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This paper presents a high order finite element implementation of the convex multi-variable electro-elasticity for large deformations large electric fields analyses and its particularisation to the case of small strains through a staggered scheme. With an emphasis on accurate geometrical representation, a high performance curvilinear finite element framework based on an a posteriori mesh deformation technique is developed to accurately discretise the underlying displacement-potential variational formulation. The performance of the method under near incompressibility and bending actuation scenarios is analysed with extremely thin and highly stretched components and compared to the performance of mixed variational principles recently reported by Gil and Ortigosa (2016) and Ortigosa and Gil (2016). Although convex multi-variable constitutive models are elliptic hence, materially stable for the entire range of deformations and electric fields, other forms of physical instabilities are not precluded in these models. In particular, physical instabilities present in dielectric elastomers such as pull-in instability, snap-through and the formation, propagation and nucleation of wrinkles and folds are numerically studied with a detailed precision in this paper, verifying experimental findings. For the case of small strains, the essence of the approach taken lies in guaranteeing the objectivity of the resulting work conjugates, by starting from the underlying convex multi-variable internal energy, whence avoiding the need for further symmetrisation of the resulting Maxwell and Minkowski-type stresses at small strain regime. In this context, the nonlinearity with respect to electrostatic counterparts such as electric displacements is still retained, hence resulting in a formulation similar but more competitive with the existing linearised electro-elasticity approaches. Virtual prototyping of many application-oriented dielectric elastomers are carried out with an eye on pattern forming in soft robotics and other potential medical applications. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a mathematical model for small deformations induced by external forces of closed surfaces that are minimisers of Helfrich-type energies. Our model is suitable for the study of deformations of cell membranes induced by the cytoskeleton. We describe the deformation of the surface as a graph over the undeformed surface. A new Lagrangian and the associated Euler-Lagrange equations for the height function of the graph are derived. This is the natural generalisation of the well-known linearisation in the Monge gauge for initially flat surfaces. We discuss energy perturbations of point constraints and point forces acting on the surface. We establish existence and uniqueness results for weak solutions on spheres and on tori. Algorithms for the computation of numerical solutions in the general setting are provided. We present numerical examples which highlight the behaviour of the surface deformations in different settings at the end of the paper. [ABSTRACT FROM AUTHOR]

Thickness stretching effect based on shear and normal deformation theory is used in this paper for magnetoelectro- elastic vibration analysis of a three-layered curved nanobeam including a nano core and two piezo-magnetic layers. Size-dependency is included in derivation of governing equations of motion based Eringen's nonlocal elasticity theory. The initial curvature is accounted in calculation of external works due to pre-mechanical, electrical and magnetic loads. The analytical method is presented to study the effect of significant parameters on the vibration characteristics. The numerical results are presented in terms of initial electro-magneto-mechanical loads, size-dependency parameter, opening angle, two parameters of Pasternak's foundation and core thickness to face-sheet thickness ratio. [ABSTRACT FROM AUTHOR]

Highlights • An elasticity sensor that can measure the elasticity of an object without the information of the pressing force and object deformation is reported. • The proposed sensor utilizes the different tactile properties regarding to object elasticity at different locations on a single sensor chip. • Simulations using finite element method were carried out to confirm the sensing principle. • Fabrication of the sensor and results of the experiment carried out using the fabricated sensor were reported. Abstract In this paper, we propose a micro-electronic-mechanical systems (MEMS)-based tactile sensor that can measure the elasticity of an object without having to measure the contact force and the object's deformation. In our sensor design, a sensor chip that has three piezoresistive cantilevers is covered by a polydimethylsiloxane (PDMS) pad. The elasticity of an object pressed against the sensor is measured from the ratio of the deformations at different locations of the PDMS pad. One cantilever (C 1) is designed to measure the deformation of the center of the PDMS pad, while the other two cantilevers (C 2 and C 3) are designed to measure the deformations of the outer ends of the PDMS pad. When the sensor is pressed against an object, the ratio of the deformations of the outer ends over that of the center of the PDMS varies depending on the object's elasticity but not on the pressing force. Therefore, it is possible to measure the object's elasticity from the ratio of the cantilevers' outputs. Here, we report on the sensor design, numerical analysis, sensor fabrication, and demonstration of the elasticity measurement using the fabricated sensor. The proposed sensor is expected to be useful in practical applications, including robotic hand manipulation and tissue stiffness discrimination in minimally invasive surgery. [ABSTRACT FROM AUTHOR]

Purpose It has been revealed that application of the differential form of Eringen’s nonlocal elasticity theory to some cases (e.g. cantilevers) leads to paradoxical results, and recourse must be made to the integral version of Eringen’s nonlocal model. The purpose of this paper, within the framework of integral form of Eringen’s nonlocal theory, is to study the bending behavior of nanoscale plates with various boundary conditions using the isogeometric analysis (IGA).Design/methodology/approach The shear deformation effect is taken into account according to the Mindlin plate theory, and the minimum total potential energy principle is utilized in order to derive the governing equations. The relations are obtained in the matrix-vector form which can be easily employed in IGA or finite element analysis. For the comparison purpose, the governing equations are also derived based on the differential nonlocal model and are then solved via IGA. Comparisons are made between the predictions of integral nonlocal model, differential nonlocal model and local (classical) model.Findings The bending analysis of nanoplates under some kinds of edge supports indicates that using the differential model leads to paradoxical results (decreasing the maximum deflection with increasing the nonlocal parameter), whereas the results of integral model are consistent.Originality/value A new nonlocal formulation is developed for the IGA of Mindlin nanoplates. The nonlocal effects are captured based on the integral model of nonlocal elasticity. The formulation is developed in matrix-vector form which can be readily used in finite element method. Comparisons are made between the results of differential and integral models for the bending problem. The proposed integral model is capable of resolving the paradox appeared in the results of differential model. [ABSTRACT FROM AUTHOR]

