Nonlinear Mechanics of Hyperelastic Structures
Date
2023
Authors
Khaniki, Hossein Bakhshi
Editors
Advisors
Ghayesh, Mergen
Chin, Rey
Chin, Rey
Journal Title
Journal ISSN
Volume Title
Type:
Thesis
Citation
Statement of Responsibility
Conference Name
Abstract
Soft flexible structures have been an important part of many operating systems used
by humans in their daily routines. These structures are more likely to undergo large
strains and deformation when facing different types of loads, and return to their
initial shape when the load is removed. Most structures show a linear stress-strain
behaviour only when the strain deformation is significantly small. However, to have
a proper analysis of structures facing large strains, it is important to have better
and more accurate modelling of their stress-strain behaviour. Rubbers, elastomers,
silicones and polymeric-based structures are capable of undergoing large deformations,
which mostly show a nonlinear elastic behaviour. Hyperelastic structures are
labelled as structures made of non-linear elastic materials that can be modelled following
a proper strain energy density function model. The significant capabilities of
soft structures, such as infinite degrees of freedom, smooth motion, and safe humanmachine
interactions, make them ideal for soft robotics, biomechanics, automotive
applications, and wearable devices.
In view of the recognition of the capabilities of nonlinear elastic structures, most
studies in this field are directed towards their application purposes (e.g., applications
of non-linear elastic structures for developing soft robots, wearable devices, packaging,
etc.). However, the need to comprehend their mechanical behaviour in order
to have a better understanding of the structure’s response and, hence, develop optimised
designs for hyperelastic structures, has only recently been fully understood.
Therefore, this thesis intends to present a comprehensive study of the nonlinear
mechanics of different isotropic hyperelastic structures under different conditions,
mainly focusing on their nonlinear dynamics behaviour. This thesis is organised using
published papers in prestigious peer-reviewed international journals as outcomes
of the research.
Paper 1: A detailed review of the static deformation of hyperelastic structures
is presented in this paper, focusing on biological tissues and polymeric structures.
The main objective of this review paper is to show the application of different
hyperelastic strain energy density models for modelling the bending and buckling
behaviour of nonlinear elastic structures. For biological structures, a wide range
of tissues including brain, artery, cartilage, liver, skeletal muscle, ligament, skin,
tongue, heel pad and adipose tissue are discussed and for polymeric structures,
beam, column, tube, plate shell and membrane hyperelastic structures are analysed.
Paper 2: The most well-known hyperelastic strain energy density models for
analysing soft isotropic structures are reviewed in this paper and the applications of
these constitutive laws for modelling the nonlinear dynamics of different hyperelastic
structures are discussed using the available literature, up to 2022. Neo-Hookean, Mooney-Rivlin, Ogden, Eight-chain, Polynomial, Gent and Blatz-Ko hyperelastic
strain energy density models are discussed, and the sensitivity of the hyperelastic
coefficients for changing the stress-stretch behaviour is analysed. Different studies
undertaken on the nonlinear dynamics of hyperelastic beams, plates, shells, membranes
and balloons are discussed. Meanwhile, the strength of each hyperelastic
strain energy density model for accurately modelling the nonlinear dynamics of
such structures is analysed.
Paper 3: Hyperelastic belts provide smooth motion in the performance of beltoperating
systems and avoid the propagation of sudden impacts. Since belt-operating
systems are one of the main applications of hyperelastic structures, this paper analysed
the nonlinear dynamic behaviour of axially-moving, incompressible, isotropic
hyperelastic belts. Using the ASTM D638 standard, the nonlinear elastic behaviour
of the structure is studied and Yeoh’s strain energy density model is used to effectively
model the experimental results. A coupled equation of motion is presented for
modelling axially-moving hyperelastic belts, and analysing the effect of both hyperelastic
coefficients and axial velocity on changing the mode shapes, linear frequencies
and the nonlinear dynamic behaviour of the structure.
Paper 4: Porosity and voids are often seen during the fabrication process of
soft structures (such as in the injection moulding or 3d-printing processes) or are
sometimes added to decrease the overall weight and optimise performance. This
paper developed a modified strain energy density model using the Mooney-Rivlin
law, which enables consideration of porosity effects. A set of experimental analyses
on soft samples with different porosities and infill rates are performed and a modified
strain energy model is presented. Using the given model, the nonlinear dynamics of
hyperelastic porous beams with uniform and nonuniform porosities is studied and
the effects of having different porosity types on the nonlinear vibration behaviour
of the structure are discussed.
Paper 5: In many applications, such as packaging, hyperelastic structures are
used as a layered (sandwich) structure. This paper investigated the nonlinear dynamics
of layered isotropic structures using different shear deformation theories. The
importance of proper modelling, layering, and material sorting is analysed comprehensively
and the effect of the thickness ratio between layers is investigated.
Paper 6: Some soft structures show significant viscoelastic behaviour together
with hyperelasticity. In order to model these soft structures appropriately, this
paper investigated the statics and dynamics of hyperelastic and visco-hyperelastic
shallow arches. The internal resonance phenomena due to the arch curvature were
also investigated in this work, alongside a discussion of the effect of viscoelasticity
in damping and changing the rich nonlinear vibration behaviour of the structure.
Paper 7: As hyperelastic structures are used in different sensing applications,
this study investigated the mass-sensing behaviour of hyperelastic isotropic plates
using both experimental testing and theoretical modelling. The effect of having
a concentrated attached mass on changing the nonlinear dynamics of hyperelastic
plates was discussed and the internal resonance phenomena due to the geometrical
properties of the plate and external attached masses were discussed.
Paper 8: Curved hyperelastic shell structures, including cylindrical, parabolic,
and doubly-curved shells are modelled and investigated in this paper as incompressible
structures. A comprehensive general model is developed, and the bending, vibration and internal resonance behaviour of the structure is analysed. The effect
of the shell curvatures in causing internal resonance and changing the nonlinear
oscillation behaviour of the structure is discussed in detail.
Through the above papers, this thesis investigated the mechanics of hyperelastic
structures in a range of well-known applications. With experimental tests supporting
the theoretical models, a detailed understanding of the statics and dynamics of such
structures has been obtained, which is an important step towards understanding
their performance and optimising their use.
School/Discipline
School of Mechanical Engineering
Dissertation Note
Thesis (Ph.D.) -- University of Adelaide, School of Mechanical Engineering, 2023
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