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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 presents the development of a methodology for microstructure analysis and modeling of hot mix asphalt (HMA). This methodology relies on using effective local material properties and strain gradient theory in the finite element analysis of HMA microstructure. The effective local properties are calculated using an analytical micromechanical model that captures the influence of percent of particles on the microscopic response of HMA. Strain gradient elasticity is used in order to account for the effect of particle size in the finite element analysis. The autocorrelation function and the moving window technique are used to determine the microstructure characteristic length scales that are used in strain gradient elasticity. A number of asphalt mixes with different aggregate types and size distributions are analyzed in this paper. [ABSTRACT FROM AUTHOR]

In this paper, a new computational framework is presented for the analysis of nonlinear beam finite elements subjected to large strains. Specifically, the methodology recently introduced in Bonet et al. (Comput Methods Appl Mech Eng 283:1061-1094, ) in the context of three dimensional polyconvex elasticity is extended to the geometrically exact beam model of Simo (Comput Methods Appl Mech Eng 49:55-70, ), the starting point of so many other finite element beam type formulations. This new variational framework can be viewed as a continuum degenerate formulation which, moreover, is enhanced by three key novelties. First, in order to facilitate the implementation of the sophisticated polyconvex constitutive laws particularly associated with beams undergoing large strains, a novel tensor cross product algebra by Bonet et al. (Comput Methods Appl Mech Eng 283:1061-1094, ) is adopted, leading to an elegant and physically meaningful representation of an otherwise complex computational framework. Second, the paper shows how the novel algebra facilitates the re-expression of any invariant of the deformation gradient, its cofactor and its determinant in terms of the classical beam strain measures. The latter being very useful whenever a classical beam implementation is preferred. This is particularised for the case of a Mooney-Rivlin model although the technique can be straightforwardly generalised to other more complex isotropic and anisotropic polyconvex models. Third, the connection between the two most accepted restrictions for the definition of constitutive models in three dimensional elasticity and beams is shown, bridging the gap between the continuum and its degenerate beam description. This is carried out via a novel insightful representation of the tangent operator. [ABSTRACT FROM AUTHOR]

Summary: This paper is concerned with the analysis and implementation of robust finite element approximation methods for mixed formulations of linear elasticity problems where the elastic body is almost incompressible. Several alternative a posteriori error estimators for the energy norm of the finite element error are introduced and analysed. We establish upper and lower bounds for the energy error in terms of these error estimators and show that the constants in the bounds are independent of the Lamé coefficients: The proposed estimators are robust in the incompressible limit. We also consider the requirement for pressure stabilisation when using lowest‐order conforming approximation. Computational results are presented that validate the theoretical estimates. The software used to generate these results is available online. [ABSTRACT FROM AUTHOR]

The focus of this paper is on aligned fiber-reinforced composites, where fiber centers were randomly distributed in their cross-sections. The volume fractions of fibers were V f = 3 0 % and V f = 5 0 %. Samples were built with the help of the simulated annealing technique according to the chosen Radial Distribution Functions (RDFs). For each sample, the fields of local stresses and heat fluxes were simulated by finite element method. Then, homogenization by volume averaging was performed in order to investigate both the effective mechanical and thermal properties. The effect of RDF shape on elastic and thermal properties was quantified along with the influence of the probability of near neighbors of fibers on the physical properties. The more the fiber distributions deviate from Poisson's Law, the higher the results compared to the lower bound of Hashin–Shtrikman. [ABSTRACT FROM AUTHOR]

Modern software's allow computers to perform symbolic calculations in addition to simple numerical computations for which they were originally designed. This fact opens new possibilities in numerical simulation. In this paper a finite element implementation using the commercial software Wolfram Mathematica is used to solve a plane stress elasticity problem. The code adaptability from the provided examples to more challenging problems can easily be performed using the present code. Numerical examples with post‐processing illustrates the new tool and its flexibility. It has been proven in this study the feasibility of Wolfram Mathematica in learning and programming finite element methods for the solution of two‐dimensional problems in elasticity. [ABSTRACT FROM AUTHOR]

In this paper, the finite element method is used to compute the deflection of a single pile, placed in a soil layer and subjected to static lateral loadings. The soil behavior is modeled as Mohr-Coulomb elastoplastic model, while the pile material behavior is modelled as linear elastic model. The main objective of this analysis is to determine the maximum deflection of the pile. In order to characterize the effect of the soil nature on the response of pile, sandy and clayey soils are considered for both soils, the influence on the pile response of the soil nonlinearity pile dimensions has been analyzed and some concluded remarks are presented Numerical results obtained from the present study, have been compared against published results and have shown a good correlation. [ABSTRACT FROM AUTHOR]

