Finite element modelling of inverse design problems in large deformations anisotropic hyperelasticity

This paper introduces a finite element model for the inverse design of pieces with large displacements in the elastic range. The problem consists in determining the initial shape of the piece, such that it attains the designed shape under the effect of service loads. The model is particularly focused on the design of parts with a markedly anisotropic behavior, like laminated turbine blades. Although the formulation expresses equilibrium on the distorted configuration, it uses a standard constitutive equations library that is expressed as usual for measures attached to the undistorted configuration. In this way, the modifications to a standard finite elements code are limited to the routines for the computation of the finite element internal forces and tangent matrix. Two examples are given, the first one for validation purposes, while the second is an application which has industrial interest for the design of turbine blades. Copyright © 2007 John Wiley & Sons, Ltd.     

Finite element formulation for modelling large deformations in elasto‐viscoplastic polycrystals

Anisotropic, elasto‐viscoplastic behaviour in polycrystalline materials is modelled using a new, updated Lagrangian formulation based on a three‐field form of the Hu‐Washizu variational principle to create a stable finite element method in the context of nearly incompressible behaviour. The meso‐scale is characterized by a representative volume element, which contains grains governed by single crystal behaviour. A new, fully implicit, two‐level, backward Euler integration scheme together with an efficient finite element formulation, including consistent linearization, is presented. The proposed finite element model is capable of predicting non‐homogeneous meso‐fields, which, for example, may impact subsequent recrystallization. Finally, simple deformations involving an aluminium alloy are considered in order to demonstrate the algorithm. Copyright © 2004 John Wiley & Sons, Ltd.     

Modelling brittle impact failure of disc particles using material point method

Understanding the impact failure of particles made of brittle materials such as glasses, ceramics and rocks is an important issue for many engineering applications. During the impact, a solid particle is turned into a discrete assembly of many fragments through the development of multiple cracks. The finite element method is fundamentally ill-equipped to model this transition. Recently a so-called material point method (MPM) has been used to study a wide range of problems of material and structural failures. In this paper we propose a new material point model for the brittle failure which incorporates a statistical failure criterion. The capability of the method for modelling multiple cracks is demonstrated using disc particles. Three impact failure patterns observed experimentally are captured by the model: Hertzian ring cracks, meridian cracks, and multi-fragment cracks. Detailed stress analysis is carried out to interpret the experimental observations. In particular it is shown that the experimentally observed dependence of a threshold velocity for the initiation of meridian cracks on the particle size can be explained by the proposed model. The material point based scheme requires a relatively modest programming effort and avoids node splitting which makes it very attractive over the traditional finite element method.     

Numerical modelling of fracture initiation in large steel specimens at impact

Dynamic mode I fracture initiation in impact loaded single edge bend specimens with a quarter notch is investigated by numerical modelling and the results are compared with sets of experimental data from two different steel qualities. The finite element analysis include 2D (two-dimensional) plane strain, 2D plane stress and 3D models. No crack growth is included in the calculations. The impact velocities are approximately 15, 30 and 45 m/s and the specimen size is 320×75 mm² with a thickness of 20 or 40 mm. Some specimens have side grooves. Details of the deflection of the specimens are accurately reproduced prior to crack initiation both by the 2D plane strain model and by the 3D model.The experiments were performed in the ductile to brittle transition region. It is assumed that cleavage fracture initiation can be predicted by the Ritchie-Knott-Rice (RKR) model, i.e. cleavage fracture initiates when the opening stress exceeds the macroscopic cleavage stress over a fixed, critical distance. At an impact velocity of 15 m/s, fracture initiation by void nucleation and growth is observed, though the RKR-conditions is seemingly fulfilled according to the computational results. Possible limitations in the use of the RKR model are discussed.     

Finite element modelling of two phase Fe–Cu polycrystals

The plastic deformation of two-phase iron–copper polycrystals was studied experimentally and modelled by a FEM model calculation, taking into account anisotropic elasticity and crystal plasticity. The two-phase materials in experiment had microstructures ranging between interpenetrating network and matrix/inclusion type and were deformed by compression at room temperature. The measured quantities (macroscopic stress and strain, elastic strains and texture) were compared with the results from the FEM model calculation. The stress vs. strain dependence as obtained from the FEM-model appears to be in good accordance with experimental results. Good predictions of the texture evolution were found in cases only, where local micromechanical interactions are not too much influenced by the heterogeneity of the microstructure. The implications of these results for the development and use of FEM schemes for modelling heterogeneous polycrystal plasticity are discussed.     

