In this paper, the porous-hyperelastic properties of soft materials are obtained experimentally and a general model for a combination of porosity (of functional type) and hyperelasticity using the ...Mooney-Rivlin strain energy density is obtained. Porous-hyperelastic samples are fabricated using thermoplastics with different porosities by varying the infill rate of 3D-printing. Following the available standards, the stress-strain behaviour for different samples are obtained and a general model for hyperelastic closed-cell porosity is presented. After obtaining model's characteristics from the experimental testings, a general beam formulation is presented for hyperelastic beams with functional porosity through the length. Both the axial and transverse motions are considered in the model of hyperelastic beams in the framework of the Mooney-Rivlin material model and Hamilton's principle. A geometrical imperfection of the beam is also considered in the formulation. The nonlinear forced vibrations of the imperfect porous-hyperelastic beam are studied by simultaneously solving the axial and transverse nonlinear coupled equations using a dynamic equilibrium technique. It is shown that having a uniform and functional porosity has a significant effect in changing the nonlinear frequency response of the system. Geometrical imperfection leads to a significant coupling between the axial and transverse coordinates when the porosity varies functionally through the length which shows the importance of considering both motions while analysing such structures. The results are useful for better understanding the effects of imperfections in studying the mechanics of soft structures and can be useful in designing soft robotics and artificial organs.
•Experimental results show a nonlinear effect of porosity on the hyperelasticity.•A new strain energy model is developed for modelling porous-hyperelastic samples.•Coupled nonlinear equations of porous-hyperelastic beams are presented and solved.•Porosity in hyperelastic structures can change the behaviour significantly.•Geometrical imperfection's effect in modelling hyperelastic structures is analysed.
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This paper presents a critical review of the nonlinear dynamics of hyperelastic structures. Hyperelastic structures often undergo large strains when subjected to external time-dependent forces. ...Hyperelasticity requires specific constitutive laws to describe the mechanical properties of different materials, which are characterised by a nonlinear relationship between stress and strain. Due to recent recognition of the high potential of hyperelastic structures in soft robots and other applications, and the capability of hyperelasticity to model soft biological tissues, the number of studies on hyperelastic structures and materials has grown significantly. Thus, a comprehensive explanation of hyperelastic constitutive laws is presented, and different techniques of continuum mechanics, which are suitable to model these materials, are discussed in this literature review. Furthermore, the sensitivity of each hyperelastic strain energy density function to coefficient variation is shown for some well-known hyperelastic models. Alongside this, the application of hyperelasticity to model the nonlinear dynamics of polymeric structures (e.g., beams, plates, shells, membranes and balloons) is discussed in detail with the assistance of previous studies in this field. The advantages and disadvantages of hyperelastic models are discussed in detail. This present review can stimulate the development of more accurate and reliable models.
Nano and micro electro-mechanical systems (NEMS and MEMS) have been attracting a large amount of attention recently as they have extensive current/potential applications. However, due to their scale, ...molecular interaction and size effects are considerably high which needs to be considered in the theoretical modelling of their electro-mechanical behaviour. Both nano- and micro-scale electrically actuated structures are discussed when subjected to constant and time-varying voltages, and different theories and models, introduced in the past few years for modelling such small structures, are discussed. It is highlighted that considering the intermolecular forces and size-dependence effects can change both the static and dynamic behaviours of such systems significantly. This review presents the current stage of the research on electrically actuated NEMS/MEMS by analysing the latest models and studies in this field in the framework of electro-mechanical coupling and small-size effects.
Structures face different types of imperfections and defects during the fabrication process, installation and working environment. In this paper, the imperfection effects in the coupled vibration ...behaviour of axially functionally graded carbon nanotube (CNT)-strengthened beam structures with different boundary conditions are analysed considering porosity as well as geometric and mass imperfections in the structure. Porosity is modelled using different types of formulations for simple-cell, open-cell and closed-cell porous structures. The porosity is assumed to be either uniform or by varying through the thickness of the hollow beam using different functions. Mass imperfection effect is added to the system by considering a concentrated mass in the system affecting the mass homogeneity of the structure. Geometry imperfection is also considered by having an initial deformation in the structure which could be caused by an improper fabrication process. Coupled axial and transverse equations of motion are obtained using Hamilton’s principle and the von Kármán geometrical nonlinearity. Governing equations are solved for different types of boundary conditions using a semi-analytical modal decomposition technique. It is shown that strengthening the base matrix with CNT fibres can improve the vibration behaviour of imperfect structures and the influence of CNT volume fraction and distribution through the length of the beam is discussed. The results provided in this paper may be used as a benchmark to validate future experimental results to prevent imperfection, delamination and stress singularities in the structures.
