FEM Elements Research Articles

Multi-Scale Nonlinear Progressive Damage and Failure Analysis for Open-Hole Composite Laminates

In order to study the nonlinear behaviors and interactions among the constituents for the composite material structure under the tensile load, multiscale damage model using generalized method of cells (GMC) and a lamina-level progressive damage model were established, respectively, for fiber reinforced composite laminates with a central hole, which were based on the thermodynamic Schapery Theory (ST) at either the micro-level or the lamina level. Once the nonlinear progressive degradation of the matrix material reached the lower limit value for the ST method, matrix failures naturally occurred, the failure of the fiber was determined by the maximum stress failure criterion. For the multiscale progressive damage model, the GMC model consisting of a fiber subcell and three matrix subcells was imposed at each integral point of FEM elements, and the three matrix subcells undergo independent damage evolution. The load versus displacement curves and failure modes of the open-hole laminates were predicted by using the two progressive failure models, and the results were compared with that obtained by the Hashin-Rotem progressive failure model and the experimental results. The results show that the ST based method can obtain the nonlinear progressive damage evolution states and failure states of the composite at both the lamina level and the multiscale level. Finally, the damage contours and failure paths obtained are also presented.

Topology Optimization of B-pillar with Respect to Mesh Type and Size

This paper deals with the influence of different mesh types and element sizes in topology optimization. Meshes from brick elements, tetrahedral elements and combination of both of them were compared in sizes 20, 10 and 7mm. B-Pillar, structural car component, is used here in order to verify the sensitivity of topology optimization due to these changes. Loading case is considering side force 140 kN. Moreover, different solvers implemented in Siemens NX 12 (RAMP, LINEAR, LATTICE and SIMP) were used to analyse how they influence this particular optimization process. It is obvious that highest number of FEM elements is rapidly improving convergence and optimization results but computational time is increasing.

The Influence of corrosion on the stresses in members of open deck railway bridges

Nowadays, many old riveted railway bridges, mainly their members of the open deck, are corroded. The paper demonstrates the influence of corrosion on a stringer beam and on a cross-girder beam of a particular steel truss railway bridge in Slovakia. This is an important step in the assessment of the loading capacity and the residual lifetime of this bridge. A simple beam FEM model was refined by modelling the investigated members as plate elements. In such a way the real boundary conditions of the members were modelled most realistically by keeping the model as simple as possible at the same time. The stresses in the members were first calculated with the original cross-sectional dimensions and the results were compared with the real measured corroded cross-sections. A future corrosion rate was estimated and calculation of this case was also performed. The influence of stringer to cross-beam rigidity, the size of 2D FEM elements, and the steel material model (linear, bilinear with 1% hardening) were investigated too.

Stochastic Elasto-Plastic Analysis of Necking Bar with Random Tvergaard Coefficients

This paper reports on the computational modelling of static extension tests of the round steel bar. The main objective was to apply the generalised stochastic perturbation technique implemented as the Stochastic Finite Element Method to carry out the numerical simulation of its elasto-plastic behaviour. This approach was based on: the general order Taylor expansion of all input random variables and the resulting state functions of their average means, as well as on the Least Squares Method employed to determine analytical functions of in-between design parameters and the given structural responses. Tvergaard coefficients were assumed as the uncorrelated Gaussian random variables to check the effect of material porosity uncertainty on the statistical scattering of its deformations and stresses. The computational implementation employed the FEM system ABAQUS and computer algebra system MAPLE, including polynomial and non-polynomial local response functions of the displacements, plastic strains and reduced stresses. Moreover, 4-node axisymmetric, continuum, reduced-integration FEM elements (CAX4R) were used in the conducted analyses. The basic probabilistic characteristics of the structural response (expectations, coefficients of variation, skewness and kurtosis) were determined throughout the entire deformation process as the functions of input uncertainty level. The obtained results were finally contrasted with the classical Monte-Carlo Simulation scheme and the semi-analytical technique for input coefficient of variation of porous plasticity coefficients not larger than 0.20.