Response sensitivities with respect to the parameters of a finite element model are useful in many applications. The direct differentiation method (DDM) is commonly utilized to obtain such results. In recent years, the DDM has been extended to include sensitivities of inelastic response with respect to material, load, and geometry parameters. While the DDM is more efficient and accurate than finite difference methods, considerable cost is still associated with the computation of response sensitivities for inelastic problems. In this paper it is demonstrated that the computational cost can be significantly reduced for certain types of problems that are common in structural engineering. A novel event-based computation strategy is suggested, whereby sensitivities of the final response are obtained more efficiently than in the ordinary DDM. It is also demonstrated that sensitivity contributions from all inelastic material points are not needed for statically determinate structures. Numerical examples involving a truss structure, a steel frame structure, and a reinforced concrete frame structure are presented to demonstrate the efficiency of the presented developments. [ABSTRACT FROM AUTHOR]

When finite element formulations are used to study the non-linear vibration problems, some simplifications, which are not consistent with the governing variational principles, are commonly employed. Three such simplifications are critically reviewed here, through beam finite element models. The first one, ‘equivalent/ quasi-linearisation technique’is shown to have a reduced non-linear stiffness. The second, where in ‘neglect of in plane displacements’takes place, is seen to register an excessive non-linear stiffness. Thirdly, when both these simplifications are introduced together, they produce results closer to those of variationally correct ones,rather fortuitously. The objective of this paper is to highlight the necessity of formulating this class of problems in a variationally correct and consistent manner. Numerical computations are performed systematically, using two different beam finite element models for various commonly studied boundary conditions and suitable conclusions are drawn. [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]

The constant γ in the strengthened Cauchy-Buniakowski-Schwarc (CBS) inequality plays a key role in the convergence analysis of the multilevel iterative methods. We consider in this paper the approximation of the two-dimensional elasticity problem by bilinear rectangle finite elements. Two semi-coarsening refinement procedures are studied. We prove for both cases new estimates of the constant γ, uniformly on the Poisson ratio. As a result of the presented analysis we obtain an optimal order algebraic multiLevel iteration (AMLI) method for the case of balanced semi-coarsening mesh refinement. The total computational complexity of the algorithm is proportional to the size of the discrete problem with a proportionality constant independent of the Poisson ratio, that is, the algorithm is of optimal order for almost incompressible elasticity problems. Copyright © 1999 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, a finite element model of a soil island is coupled to both a consistent transmitting boundary and a paraxial boundary, which are then used to model the propagation of waves in semi-infinite elastic layered media. The formulation is carried out in the frequency domain while assuming plane strain conditions. It is known that a discrete model of this type, while providing excellent results for a wide range of physical parameters in the context of a half-space problem, may deteriorate rapidly at low frequencies of excitation. This is so because at low frequencies the various waves in the model eventually attain characteristic wavelengths which exceed the distance of the bottom boundary, which then causes that boundary to fail. Also, the paraxial boundaries themselves break down at very low frequencies. In this paper, this difficulty is overcome and the model׳s performance is improved upon dramatically by incorporating an artificial buffer layer sandwiched between the bottom of the soil medium and the underlying elastic half-space. Applications dealing with rigid foundations resting on homogenous or layered half-space media are shown to exhibit significant improvement. Following extensive simulations, clear guidelines are provided on the performance of the coupled model and an interpretation is given on the engineering significance of the findings. Finally, clear recommendations are provided for the practical use of the proposed modelling strategy. [ABSTRACT FROM AUTHOR]

This paper presents a novel computational formulation for large strain polyconvex elasticity. The formulation, based on the original ideas introduced by Schröder et al. (2011), introduces the deformation gradient (the fibre map), its adjoint (the area map) and its determinant (the volume map) as independent kinematic variables of a convex strain energy function. Compatibility relationships between these variables and the deformed geometry are enforced by means of a multi-field variational principle with additional constraints. This process allows the use of different approximation spaces for each variable. The paper extends the ideas presented in Schröder et al. (2011) by introducing conjugate stresses to these kinematic variables which can be used to define a generalised convex complementary energy function and a corresponding complementary energy principle of the Hellinger–Reissner type, where the new conjugate stresses are primary variables together with the deformed geometry. Both compressible and incompressible or nearly incompressible elastic models are considered. A key element to the developments presented in the paper is the new use of a tensor cross product, presented for the first time by de Boer (1982), page 76, which facilitates the algebra associated with the adjoint of the deformation gradient. For the numerical examples, quadratic interpolation of the displacements, piecewise linear interpolation of strain and stress fields and piecewise constant interpolation of the Jacobian and its stress conjugate are considered for compressible cases. In the case of incompressible materials two formulations are presented. First, continuous quadratic interpolation for the displacement together with piecewise constant interpolation for the pressure and second, linear continuous interpolation for both displacement and pressure stabilised via a Petrov–Galerkin technique. [ABSTRACT FROM AUTHOR]

