Nonlinear Mechanics of Hyperelastic Structures

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.