The present paper generalizes the results obtained by R. Reiss for classical elastic bodies to composites modeled as mixtures of dipolar elastic materials. [ABSTRACT FROM AUTHOR]

Economical and political factors have changed the conventional point of view on the development of new submarine pipelines crossings: in fact, the laying of present lines is now driven by the increasing globalization of the market, with longer distances covered from producers to end-users, and not only by the exploitation of new offshore resources. Therefore, new capabilities to operate in deep waters are needed more and more, with ongoing development plans considering projects in water depths up to 3500 m and more. This paper is following another paper issued by the same authors in which the strains and deformations of the very same J-Lay launching system were calculated. Now we'll make a step further in order to optimize the geometry and dimensions of the structural arrangement of the launching ramps in order to have the smallest stresses inside the subsea pipe during launching. The integrity of the subsea pipe during launching from a J-Lay vessel is the most important criteria to judge a successful launching. In the JLay systems as the one presented in this paper the vessel launching structure is stressing the pipe sometimes beyond the elastic domain and the verification of the stresses inside the pipe is of a paramount importance. This paper is providing a modern involvement of Finite Elements Methods in calculating the optimum launching system arrangement in order to have the minimum equivalent stress inside the subsea pipe during launching. After optimization the maximum calculated stress inside the pipe is 8.06e7 Pa instead of 9.97e7 Pa before optimization, therefore a reduction of 19% is to be reached by simply lowering the upper ramp and decreasing the force developed by the Tensioner 1. [ABSTRACT FROM AUTHOR]

This paper presents a study to reveal actual mechanisms and seismic loading patterns on the braced-intersected beams in two-story X-braced frames (X-braced frames) and discusses the impacts of yielding beams on critical components, such as braces and connections. First, the seismic response of various X-braced frames with different heights and design assumptions is presented to observe actual mechanisms and seismic load patterns on weak and strong beams during earthquake ground motions. Then the simulations with finite element method are presented to help understand the mechanisms observed in the seismic response of the X-braced frames. The paper concludes that (1) the first-mode mechanism in multi-story concentrically braced frames, anticipated by AISC 341, is a rare occasion and leads to light sections for brace-intersected beams in X-braced frames that most likely undergo significant inelastic deformation; (2) yielding of the brace-intersected beam alters the mechanism in many ways, which, in turn, further increases inelastic deformation in the beam; (3) vertical inelastic displacement at beam middle span causes significantly additional ductility demand on braces, gusset plates, and beam-to-column connections that are not considered in current design practice; and (4) inelastic deformation of brace-intersected beams results in the redistribution of the total input energy demand among the components of the X-braced frame, adversely increasing the demand on fracture-prone components such as braces and gusset plates. [ABSTRACT FROM AUTHOR]

In the present paper, two different averaging schemes are compared in the framework of the anti-plane inclusion problem of the strain gradient elasticity. Effective longitudinal shear modulus of fiber-reinforced composites was evaluated based on the Mori-Tanaka method (MTM) within the direct approach and based on the generalized self-consistent method (GSCM) within an energy approach. It is known that, in gradient theories, the non-uniform fields are realized inside the inhomogeneity even in the presence of a uniform strain or stress field prescribed at the infinity. Therefore, in MTM, an averaged concentration tensor is utilized. GSCM is used together with Eshelby's formula, which evaluates the total strain energy of the composite representative fragment by a particular surface integral. Thus, in this energy-based approach, one does not need to use averaged field quantities. The two mentioned approaches were compared and validated by finite element modeling in the framework of the simplified strain gradient elasticity theory. It was shown that both methods capture the inclusion size effects, however the quantitative predictions of these methods are significantly different for high volume fraction of small inclusions. It was shown that MTM underestimates the effective modulus compared to numerical simulations, while GSCM provides a sufficiently good solution. Thus, it seems that energy-based averaging schemes are preferable in the framework of gradient elasticity. Nevertheless, the MTM can be useful for the effective properties approximate evaluation of composites with small volume fraction of inclusions. [ABSTRACT FROM AUTHOR]

With the development of high-performance fighters, the function of pilot helmets is also constantly upgrading, and helmet-mounted display (HMD) has become a future development trend. To solve the inter-restriction between the eye position control and the pressure comfort under high overloads of pilot helmets, this paper optimizes the helmet design by building a head-helmet finite element model: (1) Under a 10 G overload, the deformation of helmet soft liner should not exceed 2 mm; and (2) The combination of liner materials used in various areas should satisfy the requirements of most comfortable head pressure distribution (Pfront: Ptop: Pside: Pback = 2:2:1:3). The study on 46 different combinations of materials finds that the helmet can meet both the eye position maintenance requirement under overloads and the requirement of comfortable pressure distribution when linear elastic materials with Young’s modulus of 1000 pa, 55000 pa and 65000 pa are used for the side, top and front parts of the head, and nonlinear elastic hyperfoam material with two-fold stress variation is used for the head back area. [ABSTRACT FROM AUTHOR]

