1,327 research outputs found
Static Elastic Properties of Composite Materials Containing Microspheres
This thesis aims to model the uniaxial deformation of a class of materials consisting of microscopic spherical shells embedded in a rubber matrix. These shells are assumed to buckle as the stress on the material increases.
To motivate the analysis we consider the paradigm problem of the debonding of a distribution of cylindrical inclusions in an elastic material undergoing antiplane shear, with bonded and debonded inclusions playing the role of unbuckled and buckled shells respectively.
We begin the modelling of the microsphere-containing material by considering the buckling of an isolated embedded shell inclusion with a uniaxial stress field at infinity, using Koiter's theory of shallow shells. The resulting energy functional is solved as an eigenvalue problem by the Rayleigh-Ritz method. Subsequently, we analyse the buckling criterion asymptotically in the limit as the thickness ratio tends to zero by analogy with the WKB analysis of a beam on a variable-stiffness substrate.
To model the shell after buckling we consider the simplified case of an embedded shell with a crack around its equator. The system is solved by expressing the displacements in the shell and matrix as series of Love stress functions, with the resulting infinite system of equations solved numerically with the aid of a convergence acceleration method.
Finally we consider a composite material consisting of a homogenised dilute distribution of buckled and unbuckled shells, with the proportion of each type of shell dependent on the stress applied to the material, according to an asymptotic formula relating the size of the inclusions and the critical buckling stress that was obtained previously
Curvature-Induced Instabilities of Shells
Induced by proteins within the cell membrane or by differential growth,
heating, or swelling, spontaneous curvatures can drastically affect the
morphology of thin bodies and induce mechanical instabilities. Yet, the
interaction of spontaneous curvature and geometric frustration in curved shells
remains still poorly understood. Via a combination of precision experiments on
elastomeric spherical bilayer shells, simulations, and theory, we show a
spontaneous curvature-induced rotational symmetry-breaking as well as a
snapping instability reminiscent of the Venus fly trap closure mechanism. The
instabilities and their dependence on geometry are rationalized by reducing the
spontaneous curvature to an effective mechanical load. This formulation reveals
a combined pressurelike bulk term and a torquelike boundary term, allowing
scaling predictions for the instabilities in excellent agreement with
experiments and simulations. Moreover, the effective pressure analogy suggests
a curvature-induced buckling in closed shells. We determine the critical
buckling curvature via a linear stability analysis that accounts for the
combination of residual membrane and bending stresses. The prominent role of
geometry in our findings suggests the applicability of the results over a wide
range of scales.Comment: 12 pages, 9 figures (including Supporting Information
Reliability-based design optimization of shells with uncertain geometry using adaptive Kriging metamodels
Optimal design under uncertainty has gained much attention in the past ten
years due to the ever increasing need for manufacturers to build robust systems
at the lowest cost. Reliability-based design optimization (RBDO) allows the
analyst to minimize some cost function while ensuring some minimal performances
cast as admissible failure probabilities for a set of performance functions. In
order to address real-world engineering problems in which the performance is
assessed through computational models (e.g., finite element models in
structural mechanics) metamodeling techniques have been developed in the past
decade. This paper introduces adaptive Kriging surrogate models to solve the
RBDO problem. The latter is cast in an augmented space that "sums up" the range
of the design space and the aleatory uncertainty in the design parameters and
the environmental conditions. The surrogate model is used (i) for evaluating
robust estimates of the failure probabilities (and for enhancing the
computational experimental design by adaptive sampling) in order to achieve the
requested accuracy and (ii) for applying a gradient-based optimization
algorithm to get optimal values of the design parameters. The approach is
applied to the optimal design of ring-stiffened cylindrical shells used in
submarine engineering under uncertain geometric imperfections. For this
application the performance of the structure is related to buckling which is
addressed here by means of a finite element solution based on the asymptotic
numerical method
Nonlinear Dynamics of Spherical Shells Buckling under Step Pressure
This is the author accepted manuscript. The final version is available from The Royal Society via the DOI in this record.Dynamic buckling is addressed for complete elastic spherical shells subject to a rapidly applied step in external pressure. Insights from the perspective of nonlinear dynamics reveal essential mathematical features of the buckling phenomena. To capture the strong buckling imperfection-sensitivity, initial geometric imperfections in the form of an axisymmetric dimple at each pole are introduced. Dynamic buckling under the step pressure is related to the quasi-static buckling pressure. Both loadings produce catastrophic collapse of the shell for conditions in which the pressure is prescribed. Damping plays an important role in dynamic buckling because of the time-dependent nonlinear interaction among modes, particularly the interaction between the spherically symmetric 'breathing' mode and the buckling mode. In this paper we argue that the precise frequency dependence of the damping does not matter as most of the damping happens at a single frequency (the breathing frequency). In general, there is not a unique step pressure threshold separating responses associated with buckling from those that do not buckle. Instead there exists a cascade of buckling thresholds, dependent on the damping and level of imperfection, separating pressures for which buckling occurs from those for which it does not occur. For shells with small and moderately small imperfections the dynamic step buckling pressure can be substantially below the quasi-static buckling pressure
Snap-induced morphing:From a single bistable shell to the origin of shape bifurcation in interacting shells
The bistability of embedded elements provides a natural route through which to introduce reprogrammability to elastic meta-materials. One example of this is the soft morphable sheet, in which bistable elements that can be snapped up or down, are embedded within a soft sheet. The state of the sheet can then be programmed by snapping particular elements up or down, resulting in different global shapes. However, attempts to leverage this programmability have been limited by the tendency for the deformations induced by multiple elastic elements to cause large global shape bifurcations. We study the root cause of this bifurcation in the soft morphable sheet by developing a detailed understanding of the behaviour of a single bistable element attached to a flat âskirtâ region. We study the geometrical limitations on the bistability of this single element, and show that the structure of its deformation can be understood using a boundary layer analysis. Moreover, by studying the compressive strains that a single bistable element induces in the surrounding skirt we show that the shape bifurcation in the soft morphable sheet can be delayed by an appropriate design of the lattice on which bistable elements are placed
- âŠ