A zero-stiffness elastic shell structure

A remarkable shell structure is described that, due to a particular combination of geometry and initial stress, has zero stiffness for any finite deformation along a twisting path; the shell is in a neutrally stable state of equilibrium. Initially the shell is straight in a longitudinal direction, but has a constant, nonzero curvature in the transverse direction. If residual stresses are induced in the shell by, for example, plastic deformation, to leave a particular resultant bending moment, then an analytical inextensional model of the shell shows it to have no change in energy along a path of twisted configurations. Real shells become closer to the inextensional idealization as their thickness is decreased; experimental thin-shell models have confirmed the neutrally stable configurations predicted by the inextensional theory. A simple model is described that shows that the resultant bending moment that leads to zero stiffness gives the shell a hidden symmetry, which explains this remarkable property.

A new Lagrangian-Eulerian shell-fluid coupling algorithm based on level sets

We propose a computational method for the coupled simulation of a compressible flow interacting with a thin-shell structure undergoing large deformations. An Eulerian finite volume formulation is adopted for the fluid and a Lagrangian formulation based on subdivision finite elements is adopted for the shell response. The coupling between the fluid and the solid response is achieved via a novel approach based on level sets. The basic approach furnishes a general algorithm for coupling Lagrangian shell solvers with Cartesian grid based Eulerian fluid solvers. The efficiency and robustness of the proposed approach is demonstrated with a airbag deployment simulation. It bears emphasis that in the proposed approach the solid and the fluid components as well as their coupled interaction are considered in full detail and modeled with an equivalent level of fidelity without any oversimplifying assumptions or bias towards a particular physical aspect of the problem.

A cohesive approach to thin-shell fracture and fragmentation

We develop a finite-element method for the simulation of dynamic fracture and fragmentation of thin-shells. The shell is spatially discretized with subdivision shell elements and the fracture along the element edges is modeled with a cohesive law. In order to follow the propagation and branching of cracks, subdivision shell elements are pre-fractured ab initio and the crack opening is constrained prior to crack nucleation. This approach allows for shell fracture in an in-plane tearing mode, a shearing mode, or a bending of hinge mode. The good performance of the method is demonstrated through the simulation of petalling failure experiments in aluminum plates. © 2005 Elsevier B.V. All rights reserved.

Estimating material elasticity by spherical indentation load-relaxation tests on viscoelastic samples of finite thickness

A two-step viscoelastic spherical indentation method is proposed to compensate for 1) material relaxation and 2) sample thickness. In the first step, the indenter is moved at a constant speed and the reaction force is measured. In the second step, the indenter is held at a constant position and the relaxation response of the material is measured. Then the relaxation response is fit with a multi-exponential function which corresponds to a three-branch general Maxwell model. The relaxation modulus is derived by correcting the finite ramp time introduced in the first step. The proposed model takes into account the sample thickness, which is important for applications in which the sample thickness is less than ten times the indenter radius. The model is validated numerically by finite element simulations. Experiments are carried out on a 10% gelatin phantom and a chicken breast sample with the proposed method. The results for both the gelatin phantom and the chicken breast sample agree with the results obtained from a surface wave method. Both the finite element simulations and experimental results show improved elasticity estimations by incorporating the sample thickness into the model. The measured shear elasticities of the 10% gelatin sample are 6.79 and 6.93 kPa by the proposed finite indentation method at sample thickness of 40 and 20 mm, respectively. The elasticity of the same sample is estimated to be 6.53 kPa by the surface wave method. For the chicken breast sample, the shear elasticity is measured to be 4.51 and 5.17 kPa by the proposed indentation method at sample thickness of 40 and 20 mm, respectively. Its elasticity is measured by the surface wave method to be 4.14 kPa. © 2011 IEEE.

Simulation of spherical turbulent premixed flames

Outwardly-propagating spherical turbulent premixed flames are studied using Reynolds-Averaged Navier-Stokes methodology. The reaction rate closure is based on recently developed strained flamelets, where the flamelets are parametrised using the scalar dissipation rate. It is shown that the leading edge speed for the spherical flame is higher than for the planar case, for a given turbulence and thermo-chemical conditions. In addition, it is shown that including the mean curvature effects in the reaction rate closure do not influence the spherical flame speeds when compared with a model that excludes these effects.