Finite element prediction of thermal stresses and deformations in layered manufacturing of metallic parts

Summary Residual stress induced deformations are a major cause of loss in tolerances in Solid Freeform Fabrication processes employing direct metal deposition. In this paper, a 2D finite element thermo-mechanical model is presented to predict the residual stress induced deformations with application to processes where material is added using a distributed, moving heat source. A sequentially coupled thermo-mechanical analysis is performed using a kinematic thermal model and plane strain structural model. Temperature dependent material properties are used with the material modeled as elastic perfectly plastic. An interpass cooling between successive depositions is employed in accordance to the requirement of experiment. The simulation results are compared with experimental data for successive sections along deposition and it is found that, with the exception of deposition center and plate edges, the two are in very good agreement. The error at plate edges can be as high as 45%, and the reason is that a 2D model cannot capture the effect of plate bolting accurately. A case of continuous deposition, without interpass cooling, has been compared with the base case of employing interpass cooling. It has been found that continuous deposition results in higher preheating of the substrate which consequently reduces the deformation.     

Theoretical prediction of welding distortion in large and complex structures

Welding technology is widely used to assemble large thin plate structures such as ships, automobiles, and passenger trains because of its high productivity. However, it is impossible to avoid welding-induced distortion during the assembly process. Welding distortion not only reduces the fabrication accuracy of a weldment, but also decreases the productivity due to correction work. If welding distortion can be predicted using a practical method beforehand, the prediction will be useful for taking appropriate measures to control the dimensional accuracy to an acceptable limit. In this study, a two-step computational approach, which is a combination of a thermo-elastic-plastic finite element method (FEM) and an elastic finite element with consideration for large deformation, is developed to estimate welding distortion for large and complex welded structures. Welding distortions in several representative large complex structures, which are often used in shipbuilding, are simulated using the proposed method. By comparing the predictions and the measurements, the effectiveness of the two-step computational approach is verified.     

New development in extended finite element modeling of large elasto‐plastic deformations

This paper presents new achievements in the extended finite element modeling of large elasto‐plastic deformation in solid problems. The computational technique is presented based on the extended finite element method (X‐FEM) coupled with the Lagrangian formulation in order to model arbitrary interfaces in large deformations. In X‐FEM, the material interfaces are represented independently of element boundaries, and the process is accomplished by partitioning the domain with some triangular sub‐elements whose Gauss points are used for integration of the domain of elements. The large elasto‐plastic deformation formulation is employed within the X‐FEM framework to simulate the non‐linear behavior of materials. The interface between two bodies is modeled by using the X‐FEM technique and applying the Heaviside‐ and level‐set‐based enrichment functions. Finally, several numerical examples are analyzed, including arbitrary material interfaces, to demonstrate the efficiency of the X‐FEM technique in large plasticity deformations. Copyright © 2008 John Wiley & Sons, Ltd.     

Finite element modelling of hardening concrete: application to the prediction of early age cracking for massive reinforced structures

This article presents finite element modelling to predict the early age cracking risk of concrete structures. It is a tool to help practitioners choose materials and construction techniques to reduce the risk of cracking. The proposed model uses original hydration modelling (allowing composed binder to be modelled and hydric consumption to be controlled) followed by a non-linear mechanical model of concrete at early ages involving creep and damage coupling. The article considers hydration effects on this mechanical model, which is based on a non-linear viscoelastic formulation combined with an anisotropic, regularized damage model. Details of the numerical implementation are given in the article and the model is applied successively to a laboratory structure and to a massive structure in situ (experimental wall of a nuclear power plant studied in the framework of the French national research project CEOS.fr).     

Multifield modelling and failure prediction of cellular cores produced by selective laser melting

A multifield simulation approach of cellular cores produced by additive manufacturing is presented. The analysis is aiming to derive the relation between the manufacturing process parameters and the resulting material failure behaviour. To this purpose, the selective laser melting manufacturing process is initially thermo‐mechanically simulated, followed by the mechanical analysis of the nonlinear core behaviour. The methodology is demonstrated in the case of open‐lattice body‐centred‐cubic (BCC) cellular cores.     

Finite cover method for progressive failure with cohesive zone fracture in heterogeneous solids and structures

The finite cover method (FCM), which is a cover-based generalized finite element method, is extended for analyses of progressive failure processes involving cohesive zone fracture, starting from an interface debonding and evolving toward one of the constituents of heterogeneous solids and structures. Assuming that the constituents fail according to the maximum principal stress, we are able to represent the evolution of the resulting failure surfaces of discontinuity independent of mesh alignment owing to the distinctive features of the FCM. Also, interface elements with Lagrange multipliers are introduced to impose compatibility conditions on the material interface so that debonding is judged by the multipliers. Representative numerical examples demonstrate the capability of the proposed method in tracing the smooth transition of crack paths from interfacial to internal failure, and vice versa.     

