The Reproducing Kernel DMS-FEM: 3D Shape Functions and Applications to Linear Solid Mechanics

We propose a family of 3D versions of a smooth finite element method (Sunilkumar and Roy 2010), wherein the globally smooth shape functions are derivable through the condition of polynomial reproduction with the tetrahedral B-splines (DMS-splines) or tensor-product forms of triangular B-splines and ID NURBS bases acting as the kernel functions. While the domain decomposition is accomplished through tetrahedral or triangular prism elements, an additional requirement here is an appropriate generation of knotclouds around the element vertices or corners. The possibility of sensitive dependence of numerical solutions to the placements of knotclouds is largely arrested by enforcing the condition of polynomial reproduction whilst deriving the shape functions. Nevertheless, given the higher complexity in forming the knotclouds for tetrahedral elements especially when higher demand is placed on the order of continuity of the shape functions across inter-element boundaries, we presently emphasize an exploration of the triangular prism based formulation in the context of several benchmark problems of interest in linear solid mechanics. In the absence of a more rigorous study on the convergence analyses, the numerical exercise, reported herein, helps establish the method as one of remarkable accuracy and robust performance against numerical ill-conditioning (such as locking of different kinds) vis-a-vis the conventional FEM.

An experimental approach for non-destructive evaluation of fatigue damage in CFRP composites

Study of fatigue phenomenon in composites requires a dynamic tool which can detect and identify different failure mechanisms involved. The tool should also be capable of monitoring the cumulative damage progression on-line. Acoustic Emission Technique has been utilized in the experimental investigations on unidirectional carbon fiber reinforced plastic (CFRP) composite specimens subjected to tension-tension fatigue. Amplitude as well as frequency distribution of Acoustic Emission (AE) signals have been studied to detect and characterize different failure mechanisms. For a quantitative measure of degradation of the material with fatigue load cycles, reduction in stiffness of the specimen has been measured intermittently. Ultrasonic imaging could give the information on the changes in the interior status of the material at different stages of fatigue life.

Automatic decomposition of unstructured meshes employing genetic algorithms for parallel FEM computations

Parallel execution of computational mechanics codes requires efficient mesh-partitioning techniques. These mesh-partitioning techniques divide the mesh into specified number of submeshes of approximately the same size and at the same time, minimise the interface nodes of the submeshes. This paper describes a new mesh partitioning technique, employing Genetic Algorithms. The proposed algorithm operates on the deduced graph (dual or nodal graph) of the given finite element mesh rather than directly on the mesh itself. The algorithm works by first constructing a coarse graph approximation using an automatic graph coarsening method. The coarse graph is partitioned and the results are interpolated onto the original graph to initialise an optimisation of the graph partition problem. In practice, hierarchy of (usually more than two) graphs are used to obtain the final graph partition. The proposed partitioning algorithm is applied to graphs derived from unstructured finite element meshes describing practical engineering problems and also several example graphs related to finite element meshes given in the literature. The test results indicate that the proposed GA based graph partitioning algorithm generates high quality partitions and are superior to spectral and multilevel graph partitioning algorithms.

Detection and Evaluation of Impact damage in CFRP Laminates Using Ultrasound C-Scan and IR Thermography

Advanced composite structural components made up of Carbon Fibre Reinforced Polymers (CFRP) used in aerospace structures such as in Fuselage, Leading & Trailing edges of wing and tail, Flaps, Elevator, Rudder and entire wing structures encounter most critical type of damage induced by low velocity impact (<10 m/s) loads. Tool dropped during maintenance & service,and hailstone impacts on runways are common and unavoidable low-velocity impacts. These lowvelocity impacts induce defects such as delaminations, matrix cracking and debonding in the layered material, which are sub-surface in nature and are barely visible on the surface known as Barely Visible Impact Damage (BVID). These damages may grow under service load, leading to catastrophic failure of the structure. Hence detection, evaluation and characterization of these types of damage is of major concern in aerospace industries as the life of the component depends on the size and shape of the damage.In this paper, details of experimental investigations carried out and results obtained from a low-velocity impact of 30 Joules corresponding to the hailstone impact on the wing surface,simulated on the 6 mm CFRP laminates using instrumented drop-weight impact testing machine are presented. The Ultrasound C-scan and Infrared thermography imaging techniques were utilized extensively to detect, evaluate and characterize impact damage across the thickness of the laminates.