This study investigates the effects of geometric nonlinearities on the dynamical behaviour of carbon nanotube (CNT) strengthened imperfect composite beams by considering both axial and transverse ...motions. For the given general model of the beam, the system modelling has been adopted from the literature and the nonlinear dynamic response in presence of an external harmonic load is examined for the first time in the case of axially functionally graded (AFG) CNT fibre, which is used for strengthening the structure. Porosity imperfection with the ability to vary though the thickness is modelled using simple, closed and open-cell models; the porosity variation is formulated using uniform, linear, symmetric and un-symmetric models. The geometrical imperfection is considered by allowing the beam to have an initial curved longitudinal axis and the mass imperfection is modelled by introducing a concentrated mass at a certain point of the beam. Using a combination of the Galerkin scheme together with dynamic equilibrium technique, the influence of different imperfections and porosities on the frequency response of the system is examined. It is shown that, for the case of AFG CNT strengthened beam, geometrical imperfection can change the nonlinear response from a hardening to a softening behaviour. Besides, the importance of considering the interaction between axial and transverse motion is examined in detail. The influence of lumped mass imperfection and its position is also studied showing that this type of imperfection can change the nonlinear behaviour of the system significantly. Moreover, the influence of increasing the CNT volume fraction and functionally spreading the CNTs through the length is discussed. The results are useful for analysing the resonance phenomena in strengthened structures facing various imperfections.
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In this study, the time-dependent mechanics of multilayered thick hyperelastic beams are investigated for the first time using five different types of shear deformation models for modelling the beam ...(i.e. the Euler–Bernoulli, Timoshenko, third-order, trigonometric and exponential shear deformable models), together with the von Kármán geometrical nonlinearity and Mooney–Rivlin hyperelastic strain energy density. The laminated hyperelastic beam is assumed to be resting on a nonlinear foundation and undergoing a time-dependent external force. The coupled highly nonlinear hyperelastic equations of motion are obtained by considering the longitudinal, transverse and rotation motions and are solved using a dynamic equilibrium technique. Both the linear and nonlinear time-dependent mechanics of the structure are analysed for clamped–clamped and pinned–pinned boundaries, and the impact of considering the shear effect using different shear deformation theories is discussed in detail. The influence of layering, each layer’s thickness, hyperelastic material positioning and many other parameters on the nonlinear frequency response is analysed, and it is shown that the resonance position, maximum amplitude, coupled motion and natural frequencies vary significantly for various hyperelastic and layer properties. The results of this study should be useful when studying layered soft structures, such as multilayer plastic packaging and laminated tubes, as well as modelling layered soft tissues.
In this study, a comprehensive analysis of visco-hyper-elastic thick soft arches under an external time-independent as well as time-dependent loads is presented from bending and internal resonance ...phenomenon perspectives. Axial, transverse and rotation motions are considered for modelling the thick and soft arch in the framework of the Mooney–Rivlin and Kelvin–Voigt visco-hyper-elastic schemes and third-order shear deformable models. The arch is assumed to be incompressible and is modelled using von Kármán geometric nonlinearity in the strain–displacement relationship. Using a virtual work method, the bending equations are derived. For the vibration analysis, three, coupled, highly nonlinear equations of motions are obtained using force-moment balance method. The Newton–Raphson method together with the dynamic equilibrium technique is used for the bending and vibration analyses. A detailed study on the influence of having visco-hyper-elasticity and arch curvature in the frequency response of the system is given in detail, and the bending deformation due to the applied static load is presented. The influence of having thick, soft arches with different slenderness ratios is shown, and the forced vibration response is discussed. Moreover, internal resonance in the system is studied showing that the curvature term in the structure can lead to three-to-one internal resonances, showing a rich nonlinear frequency response. The results of this study are a step forward in studying the visco-hyper-elastic behaviour of biological structures and soft tissues.