SUMMARY Arterial walls in the healthy physiological regime are characterized by quasi-incompressible, anisotropic, hyperelastic material behavior. Polyconvex material functions representing such materials typically incorporate a penalty function to account for the incompressibility. Unfortunately, the penalty will affect the conditioning of the stiffness matrices. For high penalty parameters, the performance of iterative solvers will degrade, and when direct solvers are used, the quality of the solutions will deteriorate. In this paper, an augmented Lagrange approach is used to cope with the quasi-incompressibility condition. Here, the penalty parameter can be chosen much smaller, and as a consequence, the arising linear systems of equations have better properties. An improved convergence is then observed for the finite element tearing and interconnecting-dual primal domain decomposition method, which is used as an iterative solver. Numerical results for an arterial geometry obtained from ultrasound imaging are presented. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a novel three-dimensional finite element for gradient elasticity. The new finite element BR153L9 is a straightforward extension of the two-dimensional element QU34L4 developed by Shu et al. (1999) , which is based on a mixed-type formulation. Within this paper the derivation of the mixed-type finite element scheme is reviewed and details of the implementation are given. Finally, numerical results of an extended patch test and a benchmark test with the three-dimensional finite element are presented in order to validate the formulation and prove the convergence. [Copyright &y& Elsevier]

This paper studies the importance of the cohesive zone in the modelling of a fluid driven fracture under plain strain conditions. The fracture is driven by pumping of an incompressible viscous fluid at the fracture inlet. Rock deformation is modeled for linear elastic and poroelastic solids. Fluid flow in the fracture is modeled by lubrication theory. The cohesive zone approach is used as the fracture propagation criterion. Finite element analysis was used to compute the solution for the crack length, the fracture opening and propagation pressure as a function of the time and distance from the wellbore. It is demonstrated that the crack profiles and the propagation pressures are larger in the case of elastic-softening cohesive model compared to the results of the rigid-softening cohesive model for both elastic and poroelastic cohesive solids. It is found that the results are affected by the slope of the loading branch of the cohesive model and they are nearly unaffected from the exact form of the softening branch. Furthermore, the size of the process zone, the fracture geometry and the propagation pressure increase with increasing confining stresses. These results may explain partially the discrepancies in net-pressures between field measurements and conventional model predictions. [ABSTRACT FROM AUTHOR]

Abstract: This is a paper out of a series of three papers devoted to model- and hpq-adaptive finite element methods assigned for modeling and analysis of complex structures. In this paper we focus our attention on hierarchical models and hierarchical approximations, while the issues of error estimation and adaptivity control will be presented in the next papers of the series. In all the papers we consider the elastic structures of complex mechanical description. We apply 3D or 3D-based mechanical models, hierarchical modeling, and hierarchical approximations within our finite element formulation. In the proposed approach, the mechanical model and discretization parameters, such as the size h of the element, and the longitudinal and transverse approximation orders, p and q, can vary locally, i.e. they can be different in each finite element. The a posteriori error estimation is based on the residual equilibration methods applied to the assessment of the modeling and approximation errors. The error-controlled adaptive procedures are derived from a four-step strategy, with possible iterations on h- and p-steps. [ABSTRACT FROM AUTHOR]

This paper reports the use of polynomial wavelets as approximation functions in hybrid-mixed stress finite element models applied to the solution of plane elasticity problems. The stress and displacement fields in the domain and the displacements on the static boundary are independently approximated. The kinematic boundary conditions are locally satisfied. All remaining equations are enforced in a weighted residual form so designed as to ensure that the discrete model embodies the relevant properties of continuum systems, namely the static-kinematic duality and elastic reciprocity. A set of numerical applications is presented to illustrate the use of the hybrid-mixed model and to assess its efficiency and accuracy. Copyright © 2009 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper addresses the relationships between the microscopic properties of bone and its elasticity at the millimetre scale, or mesoscale. A method is proposed to estimate the mesoscale properties of cortical bone based on a spatial distribution of acoustic properties at the microscopic scale obtained with scanning acoustic microscopy. The procedure to compute the mesoscopic stiffness tensor involves (i) the segmentation of the pores to obtain a realistic model of the porosity; (ii) the construction of a field of anisotropic elastic coefficients at the microscopic scale which reflects the heterogeneity of the bone matrix; (iii) finite element computations of mesoscopic homogenized properties. The computed mesoscopic properties compare well with available experimental data. It appears that the tissue anisotropy at the microscopic level has a major effect on the mesoscopic anisotropy and that assuming the pores filled with an incompressible fluid or, alternatively, empty, leads to significantly different mesoscopic properties. [ABSTRACT FROM AUTHOR]

Much of the reported research on the dynamic analysis of pile foundations assumes linear behavior of soil that may not be valid for strong excitations. In this paper, material nonlinearity of the soil caused by plasticity and work hardening is considered in the dynamic analysis of pile foundations. An advanced plasticity based soil model, HiSS, is incorporated in a finite element technique. To simulate radiation effects, proper boundary conditions are used. The model and algorithm are verified with analytical results that are available for elastic and elastoplastic soil models. Analyses are carried out for free-field response and pile head response of end-bearing single piles. Both harmonic and transient excitations are considered in the analyses. Effects of frequency of excitation and stiffness of soil are investigated. It was found that the nonlinearity of soil has significant effects on the pile response for lower and moderate frequencies of excitations (a0<0.6) while at higher frequencies its effects are not as significant. [ABSTRACT FROM AUTHOR]