This paper presents mathematical formulations and a solution for contact problems that concern the nonlinear beam published by Gao (Nonlinear elastic beam theory with application in contact problems and variational approaches, Mech Res Commun 1996; 23: 11–17) and an elastic foundation. The beam is subjected to a vertical and also axial loading. The elastic deformable foundation is considered at a distance under the beam. The contact is modeled as static, frictionless and using the normal compliance contact condition. In comparison with the usual contact problem formulations, which are based on variational inequalities, we are able to derive for our problem a nonlinear variational equation. Solution of this problem is realized by means of the so-called control variational method. The main idea of this method is to transform the given contact problem to an optimal control problem, which can provide the requested solution. Finally, some results including numerical examples are offered to illustrate the usefulness of the presented solution method. [ABSTRACT FROM AUTHOR]

We propose in this paper analytical and numerical models that describe the in-plane uniaxial elastic properties (Young's moduli and Poisson's ratios) of a honeycomb structure with curved walls. We perform a parametric analysis of the mechanical performance of this honeycomb also by taking into account the different types of deformations acting inside the cell walls. The curved wall honeycomb possesses higher magnitudes of the Poisson's ratio ν12 in the auxetic configuration compared to classical center symmetric configuration with straight cell wall. The presence of the curvature also allows creating configurations with positive Poisson's ratio even for negative internal cell angles, and makes this honeycomb design attractive for mechanical tailoring. [ABSTRACT FROM AUTHOR]

Up to now, the indentation of hyperelastic soft materials has not been completely understood. In this paper, the spherical indentation on hyperelastic soft solids was systematically investigated through theoretical analysis and finite element method (FEM). The validation and application of the Hertzian load-displacement relation for indentation of hyperelastic soft materials were clarified, the effects of large deformation and material nonlinearity on spherical indentation of hyperelastic soft materials were analyzed and discussed. It was found that the complicated indentation behaviors of hyperelastic soft solids mainly depended on the coupling interactions of large deformation and material nonlinearity. Besides, we proposed two new nonlinear elastic contact models to separate the effects of large deformation and material nonlinearity on spherical indentation responses of hyperelastic soft solids. Our efforts might help to enhance the understanding of hyperelastic indentation problems and provided necessary instructions for the mechanical characterization of hyperelastic soft materials. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a nonlinear size-dependent finite element model incorporating surface energy effects is developed to study the mechanical behavior of tiny elastic functionally graded (FG) bodies. Here the classical elasticity theory is modified to incorporate the surface energy effects. Most of previous studies assumed that the surface energy depends only on the 2D symmetric infinitesimal surface strains and neglects the second-order products of surface strains/displacement gradients. These descriptions assume a small strain deformation of the surface and neglect the pre-strain that is, already, developed on the surface – before loading – due to the pre-tension stress σ0. Here in this paper, the pre-strain is considered which forces the surface to a state of large strain after loading instead of small strain. In this sense, in the presence of initial surface tension, the theory of surface elasticity is a hybrid formulation characterized by linearized bulk elastic material and second order finite deformation of the surface. In the proposed finite element model, the surface energy effect is taken into account in the derivation of the element stiffness matrix for the material elements located very close to the boundary surface. The proposed model is then used to study the effects of surface energy, including the 2nd order displacement gradient, on the mechanical behavior of plane-strain functionally graded elastic body. [Copyright &y& Elsevier]

This paper provides a finite element treatment for a generalized hyperelastic theory in which the deformation gradient is subject to the multiplicative two-factor decomposition that is commonly used in large strain plasticity. The multiplicative decomposition in the present context is motivated by a theory of balanced internal variables, one of which is the first factor in the decomposition. Previous studies have shown how the associated continuum mechanical formulation then leads not only to the stress equations of equilibrium but also to an additional tensor balance equation that serves to determine the individual factors in the decomposition. Such a theory has been shown to predict loading thresholds associated with the emergence of slip surfaces at grip locations in well-posed boundary value problems. However, previous numerical treatments focused on shooting method procedures that failed to resolve loading plateaus and other key features associated with the emergence of such singular surfaces. In the present work we describe a finite element treatment that resolves such previously obscure details. Additional finite element simulations illustrate new aspects of singular surface emergence in this type of theory, including the emergence of singular surfaces in the interior of the computational domain. [ABSTRACT FROM AUTHOR]

This paper proposes a general finite-element procedure for the nonlinear analysis of cables based on a mixed variational formulation in curvilinear coordinates with finite deformations. The formulation accounts for nonlinear elasticity and inelasticity, overcoming the limitation of recent numerical approaches which integrate explicitly the global balance of linear momentum for a linear elastic material with infinitesimal deformations. The formulation uses a weak form of the catenary problem and of the strain-displacement relation to derive a new family of cable finite elements with a continuous or discontinuous axial force field. Several examples from the literature on nonlinear cable analysis are used to validate the proposed formulation for St. Venant-Kirchhoff elastic materials and neo-Hookean materials. These studies show that the proposed formulation captures the displacements and the axial force distribution with high accuracy using a small number of finite elements. [ABSTRACT FROM AUTHOR]

