In the present study, a general dynamic data-driven application system (DDDAS) is developed for real-time monitoring of damage in composite materials using methods and models that account for uncertainty in experimental data, model parameters, and in the selection of the model itself. The methodology involves (i) data data from uniaxial tensile experiments conducted on a composite material; (ii) continuum damage mechanics based material constitutive models; (iii) a Bayesian framework for uncertainty quantification, calibration, validation, and selection of models; and (iv) general Bayesian filtering, as well as Kalman and extended Kalman filters. A software infrastructure is developed and implemented in order to integrate the various parts of the DDDAS. The outcomes of computational analyses using the experimental data prove the feasibility of the Bayesian-based methods for model calibration, validation, and selection. Moreover, using such DDDAS infrastructure for real-time monitoring of the damage and degradation in materials results in results in an improved prediction of failure in the system. Copyright © 2014 John Wiley & Sons, Ltd.

This paper describes the development of efficient and robust numerical integration schemes for rate-dependent crystal plasticity models. A forward Euler integration algorithm is first formulated. An integration algorithm based on the modified Euler method with an adaptive substepping scheme is then proposed, where the substepping is mainly controlled by the local error of the stress predictions within the time step. Both integration algorithms are implemented in a stand-alone code with the Taylor aggregate assumption and in an explicit finite element code. The robustness, accuracy and efficiency of the substepping scheme are extensively evaluated for large time steps, extremely low strain-rate sensitivity, high deformation rates and strain-path changes using the stand-alone code. The results show that the substepping scheme is robust and in some cases one order of magnitude faster than the forward Euler algorithm. The use of mass scaling to reduce computation time in crystal plasticity finite element simulations for quasi-static problems is also discussed. Finally, simulation of Taylor bar impact test is carried out to show the applicability and robustness of the proposed integration algorithm for the modelling of dynamic problems with contact. Copyright © 2014 John Wiley & Sons, Ltd.

This paper presents a new implementation of a constitutive model commonly used to represent plastic bonded explosives in finite element simulations of thermomechanical response. The constitutive model, viscoSCRAM, combines linear viscoelasticity with isotropic damage evolution. The original implementation was focused on short duration transient events; thus, an explicit update scheme was used. For longer duration simulations that employ significantly larger time step sizes, the explicit update scheme is inadequate. This work presents a new semi-implicit update scheme suitable for simulations using relatively large time steps. The algorithm solves a nonlinear system of equations to ensure that the stress, damaged state, and internal stresses are in agreement with implicit update equations at the end of each increment. The crack growth is advanced in time using a sub-incremental explicit scheme; thus, the entire implementation is semi-implicit. The theory is briefly discussed along with previous explicit integration schemes. The new integration algorithm and its implementation into the finite element code, Abaqus, are detailed. Finally, the new and old algorithms are compared via simulations of uniaxial compression and beam bending. The semi-implicit scheme has been demonstrated to provide higher accuracy for a given allocated computational time for the quasistatic cases considered here. Published 2014. This article is a US Government work and is in the public domain in the USA.

The problem of a high-pressure gas cavity and its interaction with surrounding liquid and a close-by structure is examined numerically. Even though this is of interest in many practical applications, here, the focus is on an underwater explosion. A one-way DD strategy coupling a radial and a 3D solver for compressible multiphase flows is proposed, and the different components are successfully validated. This is a time-space DD, which assumes the explosion that occurs sufficiently far from boundaries. It means that the radial solution is used everywhere until radial symmetry is no more applicable. When acoustic waves reach a close structure, the radial solution initiates the 3D solution near the body and continues to be applied only far from the structure and to provide the boundary conditions for the 3D sub-domain. The advantage is to limit the computational costs and preserve reliability and accuracy. The radial solution could be applied to assess local damages during the initial acoustic phase; the time-space DD needs to be used to investigate both local and global consequences on the vessels. The structure is modeled both as a rigid wall and as an orthotropic plate, which provides a good representation of the bottom grillages of ships. Copyright © 2014 John Wiley & Sons, Ltd.

This paper presents three new computational methods for calculating design sensitivities of statistical moments and reliability of high-dimensional complex systems subject to random input. The first method represents a novel integration of the polynomial dimensional decomposition (PDD) of a multivariate stochastic response function and score functions. Applied to the statistical moments, the method provides mean-square convergent analytical expressions of design sensitivities of the first two moments of a stochastic response. The second and third methods, relevant to probability distribution or reliability analysis, exploit two distinct combinations built on PDD: the PDD-saddlepoint approximation (SPA) or PDD-SPA method, entailing SPA and score functions; and the PDD-Monte Carlo simulation (MCS) or PDD-MCS method, utilizing the embedded MCS of the PDD approximation and score functions. For all three methods developed, the statistical moments or failure probabilities and their design sensitivities are both determined concurrently from a single stochastic analysis or simulation. Numerical examples, including a 100-dimensional mathematical problem, indicate that the new methods developed provide not only theoretically convergent or accurate design sensitivities, but also computationally efficient solutions. A practical example involving robust design optimization of a three-hole bracket illustrates the usefulness of the proposed methods. Copyright © 2014 John Wiley & Sons, Ltd.