This paper presents an extension of the energy momentum conserving algorithm, developed by the authors for hypoelastic constitutive models. For such a material, contrarily to hyperelastic models, no potential can be defined, and thus the conservation of the energy is ensured only if the elastic work of deformation can be restored by the scheme. In a previous paper, we proposed a new expression of internal forces at the finite element level which is shown to verify this property. We also demonstrated that the work of plastic deformation is positive and consistent with the material model. In this paper, the second order terms that were neglected in the previous work are now taken into account. Several numerical applications are presented to demonstrate the necessity of taking these terms into account once large time step sizes are used. The limitations of the Newmark algorithm in the non-linear range are also illustrated. [Copyright &y& Elsevier]

In a previous paper [Comput. Methods Appl. Mech. Eng. 191 (2001) 3], the framework for the mechanics of solids, deformable over fractal subsets, was outlined. Anomalous mechanical quantities with fractal dimensions were introduced, i.e. the fractal stress, the fractal strain and the fractal work of deformation. By means of the local fractional operators, the static and kinematic equations were obtained, and the principle of virtual work for fractal media was demonstrated. In this paper, the constitutive equations of fractal elasticity are put forward. From the definition of the fractal elastic potential, the linear elastic constitutive relation is derived. The physical dimensions of the second derivatives of the elastic potential depend on the fractal dimensions of both stress and strain. Thereby, the elastic constants undergo positive or negative scaling, depending on the topological character of deformation patterns and stress flux. The direct formulation of elastic equilibrium is derived in terms of the fractional Lame´ operators and of the equivalence equations at the boundary. The variational form of the elastic problem is also obtained, through minimization of the total potential energy. Finally, discretization of the fractal medium is proposed, in the spirit of the Ritz–Galerkin approach, and a finite element formulation is obtained by means of devil’s staircase interpolating splines. [Copyright &y& Elsevier]

In this paper, four methods for the through the thickness response evaluation of laminated composite and sandwich plates are comparatively evaluated in terms of their characteristics and numerical accuracy. The laminated composite and sandwich plates are subjected to thermo-mechanical loading. The four methods include two post-processor-type methods and two re-analysis-type methods. The post-processor-type methods based on the three-dimensional stress equilibrium equations and the three-dimensional thermo-elasticity equations. And the re-analysis methods are based on the incorporation of the nonlinear through the thickness displacements recovered using post-processing technique in the re-analysis phase. The accuracy of the proposed methods for the evaluation of the through the thickness responses of the laminated plates are assessed via numerical examples of various configurations of laminated plates. Also, applicability and computational efficiencies of the methods are discussed. [ABSTRACT FROM AUTHOR]

Above ground storage tanks (AST) are essential equipment in the oil and gas industry. In general, large field erected steel storage tanks have been studied and evaluated to understand their behavior under different loadings and identify possible design flaws. However, deep research is necessary to improve the operation of shop-built storage tanks. Particularly, API 12F storage tanks are commonly used in the upstream, exploration, and production segments of oil and gas projects. The environmental conditions of these projects will depend on their locations and might be harsh and threatening for the equipment operation. This paper investigates the brittle fracture failure of the API 12F shop-welded tanks. An elastic stress analysis using finite element models was developed to determine the response of these equipment to extreme environmental conditions and the API 579 “Fitness-for-Service” rules were implemented to perform the brittle fracture assessment. A brittle fracture evaluation is conducted to inquire the propensity of a material to fail without appreciable plastic deformation. In case of the API 12F tanks, several parameters such as ambient temperature, residual stresses, and material toughness can play significant roles in the behavior of the equipment. Complete 3D models of the current API 12F shop-welded, flat bottom tanks as well as axisymmetric and solid submodels were created to address the brittle fracture evaluation and determine whether these storage tanks can operate safely under extreme conditions. Through-wall and surface crack flaws were considered in the most critical joints of the storage tanks and toughness relative ratios between the response of the steel material and the acceptance criteria of the API 579 standard were calculated to describe the behavior of the equipment. [ABSTRACT FROM AUTHOR]

The paper is concerned with a low-order finite element method, namely the staggered cell-centered finite element method, which has been proposed and analyzed in Ong et al. (2015) for two-dimensional compressible and nearly incompressible linear elasticity problems. In this work, we extend the results to the three-dimensional case and focus on the creating of the meshes. In particular, from a general primal mesh M , we construct a polygonal dual mesh M ∗ and its submesh M ∗ ∗ in a way such that each dual control volume of M ∗ corresponds to a primal vertex and is a union (macro-element) of some fixed number of adjacent tetrahedral elements of M ∗ ∗ . The displacement is approximated by piecewise trilinear functions on the subdual mesh M ∗ ∗ and the pressure by piecewise constant functions on the dual mesh M ∗ . As for two-dimensional case, such construction of the meshes and approximation spaces satisfies the macroelement condition, which implies stability and convergence of the scheme. Numerical experiments are carried out to investigate the performance of the proposed method on various mesh types. [ABSTRACT FROM AUTHOR]

