-step relaxation test and creep recovery test are performed for different loading conditions. Finite element method results confirm the analytical approach with great compatibility.
ISSN:0001-5970
1619-6937
DOI:10.1007/s00707-020-02733-4