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.

In this paper, direct numerical simulation of fully developed turbulent pipe flow is carried out at ${\text{Re}}_{\tau }\approx 170$ and 500 to investigate the effect of the streamwise periodic length on the convergence of turbulence statistics. Mean flow, turbulence intensities, correlations, and energy spectra were computed. The findings show that in the near-wall region (below the buffer region, $r^{+}\le 30$ ), the required pipe length for all turbulence statistics to converge needs to be at least a viscous length of $O\left(6300\right)$ wall units and should not be scaled with the pipe radius $\left(\delta \right)$ . It was also found for convergence of turbulence statistics at the outer region that the pipe length has to be scaled with pipe radius and a proposed pipe length of $8\pi \delta$ seems sufficient for the Reynolds numbers considered in this study.

This work presents a detailed analysis of the flow structures relevant to extreme wall shear stress events for turbulent pipe flow direct numerical simulation data at a friction Reynolds number . The results reveal that extreme positive wall-friction events are located below an intense sweep (Q4) event originated from a strong quasi-streamwise vortex at the buffer region. This vortex transports high streamwise momentum from the overlap and the outer layers towards the wall, giving rise to a high-speed streak within the inner region. This vortical structure also relates to regions with extreme wall-normal velocity. Consequently, the conditional fields of turbulence production and viscous dissipation exhibit peaks whose magnitudes are approximately 25 times higher than the ensemble mean quantities in the vicinity of the extreme positive events. An analysis of the turbulent inertia force reveals that the energetic quasi-streamwise vortex acts as an essential source of momentum at the near-wall region. Similarly, extremely rare backflow events are studied. An examination of the wall-normal vorticity and velocity vector fields shows an identifiable oblique vortical structure along with two other large-scale roll modes. These counter-rotating motions contribute to the formation of backflow events by transporting streamwise momentum from the inner to the outer region, creating a large-scale meandering low-speed streak. It is found that extreme events are clustered below large-scale structures of positive streamwise momentum that interact with near-wall low-speed streaks, related to regions densely populated with vortical structures. Finally, a three-dimensional model is proposed to conceptualise the flow dynamics associated with extreme events.

A detailed analysis of the ‘turbulent inertia’ (TI) term (the wall-normal gradient of the Reynolds shear stress, $\mathrm{d} \langle -uv\rangle /\mathrm{d} y $ ), in the axial mean momentum equation is presented for turbulent pipe flows at friction Reynolds numbers $\delta ^{+} \approx 500$ , 1000 and 2000 using direct numerical simulation. Two different decompositions for TI are employed to further understand the mean structure of wall turbulence. In the first, the TI term is decomposed into the sum of two velocity–vorticity correlations ( $\langle v \omega _z \rangle + \langle - w \omega _y \rangle $ ) and their co-spectra, which we interpret as an advective transport (vorticity dispersion) contribution and a change-of-scale effect (associated with the mechanism of vorticity stretching and reorientation). In the second decomposition, TI is equivalently represented as the wall-normal gradient of the Reynolds shear stress co-spectra, which serves to clarify the accelerative or decelerative effects associated with turbulent motions at different scales. The results show that the inner-normalised position, $y_m^{+}$ , where the TI profile crosses zero, as well as the beginning of the logarithmic region of the wall turbulent flows (where the viscous force is leading order) move outwards in unison with increasing Reynolds number as $y_m^{+} \sim \sqrt{\delta ^{+}}$ because the eddies located close to $y_m^{+}$ are influenced by large-scale accelerating motions of the type $\langle - w \omega _y \rangle $ related to the change-of-scale effect (due to vorticity stretching). These large-scale motions of $O(\delta ^{+})$ gain a spectrum of larger length scales with increasing $\delta ^{+}$ and are related to the emergence of a secondary peak in the $-uv$ co-spectra. With increasing Reynolds number, the influence of the $O(\delta ^{+})$ motions promotes viscosity to act over increasingly longer times, thereby increasing the $y^{+}$ extent over which the mean viscous force retains leading order. Furthermore, the TI decompositions show that the $\langle v \omega _z \rangle $ motions (advective transport and/or dispersion of vorticity) are the dominant mechanism in and above the log region, whereas $\langle - w \omega _y \rangle $ motions (vorticity stretching and/or reorientation) are most significant below the log region. The motions associated with $\langle - w \omega _y \rangle $ predominantly underlie accelerations, whereas $\langle v \omega _z \rangle $ primarily contribute to decelerations. Finally, a description of the structure of wall turbulence deduced from the present analysis and our physical interpretation is presented, and is shown to be consistent with previous flow visualisation studies.

In this study, the effect of the shape of the stenosis on the flow transition in an artery is investigated. Different shapes of the stenosis including round, oval, elongated, half-moon, bean-shape, and crescent with and without eccentricity at a constant degree of stenosis $(73\%)$ are studied. A computational model, validated against the in-house Particle Image Velocimetry experimental results, is used to investigate the flow behavior. The results showed that the length of the jet region after the stenotic section varies significantly for different shapes of the stenosis. Based on the analysis of turbulent kinetic energy, power spectral density, and the spectral entropy of stream-wise velocity fluctuations, it was shown that eddies are formed after the dissipation of jet flow downstream of the stenosis. It was also shown that the intensity of the velocity fluctuations differs for different shapes of the stenosis. Furthermore, using the proper orthogonal decomposition method, it was shown that the shape of the stenosis has a significant impact on the downstream coherent structures. It was found that regardless of the degree of stenosis, specific shapes of the stenosis, such as round concentric, create less serious hemodynamic complications compared to the other shapes of the stenosis.