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•A general model of hyperelastic shell structures is formulated.•Dynamic and static behaviours are both investigated.•Donnell...s nonlinear shell theory and Mooney-Rivlin energy model are ...employed.•The model includes coupled highly-nonlinear terms.•Curvature-induced internal resonances are studied.
Investigated in this paper are comprehensive static, dynamic and internal-resonance analyses on a wide range of hyperelastic shell structures, including cylindrical, spherical, doubly-curved, and hyperbolic hyperelastic shallow shells. Donnell's nonlinear shell theory and the Mooney-Rivlin strain energy density model are used to formulate the hyperelastic shell structure. Coupled equations of motion are obtained using Hamilton's principle with highly nonlinear terms due to the curvature in the structure, together with the material nonlinearity and large deformations. The coupled equations of motion are converted to a large set of equations using a two-dimensional Galerkin technique and are solved by employing the Newton-Raphson approach and dynamic equilibrium technique. The strength of the current methodology and model is first verified by comparing the static response of the structure with those obtained by using a finite element software. After verifying the model, a detailed analysis of the bending behaviour of the structure under a time-independent pressure is presented. Moreover, the free and forced vibration responses of the shell structure are presented for different cases, showing that the curvature terms play a significant role in changing the mechanical response of the hyperelastic shell. Furthermore, it is shown that for specific sets of curvatures, internal resonances are present which leads to a complicated, rich nonlinear responses. The nonlinear forced vibration response of the hyperelastic shell is also presented for different shell types and resonances.
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•Airy stress based nonlinear analysis of nanoplates is presented without ignoring the in-plane displacements.•Different types of internal resonances are investigated.•The influence of nonlocal and ...strain gradient parameters is discussed.•Both nonlocal elasticity and strain gradient elasticity are considered.
This paper presents a novel investigation of nonlinear forced vibrations and internal resonance in nonlocal strain gradient nanoplates, taking into account in-plane motions. The study comprehensively models the nanoplate structure, employing Kirchhoff's plate theory, nonlocal elasticity theory, and strain gradient elasticity theory. The incorporation of the Airy stress function allows for the consideration of in-plane displacements. The large amplitude deformations in the nanoplate are described using the von Kármán geometric nonlinearity model, and the equations of motion are derived using the force-moment dynamic balance method. The coupled equations of motion are solved using the Galerkin scheme and a dynamic equilibrium technique. Detailed discussions are provided on the influence of nonlocal and strain gradient parameters on the nonlinear vibration response of the Airy stress nanostructure. Moreover, it is demonstrated that specific combinations of nonlocal and strain gradient parameters lead to various types of internal resonance (including two-to-one and three-to-one internal resonances), significantly affecting the nonlinear frequency responses of the nanoplate, resulting in rich nonlinear behaviours. This study contributes to the understanding of the complex dynamics of nanoplates subjected to external time-dependant loads and offers valuable insights for the design of diverse nanoplate systems, including graphene sheets, which are relevant to nanoelectromechanical systems (NEMS) applications.
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Soft structures are capable of undergoing reversible large strains and deformations when facing different types of loadings. Due to the limitations of linear elastic models, researchers have ...developed and employed different nonlinear elastic models capable of accurately modelling large deformations and strains. These models are significantly different in formulation and application. As hyperelastic strain energy density models provide researchers with a good fit for the mechanical behaviour of biological tissues, research studies on using these constitutive models together with different continuum-mechanics-based formulations have reached notable outcomes. With the improvements in biomechanical devices, in-vivo and in-vitro studies have increased significantly in the past few years which emphasises the importance of reviewing the latest works in this field. Besides, since soft structures are used for different mechanical and biomechanical applications such as prosthetics, soft robots, packaging, and wearing devices, the application of a proper hyperelastic strain energy density law in modelling the structure is of high importance. Therefore, in this review, a detailed classified analysis of the mechanics of hyperelastic structures is presented by focusing on the application of different hyperelastic strain energy density models. Previous studies on biological soft parts of the body (brain, artery, cartilage, liver, skeletal muscle, ligament, skin, tongue, heel pad and adipose tissue) are presented in detail and the hyperelastic strain energy models used for each biological tissue is discussed. Besides, the mechanics (deformation, buckling, inflation, etc.) of polymeric structures in different mechanical conditions is presented using previous studies in this field and the strength of hyperelastic strain energy density models in analysing their mechanics is presented.