We consider the solution of block-coupled large-scale linear systems of equations, arising from the finite element approximation of the linear elasticity problem. Due to the large scale of the problems we use properly preconditioned iterative methods, where the preconditioners utilize the underlying block matrix structures, involving inner block solvers and, when suited, broadly established tools such as the algebraic Multigrid method (AMG). For the considered problem, despite of its optimal rate of convergence, AMG, as implemented in some publicly available scientific libraries, imposes unacceptably high demands for computer resources. In this paper we propose and analyze an efficient multilevel preconditioner, based on the Generalized Locally Toeplitz framework, with a specialized transfer operator. We prove and numerically illustrate the optimal convergence rate of the proposed preconditioner, and experimentally report memory and CPU time savings. We also provide comparisons with respect to another aggregation-based algebraic multigrid algorithm. [ABSTRACT FROM AUTHOR]

The grain-grain interaction in a sandstone rock can result in an overall elastic response of the system, which is primarily determined by the grain contact stiffness and the grain contact volume fraction. In this paper, we propose a numerical algorithm to vary the contact volume fraction based on 3D Digital Rock images from x-ray microtomography ( μ -CT). We then calculate the effective elastic moduli of the model systems for various contact parameters using the Finite Element Method. Using an extensive fitting procedure, we find a set of empirical equations that model the effective bulk and shear moduli of the system. We show that our proposed set of empirical equations can accurately predict the mechanical properties of unconsolidated sandstones rocks. [ABSTRACT FROM AUTHOR]

The Dirichlet-to-Neumann finite element method (DtN FEM) has proven to be a powerful numerical approach to solve boundary-value problems formulated in exterior domains. However, its application to elastic semi-infinite domains, which frequently arise in geophysical applications, has been rather limited, mainly due to the lack of explicit closed-form expressions for the DtN map. In this paper, we present a DtN FEM procedure for boundary-value problems of elastostatics in semi-infinite domains with axisymmetry about the vertical axis. A semi-spherical artificial boundary is used to truncate the semi-infinite domain and to obtain a bounded computational domain, where a FEM scheme is employed. By using a semi-analytical procedure of solution in the unbounded residual domain lying outside the artificial boundary, the exact nonlocal boundary conditions provided by the DtN map are numerically approximated and efficiently coupled with the FEM scheme. Numerical results are provided to demonstrate the effectiveness and accuracy of the proposed method. [ABSTRACT FROM AUTHOR]

We study the one-dimensional problem for the linear strain gradient porous elasticity. Our aim is to analyze the behavior of the solutions with respect to the time variable when a dissipative structural mechanism is introduced in the system. We consider five different scenarios: hyperviscosity and viscosity for the displacement component and hyperviscoporosity, viscoporosity and weak viscoporosity for the porous component. We only apply one of these mechanisms at a time. We obtain the exponential decay of the solutions in the case of viscosity and a similar result for the viscoporosity. Nevertheless, in the hyperviscosity case (respectively hyperviscoporosity) the decay is slow and it can be controlled at least by t - 1 / 2 . Slow decay is also expected for the weak viscoporosity in the generic case, although a particular combination of the constitutive parameters leads to the exponential decay. We want to emphasize the fact that the hyperviscosity (respectively hyperviscoporosity) is a stronger dissipative mechanism than the viscosity (respectively viscoporosity); however, in this situation, the second mechanism seems to be more "efficient" than the first one in order to pull along the solutions rapidly to zero. This is a striking fact that we have not seen previously at any other linear coupling system. Finally, we also present some numerical simulations by using the finite element method and the Newmark- β scheme to show the behavior of the energy decay of the solutions to the above problems, including a comparison between the hyperviscosity and the viscosity cases. [ABSTRACT FROM AUTHOR]

The tractions that cells exert on a gel substrate from the observed displacements is an increasingly attractive and valuable information in biomedical experiments. The computation of these tractions requires in general the solution of an inverse problem. Here, we resort to the discretisation with finite elements of the associated direct variational formulation, and solve the inverse analysis using a least square approach. This strategy requires the minimisation of an error functional, which is usually regularised in order to obtain a stable system of equations with a unique solution. In this paper we show that for many common three-dimensional geometries, meshes and loading conditions, this regularisation is unnecessary. In these cases, the computational cost of the inverse problem becomes equivalent to a direct finite element problem. For the non-regularised functional, we deduce the necessary and sufficient conditions that the dimensions of the interpolated displacement and traction fields must preserve in order to exactly satisfy or yield a unique solution of the discrete equilibrium equations. We apply the theoretical results to some illustrative examples and to real experimental data. Due to the relevance of the results for biologists and modellers, the article concludes with some practical rules that the finite element discretisation must satisfy. [ABSTRACT FROM AUTHOR]

