“…figure 3 a , figure 4, figure 6 a and figure 7) is also material model independent as Δh¯ is determined by geometry only as well. However, the difference in the total energy between the symmetric and the asymmetric deformation modes as well as the depths of the post-bucking energy wells do change with the constitutive law, consistent with previous studies [35]. Figure 11The stretch ratio as a function of the normalized volume for ( a ) line indentation and ( b ) plane indentation.…”
Section: Indentation Of a Two-dimensional Membrane With A Cylindrical Indentersupporting
We study pneumatically inflated membranes indented by rigid indenters of different sizes and shapes. When the volume of the inflated membrane is beyond a critical value, a symmetric deformation mode becomes unstable and the system follows a path of asymmetric deformation. This bifurcation is analysed analytically for a two-dimensional membrane with either a line or plane indenter for which the stable deformation path is determined by computing the total system potential energy of different configurations. An axisymmetric membrane with indenters of different shapes and sizes is further investigated numerically. In this case, a cylindrical indenter can always trigger bifurcation while a small spherical indenter tends to be encapsulated rather than induce an asymmetric deformation mode. This result suggests that the observed bifurcation behaviour can be actively tuned and even triggered selectively by tuning indenter shape and size. We also demonstrate the effects of friction and biased bifurcation analytically through the example of a two-dimensional membrane with a line indenter.
“…figure 3 a , figure 4, figure 6 a and figure 7) is also material model independent as Δh¯ is determined by geometry only as well. However, the difference in the total energy between the symmetric and the asymmetric deformation modes as well as the depths of the post-bucking energy wells do change with the constitutive law, consistent with previous studies [35]. Figure 11The stretch ratio as a function of the normalized volume for ( a ) line indentation and ( b ) plane indentation.…”
Section: Indentation Of a Two-dimensional Membrane With A Cylindrical Indentersupporting
We study pneumatically inflated membranes indented by rigid indenters of different sizes and shapes. When the volume of the inflated membrane is beyond a critical value, a symmetric deformation mode becomes unstable and the system follows a path of asymmetric deformation. This bifurcation is analysed analytically for a two-dimensional membrane with either a line or plane indenter for which the stable deformation path is determined by computing the total system potential energy of different configurations. An axisymmetric membrane with indenters of different shapes and sizes is further investigated numerically. In this case, a cylindrical indenter can always trigger bifurcation while a small spherical indenter tends to be encapsulated rather than induce an asymmetric deformation mode. This result suggests that the observed bifurcation behaviour can be actively tuned and even triggered selectively by tuning indenter shape and size. We also demonstrate the effects of friction and biased bifurcation analytically through the example of a two-dimensional membrane with a line indenter.
“…In [19], the static and dynamic behaviour of circular cylindrical shells of homogeneous isotropic incompressible hyperelastic material modelling arterial walls were considered. In [91], the nonlinear static and dynamic behaviour of a spherical membrane of neo-Hookean or Mooney-Rivlin material, subjected to a uniformly distributed radial pressure on its inner surface, was studied, and a parametric analysis of the influence of the material constants was presented.…”
Stochastic homogeneous hyperelastic solids are characterised by strain-energy densities where the parameters are random variables defined by probability density functions. These models allow for the propagation of uncertainties from input data to output quantities of interest. To investigate the effect of probabilistic parameters on predicted mechanical responses, we study radial oscillations of cylindrical and spherical shells of stochastic incompressible isotropic hyperelastic material, formulated as quasi-equilibrated motions where the system is in equilibrium at every time instant. Additionally, we study finite shear oscillations of a cuboid, which are not quasi-equilibrated. We find that, for hyperelastic bodies of stochastic neo-Hookean or Mooney-Rivlin material, the amplitude and period of the oscillations follow probability distributions that can be characterised. Further, for cylindrical tubes and spherical shells, when an impulse surface traction is applied, there is a parameter interval where the oscillatory and non-oscillatory motions compete, in the sense that both have a chance to occur with a given probability. We refer to the dynamic evolution of these elastic systems, which exhibit inherent uncertainties due to the material properties, as "likely oscillatory motions".Key words: stochastic hyperelastic models, dynamic finite strain deformation, quasi-equilibrated motion, finite amplitude oscillations, incompressibility, applied probability."Denominetur motus talis, qualis omni momento temporis t praebet configurationem capacem aequilibrii corporis iisdem viribus massalibus sollicitati, 'motus quasi aequilibratus'. Generatim motus quasi aequilibratus non congruet legibus dynamicis et proinde motus verus corporis fieri non potest, manentibus iisdem viribus masalibus." -C. Truesdell (1962) [103]
“…The nonlinear breathing motion of hyperelastic spherical membranes has been examined by Soares et al [151] using an incompressible isotropic Mooney-Rivlin strain energy density model. It was shown that the linear viscous damping term has a significant effect in changing the nonlinear resonance behaviour of the spherical membranes (Fig.…”
Section: Nonlinear Dynamics Of Hyperelastic Membranes and Balloonsmentioning
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.
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