Swelling induced finite strain flexure in a rectangular block of an isotropic elastic material

The deformation of a rectangular block into an annular wedge is studied with respect to the state of swelling interior to the block. Nonuniform swelling fields are shown to generate these flexure deformations in the absence of resultant forces and bending moments. Analytical expressions for the deformation fields demonstrate these effects for both incompressible and compressible generalizations of conventional hyperelastic materials. Existing results in the absence of a swelling agent are recovered as special cases.

Some solutions for a compressible isotropic elastic material

In this article we obtain closed-form solutions for the combined inflation and axial shear of an elastic tube in respect of the compressible Isotropic elastic material introduced by Levinson and Burgess. Several other boundary-value problems are also examined, including the bending of a rectangular block and straightening of a cylindrical sector, both coupled with stretching and shearing, and an axially varying twist deformation. Some of the solutions appear in closed form, others are expressible in terms of elliptic functions.

Simulation of plant cell shrinkage during drying : A SPH–DEM approach

Plant based dried food products are popular commodities in global market where much research is focused to improve the products and processing techniques. In this regard, numerical modelling is highly applicable and in this work, a coupled meshfree particle-based two-dimensional (2-D) model was developed to simulate micro-scale deformations of plant cells during drying. Smoothed Particle Hydrodynamics (SPH) was used to model the viscous cell protoplasm (cell fluid) by approximating it to an incompressible Newtonian fluid. The visco-elastic characteristic of the cell wall was approximated to a Neo-Hookean solid material augmented with a viscous term and modelled with a Discrete Element Method (DEM). Compared to a previous work [H. C. P. Karunasena, W. Senadeera, Y. T. Gu and R. J. Brown, Appl. Math. Model., 2014], this study proposes three model improvements: linearly decreasing positive cell turgor pressure during drying, cell wall contraction forces and cell wall drying. The improvements made the model more comparable with experimental findings on dried cell morphology and geometric properties such as cell area, diameter, perimeter, roundness, elongation and compactness. This single cell model could be used as a building block for advanced tissue models which are highly applicable for product and process optimizations in Food Engineering.

Generalized azimuthal shear deformations in compressible isotropic elastic materials

In this article we study the azimuthal shear deformations in a compressible Isotropic elastic material. This class of deformations involves an azimuthal displacement as a function of the radial and axial coordinates. The equilibrium equations are formulated in terms of the Cauchy-Green strain tensors, which form an overdetermined system of partial differential equations for which solutions do not exist in general. By means of a Legendre transformation, necessary and sufficient conditions for the material to support this deformation are obtained explicitly, in the sense that every solution to the azimuthal equilibrium equation will satisfy the remaining two equations. Additionally, we show how these conditions are sufficient to support all currently known deformations that locally reduce to simple shear. These conditions are then expressed both in terms of the invariants of the Cauchy-Green strain and stretch tensors. Several classes of strain energy functions for which this deformation can be supported are studied. For certain boundary conditions, exact solutions to the equilibrium equations are obtained. © 2005 Society for Industrial and Applied Mathematics.

A comparison of stability and bifurcation criteria for inflated spherical elastic shells

The nonlinear stability analysis introduced by Chen and Haughton [1] is employed to study the full nonlinear stability of the non-homogeneous spherically symmetric deformation of an elastic thick-walled sphere. The shell is composed of an arbitrary homogeneous, incompressible elastic material. The stability criterion ultimately requires the solution of a third-order nonlinear ordinary differential equation. Numerical calculations performed for a wide variety of well-known incompressible materials are then compared with existing bifurcation results and are found to be identical. Further analysis and comparison between stability and bifurcation are conducted for the case of thin shells and we prove by direct calculation that the two criteria are identical for all modes and all materials.

A coupled SPH-DEM model for micro-scale structural deformations of plant cells during drying

A single plant cell was modeled with smoothed particle hydrodynamics (SPH) and a discrete element method (DEM) to study the basic micromechanics that govern the cellular structural deformations during drying. This two-dimensional particle-based model consists of two components: a cell fluid model and a cell wall model. The cell fluid was approximated to a highly viscous Newtonian fluid and modeled with SPH. The cell wall was treated as a stiff semi-permeable solid membrane with visco-elastic properties and modeled as a neo-Hookean solid material using a DEM. Compared to existing meshfree particle-based plant cell models, we have specifically introduced cell wall–fluid attraction forces and cell wall bending stiffness effects to address the critical shrinkage characteristics of the plant cells during drying. Also, a moisture domain-based novel approach was used to simulate drying mechanisms within the particle scheme. The model performance was found to be mainly influenced by the particle resolution, initial gap between the outermost fluid particles and wall particles and number of particles in the SPH influence domain. A higher order smoothing kernel was used with adaptive smoothing length to improve the stability and accuracy of the model. Cell deformations at different states of cell dryness were qualitatively and quantitatively compared with microscopic experimental findings on apple cells and a fairly good agreement was observed with some exceptions. The wall–fluid attraction forces and cell wall bending stiffness were found to be significantly improving the model predictions. A detailed sensitivity analysis was also done to further investigate the influence of wall–fluid attraction forces, cell wall bending stiffness, cell wall stiffness and the particle resolution. This novel meshfree based modeling approach is highly applicable for cellular level deformation studies of plant food materials during drying, which characterize large deformations.

