Nonlinear elastic model for faceting of vesicles with soft grain boundaries

We use an elastic model to explore faceting of solid-wall vesicles with elastic heterogeneities. We show that faceting occurs in regions where the vesicle wall is softer, such as areas of reduced wall thicknesses or concentrated in crystalline defects. The elastic heterogeneities are modeled as a second component with reduced elastic parameters. Using simulated annealing Monte Carlo simulations we obtain the vesicle shape by optimizing the distributions of facets and boundaries. Our model allows us to reduce the effects of the residual stress generated by crystalline defects, and reveals a robust faceting mechanism into polyhedra other than the icosahedron.Comment: 4.5 pages, 4 figure

Elastic theory of unconstrained non-Euclidean plates

Non-Euclidean plates are a subset of the class of elastic bodies having no stress-free configuration. Such bodies exhibit residual stress when relaxed from all external constraints, and may assume complicated equilibrium shapes even in the absence of external forces. In this work we present a mathematical framework for such bodies in terms of a covariant theory of linear elasticity, valid for large displacements. We propose the concept of non-Euclidean plates to approximate many naturally formed thin elastic structures. We derive a thin plate theory, which is a generalization of existing linear plate theories, valid for large displacements but small strains, and arbitrary intrinsic geometry. We study a particular example of a hemispherical plate. We show the occurrence of a spontaneous buckling transition from a stretching dominated configuration to bending dominated configurations, under variation of the plate thickness

On the ratchet analysis of a cracked welded pipe

This paper presents the ratchet limit analysis of a pipe with a symmetric crack in a mismatched weld by using the extended Linear Matching Method (LMM). Two loading conditions are considered: i) a cyclic temperature load and a constant internal pressure; and ii) a cyclic temperature load and a constant axial tension. Individual effects of i) the geometry of the Weld Metal (WM), ii) the size of the crack, iii) the location of the crack and iv) the yield stress of WM on the ratchet limits, maximum temperature ranges to avoid ratchetting and limit loads are investigated. Influence functions of the yield stress of WM on the maximum temperature ranges and limit loads are generated. The results confirm the applicability of the extended LMM to the cracked welded pipe

On shakedown, ratchet and limit analysis of defective pipeline

In this study, the limit load, shakedown and ratchet limit of a defective pipeline subjected to constant internal pressure and a cyclic thermal gradient are analyzed. Ratchet limit and maximum plastic strain range are solved by employing the new Linear Matching Method (LMM) for the direct evaluation of the ratchet limit. Shakedown and ratchet limit interaction diagrams of the defective pipeline identifying the regions of shakedown, reverse plasticity, ratcheting and plastic collapse mechanism are presented and parametric studies involving different types and dimensions of part-through slot in the defective pipeline are investigated. The maximum plastic strain range over the steady cycle with different cyclic loading combinations is evaluated for a low cycle fatigue assessment. The location of the initiation of a fatigue crack for the defective pipeline with different slot type is determined. The proposed linear matching method provides a general-purpose technique for the evaluation of these key design limits and the plastic strain range for the low cycle fatigue assessment. The results for the defective pipeline shown in the paper confirm the applicability of this procedure to complex 3-D structures

Programmed buckling by controlled lateral swelling in a thin elastic sheet

Recent experiments have imposed controlled swelling patterns on thin polymer films, which subsequently buckle into three-dimensional shapes. We develop a solution to the design problem suggested by such systems, namely, if and how one can generate particular three-dimensional shapes from thin elastic sheets by mere imposition of a two-dimensional pattern of locally isotropic growth. Not every shape is possible. Several types of obstruction can arise, some of which depend on the sheet thickness. We provide some examples using the axisymmetric form of the problem, which is analytically tractable.Comment: 11 pages, 9 figure

Fingerprinting and tracing the sources of soils and sediments: Earth and ocean science, geoarchaeological, forensic, and human health applications

publisher: Elsevier articletitle: Fingerprinting and tracing the sources of soils and sediments: Earth and ocean science, geoarchaeological, forensic, and human health applications journaltitle: Earth-Science Reviews articlelink: http://dx.doi.org/10.1016/j.earscirev.2016.08.012 content_type: article copyright: © 2016 Elsevier B.V. All rights reserved