A failure criterion for brittle and quasi-brittle materials under any level of stress concentration

In this paper, we present a new criterion to predict the crack initiation under quasi-static loads from a geometrical weakness presenting an arbitrary stress concentration in brittle or quasi-brittle materials. Three material parameters were used in the establishment of the criterion, namely the ultimate stress σ_c, the critical energy release rate for crack growth G_c and the critical energy release rate for fracture under uniform uniaxial tension G_u. The use of these two critical energy release rates was justified by the observation of the fracture surfaces under different stress concentrations. The proposed three parameters’ concept enables to take the different stress concentration levels into account, thus provides a unified criterion to predict crack initiation for any stress concentration, whatever it is singular or regular. Numerous experimental studies were selected to verify the accuracy and efficiency of the criterion. It was shown that the proposed criterion is physically reasonable, highly accurate and easy to apply. It can be used in crack initiation prediction of engineering structures made of brittle or quasi-brittle materials.     

Fast failure prediction of adhesively bonded structures using a coupled stress‐energetic failure criterion

The use of adhesively bonded joints in industrial structures requires reliable tools for the estimation of the failure load. The necessary and sufficient condition to predict the strength of such joints involves the implementation of a coupled stress and energetic criteria. However, its application necessitates the identification of the stress distribution along the adhesive layer, which has been approximated in this paper by a previously published closed‐form solution. This analysis along with finite element modelling results are compared with experimental data issued from a double‐notched sample tested with the Arcan fixture at various load ratios. The results show good agreement; the use of the closed‐form solution permitted to predict the failure load more rapidly and in a conservative manner compared with the experimental results. The application of the methodology is also extended to a wider range of joint geometries by means of spatial interpolation using the Kriging model.     

Finite element analysis of contact induced adhesion failure in multilayer coatings with weak interfaces

Experimental work reveals that the Ag/ZnO interface in the multilayer solar control coatings is weakest and most likely to fail during contact. In this study, a cohesive zone model embedded in a finite element code was used to model delamination in multilayer stack consisting of ZnO/Ag/ZnO on glass during contact. It shows that delamination occurs at the upper ZnO/Ag interface during loading when penetration exceeds a critical value, while, the double pinned buckling delamination failure occurs at the lower Ag/ZnO interface during the unloading cycle. Furthermore, it reveals the model based on mechanism of lateral crack at interface yields reasonably accurate values of interfacial toughness when tensile stress induced delamination occurs during unloading.     

Lagrangian modelling of large deformation induced by progressive failure of sensitive clays with elastoviscoplasticity

This paper presents a Lagrangian formulation of elastoviscoplasticity, on the basis of the particle finite element method, for progressive failure analysis of sensitive clays. The sensitive clay is represented by an elastoviscoplastic model that is a mixture of the Bingham model, for describing rheological behaviour, and the Tresca model with strain softening for capturing the progressive failure behaviour. The finite element formulation for the incremental elastoviscoplastic analysis is reformulated, through the application of the Hellinger–Reissner variational theorem, as an equivalent optimisation program that can be solved efficiently using modern algorithms such as the interior‐point method. The recast formulation is then incorporated into the framework of the particle finite element method for investigating progressive failure problems related to sensitive clays, such as the collapse of a sensitive clay column and the retrogressive failure of a slope in sensitive clays, where extremely large deformation occurs. Copyright © 2017 John Wiley & Sons, Ltd.     

Finite element modelling of core thickness effects in aluminium foam/composite sandwich structures under flexural loading

This paper models the flexural behaviour of a composite sandwich structure with an aluminium foam core using the finite element (FE) code LS-DYNA. Two core thicknesses, 5 and 20 mm, were investigated. The FE results were compared with results from previous experimental work that measured full-field strain directly from the sample during testing. The deformation and failure behaviour predicted by the FE model compared well with the behaviour observed experimentally. The strain predicted by the FE model also agreed reasonably well with the distribution and magnitude of strain obtained experimentally. However, the FE model predicted lower peak load, which is most likely due to a size effect exhibited by aluminium foam. A simple modification of the FE model input parameters for the foam core subsequently produced good agreement between the model and experimental results.     