FE-DEM with interchangeable modeling for off-road tire traction analysis

This study examines a new finite element/discrete element method (FE-DEM) with interchangeable modeling between FEM and DEM for tire traction analysis. In the method, named iFE-DEM, the soil in a soil bin is modeled initially by FEM except for the region under or near the tire, which is modeled using DEM. When the FEM tire model starts to travel over DEM soil elements, the updated tire location will activate new conversion of modeling from FEM to DEM so that the zone of influence around the contact interface between tire and soil can be analyzed continuously using DEM. Those mobilized DEM elements rearward of the tire might be converted again to FEM elements by assuming that the effect of the stress state in DEM generated by tire travel might be negligible. The computational time for two-dimensional iFE-DEM analysis of a slip of 40% using the smallest region of initial DEM under the tire could be reduced to 23% of that obtained using DEM only soil modeling.

Stabilized FEM–BEM coupled solution of MHD pipe flow in an unbounded conducting medium

In this study, we have considered the Magnetohydrodynamic (MHD) flow in a pipe with a circular or square cross section around a conducting solid and in an insulating or conducting medium. An external magnetic field is applied with an angle α with the axis of the pipe. The mathematical model of the considered physical problem can be defined in terms of coupled MHD equations in the pipe domain and the Laplace equations on the solid and external mediums. Due to the unbounded external domain and coupled form of the MHD equations, the FEM and BEM coupling approach is used which has many advantages in the view of discretization, computational time and stabilization. In the solution procedure, the fluid domain is discretized by the FEM elements, and the boundaries of the solid and the conducting mediums by the BEM elements. Proposed coupled numerical scheme is tested especially for the high values of the problem parameters and obtained stable solutions are displayed in terms of figures.

Applicable FEM Models for Layered Beams

We need to create appropriate and effective numerical (FEM) model to optimize properties of a composite product. The creation and evaluation of an efficient numerical model that could be used for an analysis of layered composite is the aim of this work. The model has to be able to take into account the properties and layout of the individual layers and must allow effective change of these parameters; thickness, material and number of layers especially. Various models of the same product are created and compared. The models differ in the type of used FEM elements. The results of models (deformation primarily) were compared with the result of analytical computation. Further, time and computational requirements of individual models are also evaluated. Element types used for investigated models are: 1D elements, 2D plane stress solid elements, 2D plane strain solid elements and shell elements. Models created form 1D and shell elements showed a close agreement with the analytical solution, and they provide the appropriate tools for the definition of layered structures and for the analysis of results.

Induction of through-thickness compressive residual stress fields in thin Al2024-T351 plates by laser shock processing

