Analysis of an efficient finite element method for embedded interface problems

A stabilized finite element method based on the Nitsche technique for enforcing constraints leads to an efficient computational procedure for embedded interface problems, in which the finite element mesh need not be aligned with the interface geometry. We consider cases in which the jump of a field across the interface is given, as well as cases in which the primary field on the interface is given. Optimal rates of convergence hold. Representative numerical examples demonstrate the effectiveness of the proposed methodology.     

Investigation of strain transfer to a sensor protection system embedded in concrete using finite element analysis

Optical fibre-based sensor systems are being used increasingly in civil engineering applications where structural integrity monitoring is of interest or concern. This paper reports on an optimisation scheme for an optical fibre-based sensor protection system designed to protect and enhance the strain-transfer characteristic when it is embedded in concrete. The sensor protection system consisted of a stainless steel tube with specified flange designs. Three flange designs were considered: disc, cone and inverted cone. Non-linear finite element analysis incorporating contact logic was performed to select and optimise the shape and dimensions of the flange. The analysis showed high stress concentrations in the vicinity of the flanges. However, this effect was localised and was not transmitted to the intended location of the sensor. The results showed that all three flange designs were effective but the 5 mm diameter disc-shaped flange gave the best results in terms of the magnitude and symmetry of the shear stress at the tube-concrete interface.     

Formulation of a triangular finite element with an embedded interface via isoparametric mapping

 This paper presents the formulation of a triangular finite element with an embedded interface, designed for the simulation of discrete crack propagation processes. The element is developed within a displacement-based framework. Linear interpolation of the displacement discontinuities along the internal interface is assumed in order to ensure compatibility across inter-element boundaries. The proper representation of the rigid body motions and the solvability of the discretised version of the mechanical problem in point are specifically addressed. Finally, the element performance is illustrated through comparison with some alternative proposals. Received 24 January 2001     

Higher-order finite element modelling of laminated composite plates

P-version finite elements based on higher-order theory are developed for the two-dimensional modelling of general bending and cylindrical bending of thin-to-thick laminated composite plates. In the case of general laminated plate elements, three displacement fields are used. In the special case of cylindrically bent laminated plate elements, two displacement fields are needed. In each case the displacement is expressed as the product of two functions—one in terms of out-of-plane co-ordinates alone and the other in terms of in-plane co-ordinates. The shape functions used to build the displacement fields are based on integral of Legendre' polynomials. The quality and performance of the elements are evaluated in terms of convergence characteristics of displacements and stresses. The predicted response quantities are compared with those available in the published literature based on analytical as well as conventional finite element models.     

Adaptive finite element methodology for tumour angiogenesis modelling

In this paper, we consider an adaptive finite element approach for reliable, efficient solution of a class of continuum models for tumour‐induced angiogenesis. The ideas are demonstrated using an established three equation reaction/transport model that simulates aspects of tumour‐induced angiogenesis in a deterministic manner. The weak variational formulation and finite element approximation scheme for the model are developed, and a statistical approach for concurrent adaptive mesh refinement and coarsening is described. The appropriate form of the model and solution dependence on choice of parameters are explored. Computational results are presented for 1D, 2D and 3D geometry models. The effectiveness of the open‐source, parallel adaptive software library (LibMesh) that is being developed in the CFDLab at the University of Texas is also demonstrated. Copyright © 2006 John Wiley & Sons, Ltd.     

Experimental validation of a computationally efficient beam element for combined finite–discrete element modelling of structures in distress

 The combined finite/discrete element method is adopted to model the pre-failure and post failure transient dynamics of reinforced concrete structures. For this purpose a novel beam element is introduced in order to increase CPU and RAM efficiency. In this paper the accuracy and reliability of this element is assessed when used in dynamic loading conditions. Experiments, which have already been undertaken at the Swiss Federal Institute of Technology, are used for comparison and validation. The results indicate that the element introduced is capable of accurately modelling inertia and contact effects in pre and post failure dynamics, up to collapse. Received: 1 August 2002 / Accepted: 9 January 2002 A debt of gratitude is owed to Prof. Bachman and Mrs. N. Ammann for their kind and sincerely appreciated assistance in the provision of the reports from the Swiss Federal Institute of Technology. The assistance provided by Dr. W. Ammann and Dr. S. Heubbe-Walker in the translation of the reports is also gratefully acknowledged.     

An efficient finite element method for embedded interface problems

A stabilized finite element method based on the Nitsche technique for enforcing constraints leads to an efficient computational procedure for embedded interface problems. We consider cases in which the jump of a field across the interface is given, as well as cases in which the primary field on the interface is given. The finite element mesh need not be aligned with the interface geometry. We present closed‐form analytical expressions for interfacial stabilization terms and simple procedures for accurate flux evaluations. Representative numerical examples demonstrate the effectiveness of the proposed methodology. Copyright © 2008 John Wiley & Sons, Ltd.     