This paper presents a novel methodology to design wind turbine blades using the Inverse Finite Element Method (IFEM). IFEM takes as domain of analysis the geometry of the blade after large elastic deformations caused by given service loads. The deformed shape of the blade is that determined to be efficient using an aerodynamics analysis. From this analysis, the aerodynamic loads on the blade are known. Then, we choose the materials to manufacture the blade. As usual, the blade is assumed to be made of multiple layers of composite materials. After materials selection, the stationary inertial loads on the blade are known. Finally, given the desired deformed shape and all the service loads, we use IFEM to compute the manufacturing shape of the blade. This is a one-step, one-direction strategy where the aerodynamics analysis feeds the structural (IFEM) analysis, and no further interaction between both solvers is required. As an application of the proposed strategy, we consider a medium power 40-KW wind turbine blade, whose whole design is detailed along this work. [ABSTRACT FROM AUTHOR]

In this paper, a finite-element implementation of linear second-strain gradient elasticity is introduced based on a Hellinger-Reissner variational principle in order to use standard finite-element methods. Displacement boundary conditions are applied to one or more vertices of different polyhedrons. As a result, a smooth deformation around deformed vertices of the polyhedrons can be observed, in contrast to the appearance of singularities in the first-order theory, i.e., a Cauchy continuum, where strain singularities appear in such cases. [ABSTRACT FROM AUTHOR]

OMNI-Max anchors are designed with the aim of diving upon pullout, gaining capacity with increasing pullout distance. However, this diving potential is yet to be confirmed; that is, the critical question to be resolved is whether or not the anchor dives upon pullout and, if so, in what conditions. This paper reports the results from three-dimensional dynamic finite-element analysis undertaken to provide insight into the behaviour of OMNI-Max anchors during pullout in non-homogeneous clay. Large-deformation finite-element (LDFE) analyses were carried out using the coupled Eulerian-Lagrangian approach, modifying the simple elastic-perfectly plastic Tresca soil model to allow strain softening, and to incorporate strain-rate dependency of the shear strength. The keying process and diving patterns during anchor pullout revealed three governing factors including: ( a) pullout inclination angle; ( b) padeye offset ratio; ( c) final installation depth. For designing anchors to dive into deeper, it was recommended that the anchor loading angle to the horizontal at the padeye should be 45° or less and the anchor padeye offset ratio should be in the range of 0·25 ∼ 0·53 (offset angle of 14 ∼ 28°). [ABSTRACT FROM AUTHOR]

Purpose The purpose of this paper is to deal with large deformation analysis of plane beams composed of functionally graded (FG) elastic material with a variable Poisson’s ratio.Design/methodology/approach The material is assumed to be linear elastic, with a Poisson’s ratio varying according to a power law along the thickness direction. The finite element used is a plane beam of any-order of approximation along the axis, and with four transverse enrichment schemes, which can describe constant, linear, quadratic and cubic variation of the strain along the thickness direction. Regarding the constitutive law, five materials are adopted: two homogeneous limiting cases, and three intermediate FG cases. The effect of both finite element kinematics and distribution of Poisson’s ratio on the mechanical response of a cantilever is investigated.Findings In accordance with the scientific literature, the second scheme, in which the transverse strain is linearly variable, is sufficient for homogeneous long (or thin) beams under bending. However, for FG short (or moderate thick) beams, the third scheme, in which the transverse strain variation is quadratic, is needed for a reliable strain or stress distribution.Originality/value In the scientific literature, there are several studies regarding nonlinear analysis of functionally graded materials (FGMs) via finite elements, analysis of FGMs with constant Poisson’s ratio, and geometrically linear problems with gradually variable Poisson’s ratio. However, very few deal with finite element analysis of flexible beams with gradually variable Poisson’s ratio. In the present study, a reliable formulation for such beams is presented. [ABSTRACT FROM AUTHOR]

Spudcan punch-through during installation and preloading process is one of the key concerns for the jack-up industry. This incident occurs in layered deposits, with new design approaches for spudcan penetration in sand-over-clay deposits reported recently. This paper reports a novel design approach for spudcan penetration in stiff-over-soft clay deposits. Large-deformation finite element (LDFE) analyses were carried out using the Coupled Eulerian-Lagrangian (CEL) approach. The clay was modelled using the extended elastic - perfectly plastic Tresca soil model allowing strain softening and rate dependency of the undrained shear strength. A detailed parametric study was undertaken, varying the strength ratio between bottom and top soil layers, the thickness of the top layer relative to the spudcan diameter, and degree of nonhomogeneity of the bottom layer. Existing data from centrifuge model tests were first used to validate the LDFE results, and then the measured and computed datasets were used to develop the formulas in the proposed design approach. The approach accounts for the soil plug in the bottom layer, and the corresponding additional resistance. Where there is the potential for punch-through, the approach provides estimations of the depth and bearing capacity at punch-through, the bearing capacity at the stiff-soft layer interface, and the bearing capacity in the bottom layer. Comparison shows that the punch-through method suggested in ISO standard 19905-1 provides a conservative estimate of the bearing capacity at punch-through, with guidelines provided to improve the method. [ABSTRACT FROM AUTHOR]