Seismic mitigation of building structural systems using passive dampers

This paper treats the seismic mitigation of medium rise frame-shear wall structures and building facade systems using passive damping devices. The frame shear wall structures have embedded viscoelastic and friction dampers in different configurations and placed in various locations in the structure. Influence of damper type, configuration and location are investigated. Results for tip deflections which provide an overall evaluation of the seismic response of the structure, are determined. Seismic mitigation of building facade systems in which visco-elastic dampers are fitted at the horizontal connections between the facades and the frame, instead of the traditional rigid connections, are also treated. Finite element techniques are used to model and analyse the two structural systems under different earthquake loadings, scaled to the same peak ground acceleration for meaningful comparison of responses. Results demonstrate the feasibility of these techniques for seismic mitigation.

Power-law viscous materials for analogue experiments: New data on the rheology of highly-filled silicone polymers

The selection of appropriate analogue materials is a central consideration in the design of realistic physical models. We investigate the rheology of highly-filled silicone polymers in order to find materials with a power-law strain-rate softening rheology suitable for modelling rock deformation by dislocation creep and report the rheological properties of the materials as functions of the filler content. The mixtures exhibit strain-rate softening behaviour but with increasing amounts of filler become strain-dependent. For the strain-independent viscous materials, flow laws are presented while for strain-dependent materials the relative importance of strain and strain rate softening/hardening is reported. If the stress or strain rate is above a threshold value some highly-filled silicone polymers may be considered linear visco-elastic (strain independent) and power-law strain-rate softening. The power-law exponent can be raised from 1 to ~3 by using mixtures of high-viscosity silicone and plasticine. However, the need for high shear strain rates to obtain the power-law rheology imposes some restrictions on the usage of such materials for geodynamic modelling. Two simple shear experiments are presented that use Newtonian and power-law strain-rate softening materials. The results demonstrate how materials with power-law rheology result in better strain localization in analogue experiments.

A particle-based micromechanics approach to simulate structural changes of plant cells during drying

This paper is concerned with applying a particle-based approach to simulate the micro-level cellular structural changes of plant cells during drying. The objective of the investigation was to relate the micro-level structural properties such as cell area, diameter and perimeter to the change of moisture content of the cell. Model assumes a simplified cell which consists of two basic components, cell wall and cell fluid. The cell fluid is assumed to be a Newtonian fluid with higher viscosity compared to water and cell wall is assumed to be a visco-elastic solid boundary located around the cell fluid. Cell fluid is modelled with Smoothed Particle Hydrodynamics (SPH) technique and for the cell wall; a Discrete Element Method (DEM) is used. The developed model is two-dimensional, but accounts for three-dimensional physical properties of real plant cells. Drying phenomena is simulated as fluid mass reductions and the model is used to predict the above mentioned structural properties as a function of cell fluid mass. Model predictions are found to be in fairly good agreement with experimental data in literature and the particle-based approach is demonstrated to be suitable for numerical studies of drying related structural deformations. Also a sensitivity analysis is included to demonstrate the influence of key model parameters to model predictions.

Finite element analysis investigation of response of pumpkin tissue under uniaxial loading

Finite element analysis (FEA) models of uniaxial loading of pumpkin peel and flesh tissues were developed and validated using experimental results. The tensile model was developed for both linear elastic and plastic material models, the compression model was develop d only with the plastic material model. The outcomes of force versus time curves obtained from FEA models followed similar pattern to the experimental curves however the curve resulted with linear elastic material properties had a higher difference with the experimental curves. The values of predicted forces were determined and compared with the experimental curve. An error indicator was introduced and computed for each case and compared. Additionally Root Mean Square Error (RMSE) values were also calculated for each model and compared. The results of modelling were used to develop material model for peel and flesh tissues in FEA modelling of mechanical peeling of tough skinned vegetables.

Study on tracheal collapsibility, compliance, and stress by considering nonlinear mechanical property of cartilage

Tracheal cartilage has been widely regarded as a linear elastic material either in experimental studies or in analytic and numerical models. However, it has been recently demonstrated that, like other fiber-oriented biological tissues, tracheal cartilage is a nonlinear material, which displays higher strength in compression than in extension. Considering the nonlinearity requires a more complex theoretical frame work and costs more to simulate. This study aims to quantify the deviation due to the simplified treatment of the tracheal cartilage as a linear material. It also evaluates the improved accuracy gained by considering the nonlinearity. Pig tracheal rings were used to exam the mechanical properties of cartilage and muscular membrane. By taking into account the asymmetric shape of tracheal cartilage, the collapse behavior of complete rings was simulated, and the compliance of airway and stress in the muscular membrane were discussed. The results obtained were compared with those assuming linear mechanical properties. The following results were found: (1) Models based on both types of material properties give a small difference in representing collapse behavior; (2) regarding compliance, the relative difference is big, ranging from 10 to 40% under negative pressure conditions; and (3) the difference in determining stress in the muscular membrane is small too: <5%. In conclusion, treating tracheal cartilage as a linear material will not cause big deviations in representing the collapse behavior, and mechanical stress in the muscular part, but it will induce a big deviation in predicting the compliance, particularly when the transmural pressure is lower than -0.5 kPa. The results obtained in this study may be useful in both understanding the collapse behavior of trachea and in evaluating the error induced by the simplification of treating the tracheal cartilage as a linear elastic material.