Finite element modelling of the mechanism of deformation and failure in metallic thin-walled hollow spheres under dynamic compression

Recent interest in lightweight metallic hollow sphere foams for aerospace applications requires a better physical understanding of dynamic properties of single spheres. Finite element modelling supported by high rate experiments was developed to investigate the underlying deformation and failure mechanisms of electrodeposited nickel thin-walled hollow spheres. Parametric simulation was performed to further explore the effect of sphere geometry (wall thickness to diameter ratio) and loading rate. It was found that decreasing the ratio of wall thickness to diameter tends to transit the side wall failure mode from bending to buckling. For a thin-walled sphere (the thickness to diameter ratio less than a critical value), the macroscopic dynamic behaviour is primarily dominated by the two deformation and failure mechanisms: (1) buckling failures of wall materials and (2) self-contacts of wall surfaces and wall-anvil contacts. At higher impact velocity (greater than a critical velocity), inertia effect due to dynamic localisation of wall crushing arises and significantly influences the deformation/failure mode of the sphere, resulting in an increased initial crushing strength and asymmetric deformation. Finally, the behaviour of hollow spheres was correlated to explore the power law behaviour of bulk foams with respect to the relative density; it was found that metallic thin-walled hollow sphere foams can be better approximated as open-cell rather than closed-cell foams.     

Finite element analysis of micromechanical failure modes in a heterogeneous ceramic material system

A micromechanical model that provides explicit accounts for arbitrary microstructures and arbitrary fracture patterns is developed and used. The approach uses both a constitutive law for the bulk solid constituents and a constitutive law for fracture surfaces. The model is based on a cohesive surface formulation of Xu and Needleman and represents a phenomenological characterization for atomic forces on potential crack/microcrack surfaces. This framework of analysis does not require the use of continuum fracture criteria which assume, for example, the existence of K-fields. Numerical analyses carried out concern failure in the forms of crack propagation and microcrack formation. Actual microstructures of brittle alumina/titanium diboride (Al₂O₃/TiB₂) composites are used. The results demonstrate the effects of microstructure and material inhomogeneities on the selection of failure modes in this material system. For example, the strength of interfaces between the phases is found to significantly influence the failure characteristics. When weak interfacial strength exists, interfacial debonding and microcrack initiation and growth are the principal mode of failure. When strong interfacial strength is derived from material processing, advancement of a dominant crack and crack branching are observed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Finite element modelling of saturated porous media at finite strains under dynamic conditions with compressible constituents

Two finite element formulations are proposed to analyse the dynamic conditions of saturated porous media at large strains with compressible solid and fluid constituents. Unlike similar works published in the literature, the proposed formulations are based on a recently proposed hyperelastic framework in which the compressibility of the solid and fluid constituents is fully taken into account when geometrical non‐linear effects are relevant on both micro‐ and macroscales. The first formulation leads to a three‐field finite element method (FEM), which is suitable for analysing high‐frequency dynamic problems, whereas the second is a simplification of the first, leading to a two‐field FEM, in which some inertial effects of the pore fluid are disregarded, hence the second formulation is suitable for studying low‐frequency problems. A fully Lagrangian approach is considered, hence all terms are expressed with reference to the material setting; the balance equations for the pore fluid are also expressed in terms of the chemical potential and the mass flux of the pore fluid in order to take the compressibility of the fluid into account. To improve the numerical response in the case of wave propagation, a discontinuous Galerkin FEM in the time domain is applied to the three‐field formulation. The results are compared with analytical and semi‐analytical solutions, highlighting the different effects of the discontinuous Galerkin method on the longitudinal waves of the first and second kind. Copyright © 2010 John Wiley & Sons, Ltd.     

Influences of complex loading and margin geometry: failure of curved brittle layer structures

This study investigates the influences of off-axis loading and of margin geometry on “margins failure” observed in loaded curved bi-layer structures, away from the contact loading point. Specimens of hemispherical bi-layer model consist of glass shells with varying margins geometry, and filled with epoxy resin substrate are prepared. These specimens are loaded with compliant PTFE Teflon cylindrical indenters, with a modulus of several orders of magnitude lower than the indented materials. Load is applied normally; axisymmetric to the dome apex, and at 45° from the axis of symmetry. In this fashion, the effect of off-axis loading and the influence of margin geometry on “margins failure” are studied. The onset of fracture is observed in situ using a video camera system. Finite element analysis is applied to determine basic stress distribution within the dome structures, and to confirm a shift in maximum tensile stress from the near-contact area to the dome sides with the use of more compliant indenters. Critical loads to initiate radial cracks and damage evolution are presented, and interpreted with the results of FEA.