Purpose – With the aid of the calculational system developed by the authors, the analysis of the problem of laser shock processing (LSP) treatment for induction of residual stress (RS) fields for fatigue life enhancement in relatively thin sheets in a way compatible with reduced overall workpiece deformation due to spring-back self-equilibration has been envisaged. Numerical results directly tested against experimental results have been obtained confirming the critical influence of the laser energy and irradiation geometry parameters. The paper aims to discuss these issues. Design/methodology/approach – Plane rectangular specimens (160 mm×100 mm×2 mm) of Al-cladded (∼80 μm) Al2024-T351 were considered both for LSP experimental treatment and for corresponding numerical simulation. The test piece is fixed on a holder and is driven along X and Y directions by means of an anthropomorphic robot. The predefined pulse overlapping strategy is used for the irradiation of extended areas of material. From the geometrical point of view, a full 3D configuration for the real geometry and for the sequential overlapping strategy of pulses has been considered. The FEM elements used for the simulation are an eight-node brick reduced integration with hourglass control in the treated area, namely C3D8RT, and a six-node trainer prism in the rest of the geometry, where there is no applied load, namely C3D6T, that ease meshing complex partitions. The element size in the nearest of the treated surface is 100×100×25 µm, being the maximum element size which allows to maintain calculation convergence. Findings – Numerical results directly tested against experimental results have been obtained confirming: first, the critical influence of the laser energy and irradiation geometry parameters on the possible thin sheets deformation, both at local and global scales. Second, the possibility of finding LSP treatment parameter regimes that, maintaining the requirements relative to in-depth RSs fields, are able to reduce the relative importance of sheet deformation. Third, the possibility of finding LSP treatment parameter regimes able to provide through-thickness compressive RSs fields at levels compatible with an effective fatigue life enhancement. Fourth, the possibility of improving this through-thickness compressive RSs fields by double-side treatments. Fifth, the capability of the experimental LSP treatment system at the authors site (CLUPM) of practically achieve the referred through-thickness compressive RSs fields in excellent agreement with the predictive assessment obtained by the used numerical code (SHOCKLAS®). Practical implications – The referred results provide a firm basis for the design of LSP treatments able to confer a broad range of RSs fields to thin components aiming the extension of their fatigue life, an enormously relevant field in which the authors are currently working. Originality/value – The LSP treatment of relatively thin specimens brings, as an additional consequence, the possible bending in a process of laser shock forming. This effect poses a new class of problems regarding the attainment of specified RS’s depth profiles in the mentioned type of sheets, and, what can be more critical, an overall deformation of the treated component. The analysis of the problem of LSP treatment for induction of tentatively through-thickness RS’s fields for fatigue life enhancement in relatively thin sheets in a way compatible with reduced overall workpiece deformation due to spring-back self-equilibration is envisaged in this paper for the first time to the authors knowledge. The coupled theoretical-experimental predictive approach developed by the authors has been applied to the specification of LSP treatments for achievement of RS’s fields tentatively able to retard crack propagation on normalized specimens.

Experiment and Elastic-Plastic Modelling of the IPN160 Beam

The paper compares the numerical models of and experiments with a beam. The purpose is to evaluate the nonlinear material model of a steel structure. The steel is modelled as an ideal elastic-plastic material. The FEM and eight-node isoparametric finite elements are considered in the analysis. The 3D calculations use different material constants and several approaches are being tested in order to create the computational models. The calculations are performed in the software application developed by our university.

Simulation on progressive collapse behaviour of whole ship model under extreme waves using idealized structural unit method

To ensure the safety of navigating ship, working loads and structural load-carrying capacity are two important aspects. In the present paper, a total simulation system combing load calculation and structural collapse analysis is applied to simulate progressive collapse behaviour of a single-hull Kamsarmax type bulk carrier. A three dimensional singularity distribution method is adopted to calculate pressure distribution with time history. A mixed structural model, collapse part simulated by ISUM elements and remaining part by elastic FEM elements with relative coarse mesh, is proposed for collapse analysis. Progressive collapse behaviour obtained by ISUM is good agreement with that by nonlinear software package, MARC. However, the calculation time of ISUM analysis is about 1/70 of MARC analysis. The applicability to structure system, high accuracy and sufficient efficiency of ISUM had been demonstrated.

FEM elements enriched with meshfree functions: overview and application

A specific method of coupling FEM and meshless/meshfree methods is presented. This method is based on placing meshfree nodes inside the finite element and as a result improving the overall approximation on that element. Advantages and disadvantages of such approach are explained. It is shown that such approach is a version of a more general one. Numerical experiments are presented and analyzed.

