A control volume-based finite element method for plane micropolar elasticity

This paper describes the development of a numerical procedure for predicting deformations and stresses in a loaded two-dimensional membrane exhibiting micropolar or Cosserat constitutive behaviour. The procedure employs a conventional finite element (FE) mesh together with a dual mesh of interconnected control volumes, each of which must satisfy equilibrium. A series of patch tests covering a variety of simple strain states are used to validate the procedure that is then employed to predict the stress concentration in a membrane containing a small hole. The predictions provided by the procedure are compared with those given previously by FEs

A control volume based formulation of the discrete Kirchoff triangular thin plate bending element

A control volume method is presented for predicting the displacement and rotation of thin transversely loaded flat plates. The new procedure uses discrete Kirchoff triangle (DKT) elements but introduces a dual mesh of interconnected control volumes (CVs) centred on the finite element (FE) vertices. Discrete equations for the unknown degrees of freedom are subsequently derived by enforcing equilibrium on these CVs; as such this implementation is a quadrature free routine. To allow a comparison, a quadrature free implementation of the DKT element, using the standard finite element procedure, was developed using symbolic methematics. The CV based procedure is validated by patch tests for a state of pure bending and twist. Convergence tests for various loading types show enhanced performance for coarse meshes over the equivalent FE method

Haversian canal structures can be associated with size effects in cortical bone

Prediction of periprosthetic failure may be improved by an improved model of bone elasticity which includes microstructural information. Micropolar theory facilitates such information to be included in a continuum model. We assessed the extent of bone’s micropolar behaviour in bending both numerically and experimentally. The numerical model was consistent with micropolar behaviour, and experimental results exhibited size effects that may have been confounded by surface roughness effects, as predicted numerically

Modelling micropolar behaviour in cortical bone

This presentation looks at modelling micropolar behaviour in cortical bon

On energy release rates in heterogeneous composite laminates

Composite laminates are usually assumed to be homogeneous when determining the energy release rates (ERRs) associated with inter-ply delamination. This short paper discusses the effect of neglecting this assumption by accounting for inter-ply interface layer thickness and the resulting influence that this may have on the ERRs. A global approach is used to analytically determine ERRs for delaminations subject to mode I and mixed mode loading in symmetric double cantilever beam (DCB) samples of a material formed of alternating stiff and compliant layers. In contrast to their homogeneously determined counterparts these ERRs and their mixity are dependent on both sample depth and interface thickness and when compared the conditions under which obvious differences become apparent can be explicitly identified. Some brief conclusions on the application of the analysis to the prescription of practical delamination testing protocols for composite laminates are drawn

A higher order control volume based finite element method to prodict the deformation of heterogeneous materials

Materials with obvious internal structure can exhibit behaviour, under loading, that cannot be described by classical elasticity. It is therefore important to develop computational tools incorporating appropriate constitutive theories that can capture their unconventional behaviour. One such theory is micropolar elasticity. This paper presents a linear strain control volume finite element formulation incorporating micropolar elasticity. Verification results from a micropolar element patch test as well as convergence results for a stress concentration problem are included. The element will be shown to pass the patch test and also exhibit accuracy that is at least equivalent to its finite element counterpart

Size effect anomalies in the behaviour of loaded 3D mechanical metamaterials

Size effects exhibited by mechanical metamaterials when loaded may be positive such that reducing overall size towards that of the length scale of the underlying structure intrinsic to the material is accompanied by increasing stiffness or rigidity, a phenomenon that has been repeatedly observed and is also forecast by various more generalised continuum theories of deformation in loaded heterogeneous continua. However, such effects may in certain circumstances be contradictory in that decreasing size is accompanied by increasing compliance, the transition from the conventional, positive to this theoretically unanticipated negative behaviour having been explained recently in terms of the distribution of material within 2D continua subject to bending. Here we report on a novel phenomenon newly observed in periodic 3D lattice materials comprised of repeated cubic unit cells formed of exterior edge and interior diagonal connectors. Subtle redistribution of matrix material from edges to diagonals causes the size effect to change dramatically, inverting from positive to negative when loaded in the torsional mode while the corresponding effect for the flexural mode remains entirely positive under the same circumstances. This observation may lead to the prospect of optimising the design of 3D periodic metamaterials to provide a stiffer response in one loading mode and a more compliant response in another, a feature that could potentially be exploited in various innovative applications

Simulating Drug-Eluting Stents: Progress Made and the Way Forward

Drug-eluting stents have significantly improved the treatment of coronary artery disease. Compared with their bare metal predecessors, they offer reduced rates of restenosis and thus represent the current gold standard in percutaneous coronary interventions. Drug-eluting stents have been around for over a decade, and while progress is continually being made, they are not suitable in all patients and lesion types. Furthermore there are still real concerns over incomplete healing and late stent thrombosis. In this paper, some modelling approaches are reviewed and the future of modelling and simulation in this field is discussed

Quantifying numerically forecast size effects in the free vibration of heterogeneous beams

This paper reports on the influence that a periodic microstructure has on the unconstrained flexural vibration of geometrically similar but differently sized heterogeneous beam samples. A numerical investigation was conducted by finite element analysis (FEA) incorporating the detailed heterogeneity to identify and quantify any effect of beam size on the transverse modal frequencies when the microstructural scale is comparable to the overall size. Finite element models of the macroscopic beam samples were created by firstly specifying microstructural scale unit cells containing a single void or inclusion using ANSYS Mechanical APDL and then repeatedly regenerating these as required. Four beam sizes consisting of one, two, three or four layers of unit cells were created while the length to depth aspect ratio was kept constant for all sizes. Void or inclusion volume fraction was also altered while keeping the homogenised mass and stiffness properties of each beam fixed. The influence of the beam boundary texture on the results was also investigated. The ANSYS results were compared to the analytical solution for a conventional Timoshenko beam and a nonlocal Timoshenko beam. Using the nonlocal Timoshenko analysis, the Eringen small length scale coefficients were estimated but found to be size dependent. Numerical predictions obtained from a novel control volume based finite element (CVFEM) procedure incorporating micropolar constitutive behaviour were therefore matched to the ANSYS results and thereby used to identify the two additional constitutive parameters featuring in planar micropolar elasticity theory, namely the characteristic length in bending and coupling number

Experimental and numerical analysis of size effects on stress intensity in anisotropic porous materials

A prominent size effect has previously been reported for the fracture behaviour of brittle porous materials, with smaller specimens behaving quite differently to their larger counterparts. In such materials, the size of the K-dominant zone has been numerically found to be greatly affected by the presence of voids in the near-tip area, thus putting the assumption of a single fracture parameter under question. In order to address this, in this study mode I tests are conducted on porous double cantilever beam specimens, while the stress distribution in the near-tip area is being observed by means of photoelasticity. Results validate the predicted size eect and suggest that the voids can indeed alter the size and shape of the stress pattern in the specimens. A parametric study is then conducted to investigate the in uence of void shape variations that can be caused by manufacturing inaccuracies on the stress concentration at the crack tip. It is found that although the stress intensity at the crack tip can be greatly aected by such factors, the size of the K-dominant zone remains unaffected