Smooth DMS-FEM: A new approach to solving nearly incompressible nonlinear elasto-static problems

The DMS-FEM, which enables functional approximations with C(1) or still higher inter-element continuity within an FEM-based meshing of the domain, has recently been proposed by Sunilkumar and Roy [39,40]. Through numerical explorations on linear elasto-static problems, the method was found to have conspicuously superior convergence characteristics as well as higher numerical stability against locking. These observations motivate the present study, which aims at extending and exploring the DMS-FEM to (geometrically) nonlinear elasto-static problems of interest in solid mechanics and assessing its numerical performance vis-a-vis the FEM. In particular, the DMS-FEM is shown to vastly outperform the FEM (presently implemented through the commercial software ANSYS (R)) as the former requires fewer linearization and load steps to achieve convergence. In addition, in the context of nearly incompressible nonlinear systems prone to volumetric locking and with no special numerical artefacts (e.g. stabilized or mixed weak forms) employed to arrest locking, the DMS-FEM is shown to approach the incompressibility limit much more closely and with significantly fewer iterations than the FEM. The numerical findings are suggestive of the important role that higher order (uniform) continuity of the approximated field variables play in overcoming volumetric locking and the great promise that the method holds for a range of other numerically ill-conditioned problems of interest in computational structural mechanics. (C) 2011 Elsevier Ltd. All rights reserved.

Ultrasonic evaluation of delamination in quasi-isotropic CFRP laminates subjected to low-velocity impact

Ultrasonic C-Scan is used very often to detect flaws and defects in the composite components resulted during fabrication and damages resulting from service conditions. Evaluation and characterization of defects and damages of composites require experience and good understanding of the material as they are distinctly different in composition and behavior as compared to conventional metallic materials. The failure mechanisms in composite materials are quite complex. They involve the interaction of matrix cracking, fiber matrix interface debonding, fiber pullout, fiber fracture and delamination. Generally all of them occur making the stress and failure analysis very complex. Under low-velocity impact loading delamination is observed to be a major failure mode. In composite materials the ultrasonic waves suffer high acoustic attenuation and scattering effect, thus making data interpretation difficult. However these difficulties can be overcome to a greater extent by proper selection of probe, probe parameter settings like pulse width, pulse amplitude, pulse repetition rate, delay, blanking, gain etc., and data processing which includes image processing done on the image obtained by the C-Scan.

Wrinkled and slack membranes: nonlinear 3D elasticity solutions via smooth DMS-FEM and experiment

The smooth DMS-FEM, recently proposed by the authors, is extended and applied to the geometrically nonlinear and ill-posed problem of a deformed and wrinkled/slack membrane. A key feature of this work is that three-dimensional nonlinear elasticity equations corresponding to linear momentum balance, without any dimensional reduction and the associated approximations, directly serve as the membrane governing equations. Domain discretization is performed with triangular prism elements and the higher order (C1 or more) interelement continuity of the shape functions ensures that the errors arising from possible jumps in the first derivatives of the conventional C0 shape functions do not propagate because the ill-conditioned tangent stiffness matrices are iteratively inverted. The present scheme employs no regularization and exhibits little sensitivity to h-refinement. Although the numerically computed deformed membrane profiles do show some sensitivity to initial imperfections (nonplanarity) in the membrane profile needed to initiate transverse deformations, the overall patterns of the wrinkles and the deformed shapes appear to be less so. Finally, the deformed profiles, computed through the DMS FEM-based weak formulation, are compared with those obtained through an experiment on an ultrathin Kapton membrane, wherein wrinkles form because of the applied boundary displacement conditions. Comparisons with a reported experiment on a rectangular membrane are also provided. These exercises lend credence to the feasibility of the DMS FEM-based numerical route to computing post-wrinkled membrane shapes. Copyright (c) 2012 John Wiley & Sons, Ltd.