The present paper is devoted to the modeling of finite deformations of hyperelastic bodies by using the Hybrid Integral Approach (HIA) model introduced by the Authors. This model combines the affine behavior of chains included in the molecular 8-chains density, the interleaving constraint part and an original phenomenological integral density which allows to balance the mismatch between model and experimental data. A total Lagrangian formulation is adopted to describe the geometrical and material non-linearities and a finite element implementation is performed in the FER software. Four test examples, including homogeneous and non-homogeneous deformations, as well as complex computation involving dynamic contact and impact are proposed to show the applicability of the developed approach and the efficiency of the model. [ABSTRACT FROM AUTHOR]

In this paper, a versatile technique for mesh deformation is discussed, targeted at the electromagnetic (EM) field simulation of high-frequency devices using the 3-D finite element method (FEM). The approach proposed applies a linear elasticity model to compute the displacements of the internal mesh nodes in 3-D when the structure geometry is changed. The technique is compared with an alternative approach based on harmonic radial basis functions. It is shown that the numerical effort needed to solve the mechanical problem is small compared with the EM simulation. The proposed mesh deformation technique is verified using the examples of a parametric analysis of high-frequency devices with the 3-D FEM method. The numerical tests demonstrate that the proposed method is fast and gives high-quality meshes, even for very large deformations of geometry. We show that the benefit of the application of mesh deformation techniques is the elimination of the remeshing noise that appears in the parametric analysis of high-frequency circuits with mesh-based methods. [ABSTRACT FROM PUBLISHER]

Solving large deformation problems of hyperelastic materials by the finite element method is still a challenging problem due to the severe mesh distortion that occurs during the computation. In Leger et al. (2014), it was shown that combining an updated Lagrangian method with an efficient adaptive remeshing algorithm, an accurate transfer method for the deformation gradient tensor as well as an efficient continuation method leads to a very stable, efficient and accurate algorithm to solve two-dimensional very large deformation problems. In this paper, we show that this method can also be generalized to solve three-dimensional problems. A number of static problems will be presented and analyzed. [ABSTRACT FROM AUTHOR]

In this paper, we propose a stabilized augmented Lagrange multiplier method for the finite element solution of small deformation elastic contact problems. We limit ourselves to friction-free contact with a rigid obstacle, but the formulation is readily extendable to more complex situations. [ABSTRACT FROM AUTHOR]

This paper investigates the natural frequency of free transverse vibration of blades in rotating disks to examine the relationship of natural frequencies, blade stiffness and nodal diameters to study how neighboring blades react upon each other and affect blade natural frequency. With the use of elastic hinge theory and a cantilever beam model subjected to either a transverse concentrated force or a bending moment at the free end, the force-deflection stiffness/moment-rotation stiffness of the beam have been developed. Thereafter, the reaction forces and moments from the neighboring blades have been determined without the need for an exact solution of large deformation of cantilever beams including geometrical nonlinearity effects. With the use of the energy conservation principle and modal theory, the natural frequency of free transverse vibration of blades in rotating disks has been determined for any nodal diameter. A comparison of the analytical and finite element solutions for a bladed disk with uniform aerofoils shows that the analytical method presented in this paper is accurate. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a method for the generalized rigid-body guidance dimensional synthesis of planar linkages. The error function is based on the elastic energy stored in a finite element model of the linkage, built with rod-type elements, when it is forced to fulfil the synthesis data. The best linkage dimensions are the ones that give the minimum energy. The nonlinear deformed equilibrium position is solved in every synthesis position to evaluate the error. To do this, a second-order method has been developed that guarantees the convergence with low computational cost. The possibility of constraints in the lengths of some rods is included in the method through the use of Lagrange multipliers. The minimization of the synthesis error function is also tackled with two different second-order methods; the best results are obtained with the use of both, each of them in different instants of the iterative process. There are several dimensional synthesis problems, but the main objective of this paper is the one that deals with the coordination of the relative positions of several elements. This kind of synthesis has interest for instance in the design of robotic hands, grippers and surgical instruments. The method presented here is also suitable for the other simpler kinds of kinematic syntheses: trajectory, function generation, rigid-body guidance, and combined synthesis, and therefore it may be considered as a general purpose one. [Copyright &y& Elsevier]

Abstract: A comprehensive computational study is undertaken to identify the influence of friction in material characterization by indentation measurement based on elasto- plastic solids. The impacts of friction on load versus indentation depth curve, and the values of calculated hardness and Young’s modulus in conical and spherical indentations are shown in this paper. The results clearly demonstrate that, for some elasto-plastic materials, the curves of load versus indentation depth obtained either by spherical or conical indenters with different friction coefficients, cannot be distinguished. However, if utilizing the parameter (see text for details), to quantify the deformation of piling-up or sinking-in, it is easy to find that the influence of friction on piling-up or sinking-in in indentation is significant. Therefore, the material parameters which are related to the projected area will also have a large error caused by the influence of friction. The maximum differences on hardness and Young’s modulus can reach 14.59% and 6.78%, respectively, for some elastic materials shown in this paper. These results do not agree with those from researchers who stated that the instrumented indentation experiments are not significantly affected by friction. [Copyright &y& Elsevier]

