Multilayered folding with voids

In the deformation of layered materials such as geological strata, or stacks of paper, mechanical properties compete with the geometry of layering. Smooth, rounded corners lead to voids between the layers, while close packing of the layers results in geometrically-induced curvature singularities. When voids are penalized by external pressure, the system is forced to trade off these competing effects, leading to sometimes striking periodic patterns. In this paper we construct a simple model of geometrically nonlinear multi-layered structures under axial loading and pressure confinement, with non-interpenetration conditions separating the layers. Energy minimizers are characterized as solutions of a set of fourth-order nonlinear differential equations with contact-force Lagrange multipliers, or equivalently of a fourth-order free-boundary problem. We numerically investigate the solutions of this free boundary problem, and compare them with the periodic solutions observed experimentally

Reduction in calcium excretion in women with breast cancer and bone metastases using the oral bisphosphonate pamidronate.

The bisphosphonate pamidronate (3 amino-1, 1-hydroxypropylidene bisphosphonate (APD), Ciba-Geigy) is a powerful inhibitor of osteoclast function and has been shown to significantly reduce osteolysis associated with bone metastases in breast cancer. Until recently, however, only an intravenous preparation has been readily available. We have evaluated the toxicity and effect on urinary calcium excretion of an enteric-coated oral preparation of pamidronate in a phase I/II trial in patients with bone metastases from breast cancer. Sixteen women with progressive disease and evidence of active bone resorption with an elevated calcium excretion (fasting urine calcium/creatinine ratio greater than 0.4 (mmol mmol-1) on two occasions prior to treatment) were studied. Four were given 150 mg daily; four 300 mg daily; four 450 mg daily and four 600 mg daily. Urinary calcium/creatinine (Ca2+/Cr) ratios were measured on all patients after an overnight fast. In patients on 150 mg daily the mean ratio fell from 0.65 (range 0.57-0.72) before treatment to 0.13 (0.02-0.19) after three weeks treatment. Mean values at entry for patients on 300, 450 and 600 mg were 1.18 (0.72-2.1), 0.76 (0.42-1.5) and 0.63 (0.52-0.82) respectively and after treatment these fell to 0.11 (0.05-0.18), 0.37 (0.14-0.68) and 0.17 (0.06-0.25). There were no significant differences in efficacy between treatment groups. Oral, enteric-coated disodium pamidronate is non-toxic and effectively reduces calcium excretion, raised in association with metastatic bone disease at doses of 150 mg or above. At the doses used to date it is as effective as weekly treatments with 30 mg of the intravenous preparation. Further studies are required in order to determine its value for preventing complications of bone disease and possibly as an adjuvant to surgery for breast cancer

A finite deformation Cosserat continuum model for uncured carbon fibre composites

A new three-dimensional, finite deformation Cosserat continuum model for the elastic response of uncured carbon fibre composites is presented. The new composite process model captures the bending contribution of bundles of fibres at the microscale within a mesoscale continuum description of a composite ply. This is achieved by introducing higher-order, independent rotational degrees of freedom into the continuum formulation. This paper demonstrates the inclusion of such mechanics is essential to accurately model various bending responses induced during typical composite manufacturing processes. This includes large deformation forming, finite strain consolidation and wrinkling (the formation of an unwanted defect). If such mechanics are not included, the literature demonstrates the resulting finite element solutions have a pathological dependence on the mesh size. As a result, simulations require users to fit mesh-dependent material parameters, which limits confidence in their predictive capabilities. The Cosserat continuum, which can be seen as a form of the regularised continuum model, overcomes these challenges. In particular, this paper presents details of the finite element formulation of the new continuum model within a nonlinear Taylor–Hood Cosserat Element. Implementation details of embedding this new element within the commercial code Abaqus are given, alongside a series of increasingly complex validation simulations. Notably, the examples include modelling the formation of internal fibre wrinkles and large deformation forming, which involves complex ply-to-ply and tool-to-ply contact. The paper concludes by describing: (1) how the elastic Cosserat model can be integrated into existing large deformation process models in the literature. The approach set out readily allows researchers to include the important effects of resin flow, cure kinetics and temperature distribution, not considered in this contribution, and (2) how it is envisaged that the ply scale model can be naturally scaled up to large laminate scale simulation using mathematical upscaling techniques

Optimum fibre-steering of composite plates for buckling and manufacturability

This paper reveals the potential weight saving in creating lightweight composite panels using the novel Continous Tow Shearing technique. The method provides a unique capability to simultaneously manipulate fibre angles and local thicknesses, whilst achieving defect-free, high curvature fibre paths. Considering the buckling of a typical aircraft wing skin, the nonlinear optimisation problem presented, shows theoretical designs with significant weights savings if compared to panels made from conventional straight fibre angles (38%) or steered using Automated Fibre Placement techniques (20%). The implications due to constraints on panelstrength, damage tolerance and manufacturing costs are then considered