Analysis of laminated doubly-curved shells by alayerwise theory and radial basis functions collocation, accounting for through-the-thickness deformations

In this paper, the static and free vibration analysis of laminated shells is performed by radial basis functions collocation, according to a sinusoidal shear deformation theory (SSDT). The SSDT theory accounts for through-the-thickness deformation, by considering a sinusoidal evolution of all displacements with the thickness coordinate. The equations of motion and the boundary conditions are obtained by the Carrera's Unified Formulation, and further interpolated by collocation with radial basis functions

Ultra-light hierarchical meta-materials on a body-centred cubic lattice

Modern fabrication techniques offer the freedom to design and manufacture structures with complex geometry on many lengthscales, offering many potential advantages. For example, fractal/hierarchical struts have been shown to be exceptionally strong and yet light (Rayneau-Kirkhope D. et al., Phys. Rev. Lett., 109 (2012) 204301). In this letter, we propose a new class of meta-material, constructed from fractal or hierarchical struts linking a specific set of lattice points. We present a mechanical analysis of this meta-material resulting from a body-centred cubic (BCC) lattice. We show that, through the use of hierarchy, the material usage follows an enhanced scaling relation, and both material property and overall efficiency can be optimised for a specific applied stress. Such a design has the potential of providing the next generation of lightweight, buckling-resistant meta-materials

A variable kinematic doubly-curved MITC9 shell element for the analysis of laminated composites

The present article considers the linear static analysis of composite shell structures with double-curvature geometry by means of a shell finite element with variable through-the-thickness kinematic. The refined models used are grouped in the Unified Formulation by Carrera (CUF) and they permit the distribution of displacements and stresses along the thickness of the multilayered shell to be accurately described. The shell element has nine nodes and the mixed interpolation of tensorial components (MITC) method is used to contrast the membrane and shear locking phenomenon. The governing equations are derived from the principle of virtual displacement (PVD) and the finite element method (FEM) is employed to solve them. Cross-ply spherical shells with simply-supported edges and subjected to bi-sinusoidal pressure are analyzed. Various laminations, thickness ratios, and curvature ratios are considered. The results, obtained with different theories contained in the CUF, are compared with both the elasticity solutions given in the literature and the analytical solutions obtained using the CUF and the Navier's method. From the analysis, one can conclude that the shell element based on the CUF is very efficient and its use is mandatory with respect to the classical models in the study of composite structures. Finally, shells with different lamination, boundary conditions, and loads are also analyzed using high-order layer-wise theories in order to provide FEM benchmark solution

An extended Bayesian sediment fingerprinting mixing model for the full Bayes treatment of geochemical uncertainties

Recent advances in sediment fingerprinting research have seen Bayesian mixing models being increasingly employed as an effective method to coherently translate component uncertainties into source apportionment results. Here, we advance earlier work by presenting an extended Bayesian mixing model capable of providing a full Bayes treatment of geochemical uncertainties. The performance of the extended full Bayes model was assessed against the equivalent empirical Bayes model and traditional frequentist optimisation. The performance of models coded in different Bayesian software (‘JAGS’ and ‘Stan’) was also evaluated, alongside an assessment of model sensitivity to reduced source representativeness and non-conservative fingerprint behaviour. Results revealed comparable accuracy and precision for the full and empirical Bayes models across both synthetic and real sediment geochemistry datasets, demonstrating that the empirical treatment of source data here represents a close approximation of the full Bayes treatment. Contrasts in the performance of models coded in JAGS and Stan revealed that the choice of software employed can impact significantly upon source apportionment results. Bayesian models coded in Stan were the least sensitive to both reduced source representativeness and non-conservative fingerprint behaviour, indicating Stan as the preferred software for future Bayesian sediment fingerprinting studies. Whilst the frequentist optimisation generally yielded comparable accuracy to the Bayesian models, uncertainties around apportionment estimates were substantially greater and the frequentist model was less effective at dealing with non-conservative behaviour. Overall, the effective performance of the extended full Bayes mixing model coded in Stan represents a notable advancement in source apportionment modelling relative to previous approaches. Both the mixing model and the software comparisons presented here should provide useful guidelines for future sediment fingerprinting studies