The effect of growth in the stability of elastic materials is studied. From a stability perspective, growth and resorption have two main effects. First a change of mass modifies the geometry of the system and possibly the critical lengths involved in stability thresholds. Second, growth may depend on stress but also it may induce residual stresses in the material. These stresses change the effective loads and they may both stabilize or destabilize the material. To discuss the stability of growing elastic materials, the theory of finite elasticity is used as a general framework for the mechanical description of elastic properties and growth is taken into account through the multiplicative decomposition of the deformation gradient. The formalism of incremental deformation is adapted to include growth effects. As an application of the formalism, the stability of a growing neo-Hookean incompressible spherical shell under external pressure is analyzed. Numerical and analytical methods are combined to obtain explicit stability results and to identify the role of mechanical and geometric effects. The importance of residual stress is established by showing that under large anisotropic growth a spherical shell can become spontaneously unstable without any external loading.

http://www.phys.ens.fr/~benamar/paper/2005-JMPS(growth).pdf

Growth and instability in elastic tissues

In this work we investigate the influence of fiber angle on the deformation of fiber-reinforced soft fluidic actuators and examine the manner in which these actuators extend axially, expand radially and twist about their axis as a function of input pressure. We study the quantitative relationship between fiber angle and actuator deformation by performing finite element simulations for actuators with a range of different fiber angles, and we verify the simulation results by experimentally characterizing the actuators. By combining actuator segments in series, we can achieve combinations of motions tailored to specific tasks. We demonstrate this by using the results of simulations of separate actuators to design a segmented wormlike soft robot capable of propelling itself through a tube and performing an orientation-specific peg insertion task at the end of the tube. Understanding the relationship between fiber angle and pressurization response of these soft fluidic actuators enables rapid explorat...

/pdf/mechanical-programming-of-soft-actuators-by-varying-fiber-2v2iz4s9th.pdf

Mechanical Programming of Soft Actuators by Varying Fiber Angle

B ifurcations of circular cylindrical elastic tubes subjected to inflation combined with axial loading are analysed. Membrane tubes are considered in detail as a background to the more difficult analysis of thickwalled tubes described in the companion paper (Part II). Our results for membranes reinforce and extend those given by R.T. Shield and his co-workers. Two modes of bifurcation are investigated: firstly, a bulging (axisyrmmetric) mode; secondly, a prismatic mode in which the cross-section of the tube becomes non-circular. Necessary and sufficient conditions for the existence of modes of either type are given in respect of an arbitrary (incompressible isotropic) form of elastic strain-energy function. For a closed tube with a fixed axial loading many features of the results have close parallels with recent findings by D.M. Haughton and R.W. Ogden for spherical membranes. On the other hand, some results for tubes with fixed ends have no such parallel. In particular, bifurcation may, under certain conditions, occur before the inflating pressure reaches a maximum. A combination of the two modes is interpreted in terms of bending for a tube under axial compression, and the relative importance of the bending and bulging modes is discussed in relation to the length to radius ratio of the tube. The analytical results are illustrated for specific forms of strain-energy function. Corresponding analysis is given for thick-walled tubes in Part II.

https://hal.archives-ouvertes.fr/hal-01302310/document

Bifurcation of inflated circular cylinders of elastic material under axial loading—II. Exact theory for thick-walled tubes

The present literature review focuses on geometrically non-linear free and forced vibrations of shells made of traditional and advanced materials. Flat and imperfect plates and membranes are excluded. Closed shells and curved panels made of isotropic, laminated composite, piezoelectric, functionally graded and hyperelastic materials are reviewed and great attention is given to non-linear vibrations of shells subjected to normal and in-plane excitations. Theoretical, numerical and experimental studies dealing with particular dynamical problems involving parametric vibrations, stability, dynamic buckling, non-stationary vibrations and chaotic vibrations are also addressed. Moreover, several original aspects of non-linear vibrations of shells and panels, including (i) fluid–structure interactions, (ii) geometric imperfections, (iii) effect of geometry and boundary conditions, (iv) thermal loads, (v) electrical loads and (vi) reduced-order models and their accuracy including perturbation techniques, proper orthogonal decomposition, non-linear normal modes and meshless methods are reviewed in depth.

/pdf/non-linear-vibrations-of-shells-a-literature-review-from-l8iw4bsr7f.pdf

Non-linear vibrations of shells: A literature review from 2003 to 2013

Recent research advances in the dynamic behavior of shells: 1989–2000, Part 2: Homogeneous shells

Theoretical and experimental studies of the free vibrations and the loss of stability of thick-walled cylindrical and spherical shells subjected to external pressure are presented. General equations for the oscillations of the shell under pressure are formulated on the basis of a rigorous theory of finite elasticity. Loss of stability is determined when the fundamental natural frequency of the prestressed shell ceases to be real-valued. Numerical solutions are obtained by solving the specialized equations that are applicable to neo-Hookean materials. Experi- ments using specimens made of silicone rubber closely verify the theoretical results.

/pdf/stability-and-vibrations-of-elastic-thick-walled-cylindrical-36177uneo7.pdf

Stability and vibrations of elastic thick-walled cylindrical and spherical shells subjected to pressure

Cylindrical shells of arbitrary wall thickness subjected to uniform radial tensile or compressive dead-load traction are investigated. The material of the shell is assumed to be homogeneous, isotropic, compressible and hyperelastic. The stability of the finitely deformed state and small, free, radial vibrations about this state are investigated using the theory of small deformations superposed on large elastic deformations. The governing equations are solved numerically using both the multiple shooting method and the finite element method. For the finite element method the commercial program ABAQUS is used. 1 The loss of stability occurs when the motions cease to be periodic. The effects of several geometric and material properties on the stress and the deformation fields are investigated.

A. Ertepinar

Papers

Stability and vibrations of elastic thick-walled cylindrical and spherical shells subjected to pressure

Stability and asymmetric vibrations of pressurized compressible hyperelastic cylindrical shells

Radial oscillations of nonhomogeneous, thick-walled cylindrical and spherical shells subjected to finite deformations

On the finite circumferential shearing of compressible hyperelastic tubes

Finite deformations of compressible hyperelastic tubes subjected to circumferential shear