We present in this paper a rigorous theoretical framework to show stability, convergence and accuracy of improved edge-based and face-based smoothed finite element methods (bES-FEM and bFS-FEM) for nearly-incompressible elasticity problems. The crucial idea is that the space of piecewise linear polynomials used for the displacements is enriched with bubble functions on each element, while the pressure is a piecewise constant function. The meshes of triangular or tetrahedral elements required by these methods can be generated automatically. The enrichment induces a softening in the bilinear form allowing the weakened weak ( W 2 ) procedure to produce a high-quality solution, free from locking and that does not oscillate. We prove theoretically that both methods confirm the uniform inf–sup and convergence conditions. Four numerical examples are given to validate the reliability of the bES-FEM and bFS-FEM. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents an extension of the reduced order finite element model to the case of circular elastohydrodynamic lubricated (EHL) contacts under isothermal Newtonian considerations. The line contact model was developed and validated in a previous work (Advances in Engineering Software, 2013; 56:51−62). The model is based on a finite element discretization of the EHL equations: Reynolds, linear elasticity and load balance with a reduced order model for the linear elasticity part. All equations are solved simultaneously in a fully-coupled framework using a damped-Newton procedure allowing fast convergence rates for the global solution. This model combines fast convergence rates, reduced memory requirements and negligible model reduction errors compared to the full model which makes it an attractive tool for EHL contact performance prediction. [Copyright &y& Elsevier]

Abstract: A one-dimensional, large-strain, mixed porohyperelastic transport and swelling (MPHETS) finite element model was developed in MATLAB and incorporated with a well-known growth model for soft tissues to allow the model to grow (increase in length) or shrink (decrease in length) at constant material density. By using the finite element model to determine the deformation and stress state, it is possible to implement different growth laws in the program in the future to simulate how soft tissues grow and behave when exposed to various stimuli (e.g. mechanical, chemical, or electrical). The essential assumptions needed to use the MPHETS model with growth are clearly identified and explained in this paper. The primary assumption in this work, however, is that the stress upon which growth acts is the stress in the solid skeleton, i.e. the effective stress, S eff . It is shown that significantly different amounts of growth are experienced for the same loading conditions when using a porohyperelastic model as compared to a purely solid model. In one particular example, approximately 51% less total growth occurred in the MPHETS model than in the solid model even though both problems were subjected to the same external loading. This work represents a first step in developing more sophisticated models capable of capturing the complex mechanical and biochemical environment in growing and remodeling tissues. [Copyright &y& Elsevier]

Abstract: This paper investigates the influence of the inelastic dynamic soil–structure interaction (DSSI) on the response of moment-resisting frame buildings. A modeling strategy related to a modified 2D in-plane approach allowing faster finite element analyses is introduced. Two regular buildings founded on sandy soil in dry and fully saturated conditions are analyzed for a suite of motions in order to assess the influence of the inelastic DSSI on the structural response. Examination of results reveals that influence of DSSI on dry soil case is highly erratic, however tends to be invariantly favorable or negligible when the soil is in saturated condition. For motions inducing extensively inelastic structural behavior and mean period close to first elastic period of the soil deposit, inelastic DSSI seems to be very important. [Copyright &y& Elsevier]

Abstract: In this paper, it is shown that, for planar systems formed from linear-elastic bodies in non-penetrative contact with Coulomb friction, the limit load can be approximated efficiently by the limit loads corresponding to a sequence of contact problems with given friction, via a finite element fixed-point approach. For the auxiliary problem with given friction, a splitting of this problem into two subproblems, one with prescribed normal contact stresses and given friction and one with prescribed tangential contact stresses, is employed. Numerical results for masonry block structures subjected to in-plane loading illustrate the predictive capabilities of this approach. [Copyright &y& Elsevier]

Abstract: The paper describes an efficient procedure, based on standard finite element techniques, for the failure analysis of bonded structures. Modelled with structural elements, the adherends are attached by means of standard kinematic constraints to a single layer of solid elements reproducing the adhesive. The work assesses the accuracy of the proposed method in the prediction of the post-elastic response of adhesive joints by applying a singularity-free stress failure criterion. Benchmarks for the model are the load–deflection curves obtained by an ad-hoc experimental campaign on steel and aluminium T-peel joints. The accuracy of the model appears very good with respect to the experimental results, both in terms of maximum force and post-elastic behaviour. The failure criterion adopted appears well-founded and the CPU time needed for the analysis is minimum thus corroborating this efficient procedure for the analysis of very complex structures. [Copyright &y& Elsevier]

This paper presents a structural damage detection system. Variations in elasticity module are used as a damage condition in a structural finite element model. This deviation alters vibration natural frequencies and shape modes; which is the fault indicator in this proposal. Noise and incomplete data are used to emulate real conditions in a beam and truss in different fault scenarios. Simulations show satisfactory performance in all cases studied. Therefore, this system can be used as suitable structural damage detection system. [ABSTRACT FROM AUTHOR]