This paper shows that for perfect plasticity, the closest point projection method (CPPM) and the cutting plane algorithm (CPA) for return mapping are exactly equivalent for piecewise linear yield criteria under both associated and nonassociated plastic flow. The paper demonstrates this by presenting closed-form expressions for returned stresses in terms of predicted stresses. A consequence of this exact approach is that the final stresses can be obtained in a single iteration. The equivalence of CPPM and CPA is further demonstrated numerically by comparing five previously published algorithms for return mapping to Mohr–Coulomb in a finite-element analysis of bearing capacity. The analyses also highlight issues relating to singularities that occur at the corners of the Mohr–Coulomb surface. It is shown that many of these problems can be avoided if the return mapping is performed in principal stress space as opposed to general stress space. [ABSTRACT FROM AUTHOR]

Purpose - This paper aims to provide a more rapid stress updating algorithm for von-Mises plasticity with mixed-hardening and to compare it with the previous works. Design/methodology/approach - An augmented stress vector is defined. This can convert the original nonlinear differential equation system to a quasi-linear one. Then the dynamical system can be solved with an exponential map approach in a semi-implicit manner. Findings - The presented stress updating algorithm gives very accurate results and it has a quadratic convergence rate. Research limitations/implications - Von-Mises plasticity in a small strain regime is considered. Furthermore, the material is supposed to have linear hardening. Practical implications - Stress updating is the heart of a nonlinear finite element analysis due to the large consumption of computation time. The efficiency and accuracy of the calculations of nonlinear finite element analysis are strongly influenced by the efficiency and accuracy of stress updating schemes. Originality/value - The paper offers a new stress updating strategy based on exponential maps. This may be used as a routine in a nonlinear finite element analysis software to enhance its performance. [ABSTRACT FROM AUTHOR]

The objective of this paper is to derive goal-oriented a posteriori error estimators for the error obtained while approximately evaluating the nonlinear J-integral as a fracture criterion in linear elastic fracture mechanics (LEFM) using the finite element method. Such error estimators are based on the well-established technique of solving an auxiliary dual problem. In a straightforward fashion, the solution to the discretized dual problem is sought in the same FE-space as the solution to the original (primal) problem, i.e. on the same mesh, although it merely acts as a weight of the discretization error only. In this paper, we follow the strategy recently proposed by Korotov et al. [J Numer Math 11:33–59, 2003; Comp Lett (in press)] and derive goal-oriented error estimators of the averaging type, where the discrete dual solution is computed on a different mesh than the primal solution. On doing so, the FE-solutions to the primal and the dual problems need to be transferred from one mesh to the other. The necessary algorithms are briefly explained and finally some illustrative numerical examples are presented. [ABSTRACT FROM AUTHOR]

This paper is concerned with finite element predictions of the impact performance of plastics mouldings using elastic–plastic models. It is the second part of two papers. Part 1 contains detailed descriptions of three elastic–plastic models: von Mises, linear Drucker-Prager and the National Physical Laboratory developed cavitation model plus calculation of the relevant model parameters. This part contains complementary coverage of the elastic plastic models. The main emphasis of this part is the use of these models to predict the deformation of subcomponents cut from interior door trim mouldings supplied by Jaguar Land Rover. Predictions are compared with measurements at a range of loading speeds. The finite element simulation has been analysed by using different element types (solid/shell), different analysis types (rate independent/rate dependent) and studying the influence of friction and impact location. Results are presented of a small study carried out to indicate how sensitive the predictions are to changes in the cavitation model parameters. [ABSTRACT FROM AUTHOR]

A 2-dimensional, elastic-plastic finite element model has been developed to simulate plasticity induced crack closure in slanted and deflected cracks growing outside the small scale yielding (SSY) regime. The finite element model allows for contact between deformable surfaces to capture the complex contact interaction between the crack faces. Coulomb's friction law has been used to model friction between the crack faces and has been incorporated in the finite element model. This paper examines the mode I and mode II behavior of slanted cracks subjected to remote mode I, constant amplitude cyclic loading. Two possible types of mode II crack face interaction have been identified: (a) complete slip in mode II before mode I opening and, (b) mode I crack opening before the crack faces undergo mode II displacements. Both types of interactions were observed in slanted cracks. The finite element study also reveals a clear dependence of mode I and mode II crack opening levels for a slanted crack on R ratio and maximum stress, Smax/δ0. The crack opening levels for a slanted crack are found to be significantly higher than the stable opening values for a straight crack growing in pure mode I. The mode I and mode II crack opening levels are also found to depend on the friction between the crack faces. A four-fold increase in friction coefficient resulted in almost 50% increase in normalized mode I and mode II opening values. This paper also describes the effect of crack deflection on closure. Deflection of a fatigue crack from 45° inclination to pure mode I caused a decrease in mode I opening level, but, an increase in mode II opening level. This difference in opening behavior is attributed to the transition of the nature of crack interaction from `complete slip before opening' to `opening in mode I before mode II shear offset'. Final stable opening levels for a deflected crack are found to be close to the stable value for straight cracks. [ABSTRACT FROM AUTHOR]