Element-wise fracture algorithm based on rotation of edges

We propose an alternative, simpler algorithm for FEM-based computational fracture in brittle, quasi-brittle and ductile materials based on edge rotations. Rotation axes are the crack front edges (respectively nodes in surface discretizations) and each rotated edge affects the position of only one or two nodes. Modified positions of the entities minimize the difference between the predicted crack path (which depends on the specific propagation theory in use) and the edge or face orientation. The construction of all many-to-many relations between geometrical entities in a finite element code motivates operations on existing entities retaining most of the relations, in contrast with remeshing (even tip remeshing) and enrichment which alter the structure of the relations and introduce additional entities to the relation graph (in the case of XFEM, enriched elements which can be significantly different than classical FEM elements and still pose challenges for ductile fracture or large amplitude sliding). In this sense, the proposed solution has algorithmic and generality advantages. The propagation algorithm is simpler than the aforementioned alternatives and the approach is independent of the underlying element used for discretization. For history-dependent materials, there are still some transfer of relevant quantities between meshes. However, diffusion of results is more limited than with tip or full remeshing. To illustrate the advantages of our approach, two prototype models are used: tip energy dissipation (LEFM) and cohesive-zone approaches. The Sutton crack path criterion is employed. Traditional fracture benchmarks and newly proposed verification tests are solved. These were found to be very good in terms of crack path and load/deflection accuracy.

Element-wise algorithm for modeling ductile fracture with the Rousselier yield function

Within the theme of ductile fracture in metals, we propose an algorithm for FEM-based computational fracture based on edge rotations and smoothing of complementarity conditions. Rotation axes are the crack front nodes in surface discretizations and each rotated edge affects the position of only one or two nodes. Modified edge positions correspond to the predicted crack path. To represent softening, porous plasticity in the form of the Rousselier yield function is used. The finite strain integration algorithm makes use of a consistent updated Lagrangian formulation which makes use of polar decomposition between each increment. Constitutive updating is based on the implicit integration of a regularized non-smooth problem. The proposed alternative is advantageous when compared with enriched elements that can be significantly different than classical FEM elements and still pose challenges for ductile fracture or large amplitude sliding. For history-dependent materials, there are still some transfer of relevant quantities between meshes. However, diffusion of results is more limited than with tip or full remeshing. To illustrate the advantages of our approach, fracture examples making use of the Rousselier yield function are presented. The Ma-Sutton crack path criterion is employed. Traditional fracture benchmarks and newly proposed verification tests are solved. These were found to be very good in terms of crack path and load/displacement accuracy.

Adaptive atomistic‐to‐continuum modeling of propagating defects

SUMMARYAn adaptive atomistic‐to‐continuum method is presented for modeling the propagation of material defects. This method extends the bridging domain method to allow the atomic domain to dynamically conform to the evolving defect regions during a simulation, without introducing spurious oscillations and without requiring mesh refinement. The atomic domain expands as defects approach the bridging domain method coupling domain by fine graining nearby finite elements into equivalent atomistic subdomains. Additional algorithms coarse grain portions of the atomic domain to the continuum scale, reducing the degrees of freedom, when the atomic displacements in a subdomain can be approximated by FEM or extended FEM elements to within a certain homogeneity tolerance. The extended FEM approximations are created by fitting the broken inter‐atomic bonds of fractured surfaces and dislocation slip planes. Because atomic degrees of freedom are maintained only where needed for each timestep, the solution retains the advantages of multiscale modeling, with a reduced computational cost compared with other multiscale methods. Copyright © 2012 John Wiley & Sons, Ltd.

The equations of motion of the main structure with attached multiple tuned mass dampers

A mathematical model of structure with multiple tuned mass dampers (MTMD) is presented in this paper. An important difficulty, connected with these model, is building a global damping matrix of the system. The own proposals FEM elements describing additional elements attached to the main system in the form of tuned dampers have been proposed here. The benefits of the new FEM elements have been briefly discussed.

The equations of motion of the main structure with attached dampers described by standard rheological model

A mathematical model of structure with multiple tuned mass dampers (MTMD) is presented in this paper. An important difficulty, connected with these model, is building a global damping matrix of the system. The own proposals of FEM elements describing additional elements attached to the main system in the form of tuned dampers are presented here. The benefits of the new FEM elements are briefly discussed.