Abstract: The numerical modelling of interacting elastodynamic solids and acoustic fluids by time-domain finite element procedures is discussed here. In this study, the global model is divided into solid and fluid sub-domains and each sub-domain is analyzed independently, as an uncoupled model. The interaction between the different sub-domains is accomplished by interface forces. In order to improve the efficiency, accuracy and flexibility of the methodology, a multi-time-step method is also considered, allowing optimal time-steps to be selected for each sub-domain of the model. At the end of this paper, numerical applications illustrate the performance and potentialities of the proposed techniques. [Copyright &y& Elsevier]

Abstract: This paper investigates higher-order and higher-continuity functions in isogeometric structural analysis under distortion of the control and physical meshes. First, the concepts behind isogeometric analysis are briefly reviewed. The effect of perturbing control points upon the geometrical mapping is observed in the one-dimensional setting. The concept is extended to multiple dimensions with a series of cases where the interior of a cube is distorted in different ways and patch tests are performed to assess accuracy. A circular fillet patch is introduced through the appropriate degeneration of a control mesh in order to address the problem of modeling small features in finite element models. The fillet patch is tested with two problems of linear elasticity and is shown to be accurate. The investigation is further extended to the setting of large-deformation nearly incompressible nonlinear elasticity with two examples which make use of the recently proposed projection method. [Copyright &y& Elsevier]

In this paper we compare the solution of the one-dimensional beam model and the numerical solution of the two-dimensional linearized elasticity problem for rectangular domain of the beam-like form. We first derive the beam model starting from the two-dimensional linearized elasticity, the same way it is derived from the three-dimensional linearized elasticity. Then we present the numerical solution of the two-dimensional problem by finite element method. As expected the difference of two approximations becomes smaller as the thickness of the beam tends to zero. We then analyze the applicability of the one-dimensional model and verify the main properties of the beam modeling for thin beams. [ABSTRACT FROM AUTHOR]

Abstract: Bending an elastic beam leads to a complicated 3D stress distribution, but the shear and transverse stresses are so small in a slender beam that a good approximation is obtained by assuming purely uniaxial stress. In this paper, we demonstrate that the same is true for a saturated poroelastic beam. Previous studies of poroelastic beams have shown that, to satisfy the Beltrami–Michell compatibility conditions, it is necessary to introduce either a normal transverse stress or shear stresses in addition to the bending stress. The problem is further complicated if lateral diffusion is permitted. In this study, a fully coupled finite element analysis (FEA) incorporating the lateral diffusion effect is presented. Results predicted by the “exact” numerical solution, including load relaxation, pore pressure, stresses and strains, are compared to an approximate analytical solution that incorporates the assumptions of simple beam theory. The applicability of the approximate beam-bending solution is investigated by comparing it to FEA simulations of beams with various aspect ratios. For “beams” with large width-to-height ratios, the Poisson effect causes vertical deflections that cannot be neglected. It is suggested that a theory of plate bending is needed in the case of poroelastic media with large width-to-height ratios. Nevertheless, use of the approximate solution yields very small errors over the range of width-to-height ratios (viz., 1–4) explored with FEA. [Copyright &y& Elsevier]

Abstract: This paper addresses accuracy issues of nodal stresses in both finite elements and finite volumes. Strategies to evaluate nodal stresses for finite elements are also briefly discussed. Emphasis is placed on the application of finite volumes to solid mechanics and an overview of recent advancements is presented. Numerical simulation of test problems shows that accuracy of nodal stresses evaluated using finite elements is strongly dependent on the recovery strategy. In all cases, stress recovery at boundary nodal points renders large errors for all non-patch schemes. Contrastingly, finite volumes provide an accurate computation of nodal stresses, including at domain boundaries. [Copyright &y& Elsevier]

Abstract: In this paper, the dynamics of two dimensional elastic particles in a Newtonian viscous shear flow is studied numerically. To describe the elastic deformation, an evolution equation for the Eulerian Almansi strain tensor is derived. A constitutive equation is thus constructed for an incompressible “Neo–Hookean” elastic solid where the extra stress tensor is assumed to be linearly proportional to the Almansi strain tensor. The displacement field does not appear in this formulation. A monolithic finite element solver which uses Arbitrary Lagrangian–Eulerian moving mesh technique is then implemented to solve the velocity, pressure and stress in both fluid and solid phase simultaneously. It is found that the deformation of the particle in the shear flow is governed by two non-dimensional parameters: Reynolds number (Re) and Capillary number (Ca, which is defined as the ratio of the viscous force to the elastic force). In the Stokes flow regime and when Ca is small (), the particle deforms into an elliptic shape while the material points inside the particle experience a tank-treading like motion with a steady velocity field. The deformation of the elastic particle is observed to vary linearly with Ca, which agrees with theoretical results from a perturbation analysis. Interactions between two particles in a viscous shear flow are also explored. It is observed that after the initial complicated interactions, both particles reach an equilibrium elliptic shape which is consistent with that of a single particle. [Copyright &y& Elsevier]