This paper presents a residual-based a posteriori error estimator for the Arnold–Winther mixed finite element that utilises a post-processing for the skew-symmetric part of the strain. Numerical experiments verify the proven reliability and efficiency for suitable approximation of the skew-symmetric deformation gradient. Numerical evidence supports that the L 2 -stress error estimator is robust in the Poisson ratio and allows stable error control even in the incompressible limit. [ABSTRACT FROM AUTHOR]

A novel non-local lattice particle method for three-dimensional elasticity and fracture simulation of isotropic solids is proposed in this paper. First, the basic concept and detailed derivation of the proposed model are given. Three cubic lattice packing are investigated using the proposed model and simulation results are compared with classical finite element method solutions. The performance of these lattice structures are assessed using several benchmarks, for both deformation and brittle fracture problems. From the simulation results, good agreements with both analytical solution and experimental data are observed. Conclusions and future work are drawn based on this study. [ABSTRACT FROM AUTHOR]

Surface development origins from the cloth-making and computer graphics without consideration of the thickness, involving nonlinear optimization and constraints. Moreover the research of surface development mainly focuses on the planar development. In this paper, the development of the non-developable sheet to planar, singly-curved and doubly-curved surface patterns is investigated. An optimal developing algorithm is formulated to minimize the strain energy required for the deformation of the sheet, in which an orthogonal curvilinear coordinate system is used for three target patterns to simplify the constraints for the developing process, resulting in an unconstrained quadratic optimization. Both shell element and solid element are utilized in the finite element analysis. Similar developed results are obtained for planar and spherical patterns by using these two types of elements. But for the cylindrical pattern, the solid element model gives more accurate result due to no contribution of the shell element to the translation of the rotational freedom. [ABSTRACT FROM AUTHOR]

Soft elastohydrodynamic lubrication regime is typical for many elastomeric and biological contacts. As one or both contacting bodies are then highly compliant, relatively low contact pressures may lead to large deformations which are neglected in the classical EHL theory. In the paper, the related finite-deformation effects are studied for two representative soft-EHL problems. To this end, a fully-coupled nonlinear formulation has been developed which combines finite-strain elasticity for the solid and the Reynolds equation for the fluid, both treated using the finite element method with full account of all elastohydrodynamic couplings. Results of friction measurements are also reported and compared to theoretical predictions for lubricated contact of a rubber ball sliding against a steel disc under high loads. [ABSTRACT FROM AUTHOR]

In this paper the impact of a hollow elastic ellipsoidal thin shell with an elastic flat half space is analyzed. Due to the nonlinearity and complexity of the impact equation, classical numerical solutions cannot be employed. A closed-form solution for this problem is accomplished, using Hertzian theory [6] and the Vella ’ s analysis [17] in conjunction with the Newtonian method and a linearization scheme. The closed-form solution facilitates a parametric study of this problem. In next step, the closed-form analytical solution is validated by other research studies and explicit finite element method. Good agreement between the closed-form solution and other numerical results is observed. Based on the closed-form solution the maximum total deformation of the shell, the maximum transmitted force and the time duration of the contact were determined. The variations of the total deflection and the transmitted force as a function of the shell thickness and the different geometry of the shell were also determined. Finally it is concluded that the closed form equations are trustworthy and appropriate to investigate the impact of elastic ellipsoidal shells. [ABSTRACT FROM AUTHOR]

This paper deals with the investigation on the potential of welding deformation's prediction tool using linear thermal elastic numerical method. The weld-induced distortion was analyzed on combined butt and T-joints with thickness of 9 mm which is commonly applied in ship panel structure. In this research, the distortion behavior was predicted by means of a relatively new finite element (FEM) code developed by INPRO and ESI Group which utilizes shell elements in the numerical method to allow fast computational time. In order to verify the simulation results, a series of experiments using a fully automated welding process were carried out to measure the weld-induced distortions. By comparing the results between both methods, it can be summarized that the linear elastic FEM using this software is capable of predicting the distortion within minutes while providing a reasonable agreement with the experiments. [ABSTRACT FROM AUTHOR]

The present paper is aimed to study the deformability effect of the bearing surface on the lubrication performance of cylindrical journal bearing with finite length. The bush is coated with thin resilient layer with smooth surface. The steady state EHD problem is investigated under elasticity conditions in accordance with a Vlassov model of an elastic foundation adapted for thin liner. The Reynolds equation is solved numerically by successive over-relaxation technique on a finite difference grid. The converged solutions for the lubricant flow and elastic deformations are obtained. The variety of simulation models of the tribological system is presented. The comparative analysis between the solutions by hydrodynamic (HD) theory and elastohydrodynamic (EHD) theory of bearings lubrications carried out. [ABSTRACT FROM AUTHOR]