Wavefront sensor architectures fully embedded in an image sensor

Several architectures of wavefront sensors have been developed since the rise of adaptive optics. In all cases, optical elements are placed in front of image sensors. This makes the sensor quite bulky, expensive, and sensitive to optical misalignment. I propose two novel architectures fully embedded in the image sensor that require no additional optical element. The sensor can be placed directly in the beam to analyze, leading to small, easy to use, and cost-efficient systems. The two architectures are described before testing by simulation of their ability to sense the wavefront distortion and their sensitivity to signal-to-noise ratio.     

Experimental observations and finite element modelling of damage initiation and evolution in carbon/epoxy non-crimp fabric composites

Damage in carbon/epoxy non-crimp stitched fabric (NCF) reinforced composites, produced by the resin transfer moulding (RTM) process is described. Formation of the stitching loop results in a certain disturbance of the uniform placement of the fibres. These deviations in fibre placement produce resin-rich zones that can influence the mechanical behaviour of the composite part. Tensile tests on quadriaxial (45°/90°-45°/0°)_s laminates are performed accompanied by acoustic emission (AE) registration and X-ray imaging. Early initiation of damage (matrix cracking) in plies with different fibre orientation has been detected. Damage sites correlate with the resin-rich zones created by the stitching. Finite element (FE) analysis is carried out to develop a model that describes damage of the NCF composites. Numerical multi-level FE homogenization is performed to obtain effective elastic orthotropic properties of NCF composite at micro (unit cell of unidirectional tow) and meso (fabric unit cell) levels. A hierarchical sequence of FE models of different scales is created to analyze in detail the 3D stress state of the NCF composite (meso unit cell). A multi-level submodeling approach is applied during FE analysis. Zones of matrix-dominated damage are predicted. A comparison of non-destructive testing results with computational model is performed. Fracture mechanics parameters of matrix crack are computed and cracks growth stability is studied.     

An embedded mesh method for treating overlapping finite element meshes

A new technique for treating the mechanical interactions of overlapping finite element meshes is presented. Such methods can be useful for numerous applications, for example, fluid–solid interaction with a superposed meshed solid on an Eulerian background fluid grid. In this work, we consider the interaction of two elastic domains: one mesh is the foreground and defines the surface of interaction, the other is a background mesh and is often a structured grid. Many of the previously proposed methods employ surface defined Lagrange multipliers or penalties to enforce the boundary constraints. It has become apparent that these methods will cause mesh locking under certain conditions. Appropriately applied, the Nitsche method can overcome this locking, but, in its canonical form, is generally not applicable to non‐linear materials such as hyperelastics. The relationship between interior point penalty, discontinuous Galerkin and Nitsche's method is well known. Based on this relationship, a nonlinear theory analogous to the Nitsche method is proposed to treat nonlinear materials in an embedded mesh. Here, a discontinuous Galerkin derivative based on a lifting of the interface surface integrals provides a consistent treatment for non‐linear materials and demonstrates good behavior in example problems. Published 2012. This article is a US Government work and is in the public domain in the USA.     

Atomic-scale finite element modelling of mechanical behaviour of graphene nanoribbons

International Journal of Mechanics and Materials in Design - Experimental characterization of Graphene NanoRibbons (GNRs) is still an expensive task and computational simulations are therefore seen...     

A geometric nonlinear triangular finite element with an embedded discontinuity for the simulation of quasi-brittle fracture

This paper is aimed to model the appearance and evolution of discrete cracks in quasi-brittle materials using triangular finite elements with an embedded interface in a geometric nonlinear setting. The kinematics for the discontinuous displacement field is presented and the standard variational formulation with respect to the reference configuration is extended to a body with an internal discontinuity. Special attention is paid to the algorithmic treatment. The discontinuity is modeled by additional global degrees of freedom and the continuity of the displacements across the element boundaries is enforced. Finally, representative numerical examples for mode-I and mixed-mode fracture, namely a tension test, different three-point bending tests and a single edge notched beam with structured and unstructured finite element meshes are discussed to study the evolving crack pattern and to show the ability of the model.     

Delamination modelling of GLARE using the extended finite element method

In this paper, an application of the Extended Finite Element Method (XFEM) for simulation of delamination in fibre metal laminates is presented. The study consider a double cantilever beam made of fibre metal laminate in which crack opening in mode I and crack propagation were studied. Comparison with the solution by standard Finite Element Method (FEM) as well as with experimental tests is provided. To the authors’ knowledge, this is the first time that XFEM is used in the fracture analysis of fibre metal laminates such as GLARE. The results indicated that XFEM could be a promising technique for the failure analysis of composite structures.     

A multiplicative finite strain finite element framework for the modelling of semicrystalline polymers and polycarbonates

This paper presents a phenomenological model for the simulation and analysis of stress‐induced orientational hardening in semicrystalline polymers and polycarbonates at finite strains. The notion of intermediate (local) stress‐free configuration is used to develop a set of constitutive equations, and its relation to the multiple natural (stress‐free) configurations in the class of materials being considered here is discussed. A hyperelastic stored energy function, written with respect to the intermediate stress‐free configuration is presented to model the finite elastic response. It is then combined with the J₂‐flow theory to model the finite inelastic response. The isochoric constraint during inelastic deformation is treated via an exact multiplicative decomposition of the deformation gradient into volume‐preserving and spherical parts. The numerical solution algorithm is based on the use of operator splitting technique that results in a product formula algorithm with elastic‐predictor/inelastic‐corrector components. Numerical results are presented to show the behaviour of the model. Copyright © 2000 John Wiley & Sons, Ltd.     