A hybrid FEM model to simulate the electrical characteristics of biological tissues at the cellular level

Cancer screening is possible with multi-frequency electrical impedance tomography since specific impedance variations are observable as a function of frequency. Through genetic mutations, malignant cells have different cellular characteristics than benign cells and a different impedance signature as a function of frequency. The objective of this project is to develop a FEM model to simulate the electrical characteristics of benign and malignant cells at the cellular level. Traditional tetrahedral element meshing techniques were first considered but the narrowness of the extracellular space and thinness of cell membranes made it impractical since the number of FEM elements quickly reached values that were computationally unmanageable on a typical workstation. We are therefore proposing a hybrid FEM model which combines a standard tetrahedral element meshing technique with 2D surfaces to model the extracellular fluid and discrete electrical components to represent cell membranes. The proposed hybrid modelling approach was used to develop a 3D FEM model of the skin with cellular-level details that can be used to better understand how impedance measurements performed on the skin are affected by lesions as a function of frequency as well as cellular geometrical and electrical parameters.

Analyses of reactor building by 3D nonlinear FEM models considering basemat uplift for simultaneous horizontal and vertical ground motions

The nonlinear behavior of basemat uplift, which is an important point in seismic designs of nuclear power plants in Japan, has been investigated by arranging joint elements between the reactor building basemat and the soil on a three-dimensional (hereafter referred to as 3D) FEM model of the soil. However, the nonlinearity of the basemat uplift has been investigated separately from the nonlinearity of reactor buildings. These nonlinearities have yet to be taken into account simultaneously in past studies. In this paper, models of the building and the soil using 3D FEM elements with consideration to the nonlinearity of building materials as well as the nonlinearity of the basemat uplift were subjected. The behavior of the building's elements were investigated by carrying out seismic response analyses for horizontal ground motions only, as well as for simultaneous horizontal and vertical ground motions using these models. As a result, it was found that there was little difference in the horizontal response of the building between the horizontal input motions only and the simultaneous horizontal and vertical input motions. The effects of the vertical ground motions on the basemat uplift behavior which is represented by the ground contact ratio were also slight.

Different approaches for efficient finite element modelling of absorbers in small rooms

The FEM is a powerful tool for the numerical simulation of sound fields in enclosures. It accounts for the modal characteristics of the sound field, which are dominant at frequencies below the Schroeder frequency and it is also possible to model the mutual coupling between airborne and structure borne sound fields, when an appropriate structure model is implemented. When applying the FEM to complex room acoustics applications, like e.g. a control room in a recording studio, it is a challenging task to specify realistic boundary conditions. Different kinds of acoustical absorbers like Helmholtz resonators, plate absorbers and complex layered porous absorbers are found in these environments. While it is possible in principle to use complex and exhaustive models for these acoustical absorbers, it is often computationally much more efficient to use acoustic impedances or two-port network FEM elements to represent the fluid structure interactions. In the course of this study we compare different approaches for the modelling of Helmholtz resonators (without and without flow resistance), since it has proven very costly in terms of computation time to explicitly model every single hole in the resonator boxes. The simulation results are compared with results measured in a model room.

Application of the 2-D constant strain assumption to FEM elements consisting of an arbitrary number of nodes

The formulation for the constant strain element is revisited to develop multi-noded elements that can be used as transition elements in a finite element mesh. Although the constant strain approach is computationally attractive, spurious force-free displacement modes arise for elements consisting of more than three nodes. These unstable mode shapes are typified by “hourglassing” which develops in quadrilateral elements when constant strain is assumed within the element. The means for stabilizing spurious mode shapes for quadrilateral elements is well documented in the literature, however, in this paper, a general formulation for stabilizing forces is presented for elements having an arbitrary number of nodes and therefore is not restricted to quadrilateral elements. This paper examines the use of meshes consisting of constant strain elements created from polygons having differing numbers of element nodes. The effectiveness of the stabilization procedure is illustrated along with “patch test” examples to assess the consistency of the approximation. The elements are shown to be surprisingly robust, yielding reasonable results even when poorly designed mesh transitions are used.