The paper deals with finite element analysis of damped modal vibrations Q-factor values determined by taking into account the thermally-elastic damping. Modal properties of square- and ring-shaped MEMS resonators have been investigated by taking into account the layered structure of MEMS and the influence of the geometry of the clamping zone. The calculations have been performed by employing the COMSOL Multiphysics finite element software. The solution method has been verified comparing numerically and analitically obtained damped modal properties of cantilever MEMS resonator. Experimental investigations of Q-factor values have been performed. The comparison of calculated and experimentally obtained resonant frequencies and Q-factor values indicated good agreement of tendencies of change of the quantities against temperature. [ABSTRACT FROM AUTHOR]

Abstract: The conventional method to extract elastic properties in the nanoindentation of linearly elastic solids relies primarily on Sneddon’s solution (1948). The underlying assumptions behind Sneddon’s derivation, namely, (1) an infinitely large incompressible specimen; (2) an infinitely sharp indenter tip, are generally violated in nanoindentation. As such, correction factors are commonly introduced to achieve accurate measurements. However, little is known regarding the relationship between the correction factors and how they affect the overall accuracy. This paper first proposes a criterion for the specimen’s geometry to comply with the first assumption, and modifies Sneddon’s elastic relation to account for the finite tip radius effect. The relationship between the finite tip radius and compressibility of the specimen is then examined and a composite correction factor that involves both factors, derived. The correction factor is found to be a function of indentation depth and a critical depth is derived beyond which, the arbitrary finite tip radius effect is insignificant. Techniques to identify the radius of curvature of the indenter and to decouple the elastic constants (E and ν) for linear elastic materials are proposed. Finally, experimental results on nanoindentation of natural latex are reported and discussed in light of the proposed modified relation and techniques. [Copyright &y& Elsevier]

Abstract: This paper introduces a multiscale Monte Carlo finite element method (MCFEM) for determining mechanical properties of polymer nanocomposites (PNC) that consist of polymers reinforced with single-walled carbon nanotubes (SWCNT). Note that several approaches discussed in the open literature suggest values for the mechanical properties of PNC that differ significantly from the corresponding ones derived by experimental procedures. This discrepancy is addressed by the proposed MCFEM which accounts for the effect of the non-uniform dispersion and distribution of SWCNT in polymers in the macroscopic mechanical behavior of PNC. Specifically, the method uses a multiscale homogenization approach to link the structural variability at the nano-/micro scales with the local constitutive behavior. Subsequently, the method incorporates a FE scheme to determine the Young’s modulus and Poisson Ratio of PNC. The use of the computed properties in macroscale modeling is validated by comparison with experimental tensile test data. [Copyright &y& Elsevier]

Abstract: Finite element analysis of problems in structural and geotechnical engineering results in linear systems where the unknowns are displacements and rotations at nodes. Although the solution of these systems can be carried out using either direct or iterative methods, in practice the matrices involved are usually very large and sparse (particularly for 3D problems) so an iterative approach is often advantageous in terms of both computational time and memory requirements. This memory saving can be further enhanced if the method used does not require assembly of the full coefficient matrix during the solution procedure. One disadvantage of iterative methods is the need to apply preconditioning to improve convergence. In this paper, we review a range of established element-based preconditioning methods for linear elastic problems and compare their performance with a new method based on preconditioning with element displacement components. This new method appears to offer a significant improvement in performance. [Copyright &y& Elsevier]

Abstract: This paper presents a new energy-dissipative momentum-conserving algorithm for multiplicative models of finite strain plasticity. The proposed scheme preserves exactly the conservation laws of linear and angular momenta, and leads to the exact energy dissipation between the two computed solutions in a given time step. In particular, the energy is exactly conserved if the step is elastic, thus recovering existing energy–momentum-conserving schemes in the purely elastic range. Extensions accommodating a strictly non-negative numerical energy dissipation in the high-frequency to handle the numerical stiffness of the problem are also discussed briefly. These conservation/dissipation properties are proven rigorously in the very nonlinear setting of multiplicative finite strain plasticity. In fact, the analysis drives the design of the new return mapping algorithm proposed to integrate the plastic evolution equations so the above dissipation/conservation properties hold. These analyses account for the spatial discretization of the problem in the context of the finite element method. Several representative numerical simulations are presented to illustrate the performance of the new algorithm. [Copyright &y& Elsevier]

Abstract: This paper illustrates the use of wavelets defined on the interval as approximation functions in hybrid-mixed stress finite element models applied to the solution of linear elastic plate stretching and plate bending problems. Special attention is given to the algorithms and techniques involved in the generation and manipulation of such functions. A set of numerical examples is presented to illustrate the use of the hybrid-mixed model. [Copyright &y& Elsevier]

This paper presents a theoretical formulation in which the stream-tube method (STM) is examined through a variational approach for solving solid strain and fluid flow problems with finite elements. The analysis considers a reference domain, used as computational domain, related to the physical domain by an unknown transformation function to be determined numerically. Mass conservation is automatically verified by STM. The variational approach leads to eliminate the pressure in fluid problems and avoids to set up a mixed displacement–pressure procedure in the case of incompressible solids. Examples are given for fluid flows, applications and comparisons are also provided in the bending problem in elasticity. [Copyright &y& Elsevier]