All the five independent elastic properties/constants of micro- and nano-structured hierarchical and self-similar random irregular honeycombs with different degrees of cell regularity are obtained by analysis and computer simulation in this paper. Cell wall bending, stretching, and transverse shearing are the main deformation mechanisms of hierarchical honeycombs. The strain gradient effects at the micro-meter scale, and the surface elasticity and initial stress effects at the nano-meter scale are incorporated into all the deformation mechanisms in the analysis and finite element simulations. The results show that the elastic properties of hierarchical random irregular honeycombs strongly depend on the thickness of the first-order cell walls if it is at the micro-meter scale, and that if the thickness of the first-order cell walls is at the nano-meter scale, the elastic properties of hierarchical random irregular honeycombs are not only size-dependent, but are also tunable and controllable over large ranges. In addition, the geometrical properties of nano-structured hierarchical random irregular honeycombs are also tunable and controllable. [ABSTRACT FROM AUTHOR]

This paper describes an experimental study that was completed to investigate the resilient constitutive characteristics of a granular limestone, as well as to assess the applicability of conventional modelling within the framework of elasticity theory for the material that was studied. Test results corresponding to various stress paths are reported for a well-graded, sub-angular coarse sand. Noticeable differences are found with regard to the measured deformation responses when compared with those from linear elastic model predictions. On the basis of studying the stress–strain responses in terms of invariants, the authors conclude that the difference in the resilient responses of the material for various stress paths is largely due to the inherent nonlinear anisotropic nature of the material, and that stress-induced fabric associated with, for example, rearrangement of particles and particle connectivity should be taken into account for better interpretation of resilient behaviour of granular soil. [ABSTRACT FROM PUBLISHER]

Robotic grasping of deformable objects is difficult and under-researched, not simply due to the high computational cost of modeling. More fundamentally, several issues arise with the deformation of an object being grasped: a changing wrench space, growing finger contact areas, and pointwise varying contact modes inside these areas. Consequently, contact constraints needed for deformable modeling are hardly established at the beginning of the grasping operation. This paper presents a grasping strategy that squeezes the object with two fingers under specified displacements rather than forces. A ‘stable’ squeeze minimizes the potential energy for the same amount of squeezing, while a ‘pure’ squeeze ensures that the object undergoes no rigid body motion as it deforms. Assuming linear elasticity, a finite element analysis guarantees equilibrium and the uniqueness of deformation during a squeeze action. An event-driven algorithm tracks the contact regions as well as the modes of contact in their interiors under Coulomb friction, which in turn serve as the needed constraints for deformation update. Grasp quality is characterized as the amount of work performed by the grasping fingers in resisting a known push by some adversary finger. Simulation and multiple experiments have been conducted to validate the results over solid and ring-like 2D objects. [ABSTRACT FROM PUBLISHER]

The paper discusses nonlinear equations of in-plane bending of curved tubes formulated by E. Reissner in terms of two unknown functions and two unknown parameters. To solve the equations, a numerical method based on the finite-difference approximations and Newton-Raphson iteration technique is proposed. Deformations and stresses in tubes of circular and noncircular cross sections are studied for a wide range of geometrical parameters. The accuracy of the equations is evaluated by comparing the numerical results with predictions obtained by a special shell finite element. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we revisit an elastic constitutive equation proposed in two previous works and extend it in order to include all higher-order terms on the deformations. Our purpose is to assess the influence of these terms on the elastic buckling of thin-walled rods. The resulting material model was incorporated into a geometrically exact rod formulation and implemented into a nonlinear finite element code. By means of simple numerical examples we show that the higher order terms may play a significant role on the values of the buckling loads and on the post-buckling behavior of thin-walled beams and columns. [Copyright &y& Elsevier]

Abstract: The main purpose of this work is the computational simulation of the sensitivity coefficients of the homogenized tensor for a polymer filled with rubber particles with respect to the material parameters of the constituents. The Representative Volume Element (RVE) of this composite contains a single spherical particle, and the composite components are treated as homogeneous isotropic media, resulting in an isotropic effective homogenized material. The sensitivity analysis presented in this paper is performed via the provided semi-analytical technique using the commercial FEM code ABAQUS and the symbolic computation package MAPLE. The analytical method applied for comparison uses the additional algebraic formulas derived for the homogenized tensor for a medium filled with spherical inclusions, while the FEM-based technique employs the polynomial response functions recovered from the Weighted Least-Squares Method. The homogenization technique consists of equating the strain energies for the real composite and the artificial isotropic material characterized by the effective elasticity tensor. The homogenization problem is solved using ABAQUS by the application of uniform deformations on specific outer surfaces of the composite RVE and the use of tetrahedral finite elements C3D4. The energy approach will allow for the future application of more realistic constitutive models of rubber-filled polymers such as that of Mullins and for RVEs of larger size that contain an agglomeration of rubber particles. [Copyright &y& Elsevier]

THIS PAPER DEALS WITH the development of a family of gradient-enhanced elasticity-damage-plasticity models for the simulation of failure in metallic and composite materials. The model incorporates finite deformations and is developed with the assumption of isotropy and isothermal conditions. The gradient enhancement applied to the damage part of the model aims at removing pathological sensitivity to the finite element discretization which can occur due to material softening. The attention is focused on the algorithmic aspects and on the implementation of the model using AceGen tool. The numerical verification tests of the described model are performed using the Mathematica-based package AceFEM. Particularly, uniaxial tension test for a bar with a variable cross-section and tension of a perforated plate are examined. [ABSTRACT FROM AUTHOR]