Comparison between analytical and 3D finite element solutions for borehole stresses in anisotropic elastic rock

We present a rigorous validation of the analytical Amadei solution for the stress concentration around an arbitrarily orientated borehole in general anisotropic elastic media. First, we revisit the theoretical framework of the Amadei solution and present analytical insights that show that the solution does indeed contain all special cases of symmetry, contrary to previous understanding, provided that the reduced strain coefficients b11 and b55 are not equal. It is shown from theoretical considerations and published experimental data that the b11 and b55 are not equal for realistic rocks. Second, we develop a 3D finite element elastic model within a hybrid analytical–numerical workflow that circumvents the need to rebuild and remesh the model for every borehole and material orientation. Third, we show that the borehole stresses computed from the numerical model and the analytical solution match almost perfectly for different borehole orientations (vertical, deviated and horizontal) and for several cases involving isotropic, transverse isotropic and orthorhombic symmetries. It is concluded that the analytical Amadei solution is valid with no restriction on the borehole orientation or the symmetry of the elastic anisotropy.

Higher-order non-linear analysis of steel structures. Part I : elastic second-order formulation

This paper presents a higher-order beam-column formulation that can capture the geometrically non-linear behaviour of steel framed structures which contain a multiplicity of slender members. Despite advances in computational frame software, analyses of large frames can still be problematic from a numerical standpoint and so the intent of the paper is to fulfil a need for versatile, reliable and efficient non-linear analysis of general steel framed structures with very many members. Following a comprehensive review of numerical frame analysis techniques, a fourth-order element is derived and implemented in an updated Lagrangian formulation, and it is able to predict flexural buckling, snap-through buckling and large displacement post-buckling behaviour of typical structures whose responses have been reported by independent researchers. The solutions are shown to be efficacious in terms of a balance of accuracy and computational expediency. The higher-order element forms a basis for augmenting the geometrically non-linear approach with material non-linearity through the refined plastic hinge methodology described in the companion paper.

A comparative study of the semi-elastic and fully-elastic MapReduce models

MapReduce is a computation model for processing large data sets in parallel on large clusters of machines, in a reliable, fault-tolerant manner. A MapReduce computation is broken down into a number of map tasks and reduce tasks, which are performed by so called mappers and reducers, respectively. The placement of the mappers and reducers on the machines directly affects the performance and cost of the MapReduce computation in cloud computing. From the computational point of view, the mappers/reducers placement problem is a generation of the classical bin packing problem, which is NP-complete. Thus, in this paper we propose a new heuristic algorithm for the mappers/reducers placement problem in cloud computing and evaluate it by comparing with other several heuristics on solution quality and computation time by solving a set of test problems with various characteristics. The computational results show that our heuristic algorithm is much more efficient than the other heuristics and it can obtain a better solution in a reasonable time. Furthermore, we verify the effectiveness of our heuristic algorithm by comparing the mapper/reducer placement for a benchmark problem generated by our heuristic algorithm with a conventional mapper/reducer placement which puts a fixed number of mapper/reducer on each machine. The comparison results show that the computation using our mapper/reducer placement is much cheaper than the computation using the conventional placement while still satisfying the computation deadline.

Comparison of mechanical and ultrasound elastic modulus of ovine tibial cortical bone

Finite element models of bones can be created by deriving geometry from anx-ray CT scan. Material properties such as the elastic modulus can then be applied using either a single or set of homogeneous values, or individual elements can have local values mapped onto them. Values for the elastic modulus can be derived from the CT density values using an elasticityversus density relationship. Many elasticity–density relationships have been reported in the literature for human bone. However, while ovine in vivo models are common in orthopaedic research, no work has been done to date on creating FE models of ovine bones. To create these models and apply relevant material properties, an ovine elasticity-density relationship needs to be determined. Using fresh frozen ovine tibias the apparent density of regions of interest was determined from a clinical CT scan. The bones were the sectioned into cuboid samples of cortical bone from the regions of interest. Ultrasound was used to determine the elastic modulus in each of three directions – longitudinally, radially and tangentially. Samples then underwent traditional compression testing in each direction. The relationships between apparent density and both ultrasound, and compression modulus in each directionwere determined. Ultrasound testing was found to be a highly repeatable non-destructive method of calculating the elastic modulus, particularly suited to samples of this size. The elasticity-density relationships determined in the longitudinal direction were very similar between the compression and ultrasound data over the density range examined.A clear difference was seen in the elastic modulus between the longitudinal and transverse directions of the bone samples, and a transverse elasticity-density relationship is also reported.