An adaptive singular ES-FEM for mechanics problems with singular field of arbitrary order

This paper presents a singular edge-based smoothed finite element method (sES-FEM) for mechanics problems with singular stress fields of arbitrary order. The sES-FEM uses a basic mesh of three-noded linear triangular (T3) elements and a special layer of five-noded singular triangular elements (sT5) connected to the singular-point of the stress field. The sT5 element has an additional node on each of the two edges connected to the singular-point. It allows us to represent simple and efficient enrichment with desired terms for the displacement field near the singular-point with the satisfaction of partition-of-unity property. The stiffness matrix of the discretized system is then obtained using the assumed displacement values (not the derivatives) over smoothing domains associated with the edges of elements. An adaptive procedure for the sES-FEM is proposed to enhance the quality of the solution with minimized number of nodes. Several numerical examples are provided to validate the reliability of the present sES-FEM method. (C) 2012 Elsevier B.V. All rights reserved.

On the Utility of Microscopy and C-Scan Techniques in the Study of Defects Arising From Resin Infusion Process and a Study on the Influence of Voids on the Impact Behavior of CFRP Composites

Carbon Fiber Reinforced Plastic composites were fabricated through vacuum resin infusion technology by adopting two different processing conditions, viz., vacuum only in the first and vacuum plus external pressure in the next, in order to generate two levels of void-bearing samples. They were relatively graded as higher and lower void-bearing ones, respectively. Microscopy and C-scan techniques were utilized to describe the presence of voids arising from the two different processing parameters. Further, to determine the influence of voids on impact behavior, the fabricated +45 degrees/90 degrees/-45 degrees composite samples were subjected to low velocity impacts. The tests show impact properties like peak load and energy to peak load registering higher values for the lower void-bearing case where as the total energy, energy for propagation and ductility indexes were higher for the higher void-bearing ones. Fractographic analysis showed that higher void-bearing samples display lower number of separation of layers in the laminate. These and other results are described and discussed in this report.

Mechanical properties of CNT-Bisphenol E cyanate ester-based CFRP nanocomposite developed through VARTM process

This paper reports on the effect of multiwall carbon nanotubes (CNTs) without and with chemical functionalization on the mechanical properties of Bisphenol E cyanate ester resin (BECy) based carbon fibre reinforced plastic (CFRP) laminated composites. BECy with its low viscosity, low moisture uptake and superior mechanical properties is selected for its application in CFRP laminates through the cost-effective Vacuum Assisted Resin Transfer Moulding (VARTM) process. However, unlike CNT-epoxy-CFRP composites, processing and performance issues such as dispersion of CNTs, chemical bonding with resin, functionalization effects, effects on mechanical properties, etc. for BECy-CNT-CFRP composite system are not well reported. The objective of this study is to improve the mechanical properties of BECy resin with small additions of CNTs and functionalized CNTs in CFRP laminates. CNTs and fCNTs are infused into BECy using ultrasonication and standard mixing methods. Improvements in Young's modulus and strength in tension, compression, shear, flexure and interlaminar shear strength are analysed. It is observed that addition of 0.5wt% CNTs effected for maximum mechanical properties of the resin and 1wt% CNTs for the mechanical properties of CNT-CFRP nanocomposite. Further, improvements obtained with fCNTs are marginal. Dispersion behaviour and effect of CNTs/fCNTs in load transfer corroborated with SEM pictures are presented. The enhanced mechanical properties realized in VARTM processing of BECy-CFRP laminate indicate clear advantage of CNT based modification of the process.

A comparative study of failure features in aerospace grade unidirectional and bidirectional woven CFRP composite laminates under four-point bend fatigue loads

Damage mechanisms in unidirectional (UD) and bi-directional (BD) woven carbon fiber reinforced polymer (CFRP) laminates subjected to four point flexure, both in static and fatigue loadings, were studied. The damage progression in composites was monitored by observing the slopes of the load vs. deflection data that represent the stiffness of the given specimen geometry over a number of cycles. It was observed that the unidirectional composites exhibit gradual loss in stiffness whereas the bidirectional woven composites show a relatively quicker loss during stage II of fatigue damage progression. Both, the static and the fatigue failures in unidirectional carbon fiber reinforced polymer composites originates due to generation of cracks on compression face while in bidirectional woven composites the damage ensues from both the compression and the tensile faces. These observations are supported by a detailed fractographic analysis.