An embedded atom hyperelastic constitutive model and multiscale cohesive finite element method

Based on embedded atom method (EAM), an embedded atom hyperelastic (EAH) constitutive model is developed. The proposed EAH constitutive model provides a multiscale formalism to determine mesoscale or macroscale material behavior by atomistic information. By combining the EAH with cohesive zone model (CZM), a multiscale embedded atom cohesive finite element model (EA-cohesive FEM) is developed for simulating failure of materials at mesoscale and macroscale, e.g. fracture and crack propagation etc. Based on EAH, the EA-cohesive FEM applies the Cauchy-Born rule to calculate mesoscale or macroscale material response for bulk elements. Within the cohesive zone, a generalized Cauchy-Born rule is applied to find the effective normal and tangential traction-separation cohesive laws of EAH material. Since the EAM is a realistic semi-empirical interatomic potential formalism, the EAH constitutive model and the EA-cohesive FEM are physically meaningful when it is compared with experimental data. The proposed EA-cohesive FEM is validated by comparing the simulation results with the results of large scale molecular dynamics simulation. Simulation result of dynamic crack propagation is presented to demonstrate the capacity of EA-cohesive FEM in capturing the dynamic fracture.     

An embedded statistical method for coupling molecular dynamics and finite element analyses

The coupling of molecular dynamics (MD) simulations with finite element methods (FEM) yields computationally efficient models that link fundamental material processes at the atomistic level with continuum field responses at higher length scales. The theoretical challenge involves developing a seamless connection along an interface between two inherently different simulation frameworks. Various specialized methods have been developed to solve particular classes of problems. Many of these methods link the kinematics of individual MD atoms with finite element (FE) nodes at their common interface, necessarily requiring that the FE mesh be refined to atomic resolution. Some of these coupling approaches also require simulations to be carried out at 0 K and restrict modelling to two‐dimensional material domains due to difficulties in simulating full three‐dimensional material processes. In the present work, a new approach to MD–FEM coupling is developed based on a restatement of the standard boundary value problem used to define a coupled domain. The method replaces a direct linkage of individual MD atoms and FE nodes with a statistical averaging of atomistic displacements in local atomic volumes associated with each FE node in an interface region. The FEM and MD computational systems are effectively independent and communicate only through an iterative update of their boundary conditions. Thus, the method lends itself for use with any FEM or MD code. With the use of statistical averages of the atomistic quantities to couple the two computational schemes, the developed approach is referred to as an embedded statistical coupling method (ESCM). ESCM provides an enhanced coupling methodology that is inherently applicable to three‐dimensional domains, avoids discretization of the continuum model to atomic scale resolution, and permits finite temperature states to be applied. Published in 2009 by John Wiley & Sons, Ltd.     

A mixed 3D finite element for modelling thick plates

Based on the Hellinger-Reissner variational principle, we formulate a mixed 3-d finite element for plate bending. This element is used to model thick plates and alleviates the problem of shear-locking in plates with large length/thickness ratios. The computer code which was used here, is available.     

Proposal of an active composite with embedded sensor

Though advanced composites with embedded actuator materials such as shape memory alloys and piezo ceramics have been developed as active materials, another one by making use of thermal deformation of composites was proposed and an active laminate was prepared as an example by hot-pressing of aluminum plate as material of high coefficient of thermal expansion (CTE), uni-directional carbon fiber reinforced plastics (CFRP) prepreg as low CTE material and electric resistance heater, polymer adhesive film as insulator between them, and copper foils as electrodes. Actuation of this laminate is different from that of bimetal because CTE of the CFRP layer is strongly anisotropic due to directionality of its reinforcement fiber. As CTEs of the CFRP layer and the aluminum plate in the fiber direction are quite different from each other though they are close to each other in the transverse direction, smooth and uni-directional actuation becomes possible. In this study, its fundamental performances such as shape change and output force were observed and evaluated, and after establishment of its fabrication, an optical loss type sensor was formed in the active composite, by embedding multiply pre-notched optical fiber in the CFRP layer and breaking it at the pre-notches under bending, followed by lamination on aluminum plate with adhesive. As the sensing part can be formed inside the matrix without any complicated processes, a robust and low cost sensor is obtained. From the results, it becomes clear that: (1) curvature of the active composite linearly changes as a function of temperature between room temperature and its hot pressing temperature by electric resistance heating of the CFRP layer and cooling, (2) its output force against a fixed punch during heating from room temperature up to around glass transition temperature of the resin phase almost linearly increases with increasing temperature, (3) the multiply pre-notched, embedded and fractured optical fiber works as a sensitive sensor for monitoring the curvature of the active composite.