A micromechanical model for polycrystalline shape memory alloys (SMAs) was introduced in a series of papers by Hackl and coauthors. In order to model the polycrystalline aspect, they assumed a specific set of orientation distribution functions that had to be resolved with high numerical effort. Although this model displays interesting aspects, its use to simulate macroscopic specimens is problematic due to the long calculation time.

In this paper, we present a new approach to modeling and simulation of polycrystalline SMAs that is based on parameterization of a class of orientation distribution functions by using only a few parameters. A variational concept is applied to derive evolution equations for these parameters. The resultant material model drastically reduces the calculation time and may thus provide an approach to efficient micromechanical simulation of specimens that are of engineering interest.

This study presents a variety of different numerical examples, such as pseudoelastic and pseudoplastic material behavior for CuAlNi and NiTi SMAs, to demonstrate the broad applicability of the material model. The numerical benefit of the presented modeling approach is demonstrated by comparative calculations of the new model versus the previous model. Copyright © 2014 John Wiley & Sons, Ltd.

A computationally efficient multiscale–multiphysics model aimed at predicting mechanical response of thermoplastic composites subjected to different levels of moisture was developed. The mathematical model of the coupled moisture-diffusion–mechanical-deformation phenomenon was stated at the microscale, based on the observed experimental data, and then upscaled using a mathematical homogenization approach. A two-way coupling between moisture diffusion and mechanical deformation was introduced by which diffusivity was enhanced by hydrostatic strain, whereas strength and stiffness were assumed to degrade because of moisture ingression, which also gives rise to swelling. The computational complexity of analyzing the two coupled physical processes at multiple scales was reduced via a model reduction scheme for multiple physical processes. The model was validated for 30% by weight filled glass fiber and carbon fiber reinforced thermoplastic composites. The moisture conditioning and uniaxial tension experiments were utilized to identify diffusion and mechanical properties at a fine scale. The identified properties were then used to validate the formulation in the three-point bending test. Copyright © 2014 John Wiley & Sons, Ltd.

A cell-based smoothed discrete shear gap method (CS-FEM-DSG3) based on the first-order shear deformation theory (FSDT) was recently proposed for static and dynamic analyses of Mindlin plates. In this paper, the CS-FEM-DSG3 is extended to the C^{0}-type higher-order shear deformation plate theory (C^{0}-HSDT) and is incorporated with damping–spring systems for dynamic responses of Mindlin plates on viscoelastic foundations subjected to a moving sprung vehicle. At each time step of dynamic analysis, one four-step procedure is performed including the following: (1) transformation of the weight of a four-wheel vehicle into the sprung masses at wheels; (2) dynamic analysis of the sprung mass of wheels to determine the contact forces; (3) transformation of the contact forces into loads at nodes of plate elements; and (4) dynamic analysis of the plate elements on viscoelastic foundations. The accuracy and reliability of the proposed method are verified by comparing its numerical solutions with those of other available numerical results. Copyright © 2014 John Wiley & Sons, Ltd.

An element-free Galerkin (EFG) method with linear, quadratic and cubic approximations, which can exactly, in a numerical sense, pass the corresponding patch tests is proposed and is named as consistent EFG (CEFG) method. The development of this method is based on the Hu–Washizu three-field variational principle. Numerical integration schemes with corrected nodal derivatives at quadrature points are proposed according to the satisfaction of the orthogonality condition between stress and strain difference. Thus, the method is variationally consistent. The consistency of the corrected nodal derivatives and the satisfaction of patch test conditions are theoretically proved and also numerically validated. Numerical results show that the proposed CEFG method greatly improves the numerical performance of the EFG method in terms of accuracy, convergence, efficiency and stability, especially the proposed cubic CEFG method, which shows exceptional accuracy and convergence. Copyright © 2014 John Wiley & Sons, Ltd.

Particle methods are a class of numerical methods that belong to the family of meshless methods and are not based on an underlying mesh or grid, but rather on any general distribution of particles. They are nowadays widely applied in many fields, including, for example, solid mechanics, fluid dynamics, and thermodynamics.

In this paper, we start from the original formulation of the so-called modified finite particle method (MFPM) and develop a novel formulation. In particular, after discussing the position of the MFPM in the context of the existing literature on meshless methods, and recalling and discussing the 1D formulation and its properties, we introduce the novel formulation along with its extension to the approximation of 2D and 3D differential operators. We then propose applications of the discussed methods to some elastostatic and elastodynamic problems. The obtained results confirm the potential and the flexibility of the considered methods, as well as their second-order accuracy, proposing MFPM as a viable alternative for the simulation of solids and structures. Copyright © 2014 John Wiley & Sons, Ltd.

This paper shows the use of the dual integrated force method (IFMD) in finite elements method and its application to composite materials. This method was developed by S.N. Patnaik in isotropic materials, considering not only the equilibrium equations but also the compatibility conditions. In the IFMD, the principal unknowns are the displacements, and the structure of governing equation is similar to the stiffness method. It is shown that the governing equation of the IFMD is the same than in the case of the hybrid method of Pian. The method is applied to two examples, a cantilever beam of orthotropic material loaded at the end and one off-axis tensile test in a unidirectional composite specimen. The results of this method have been compared with the ones obtained from the application of the stiffness method and with analytical results. Copyright © 2014 John Wiley & Sons, Ltd.

A rigorous computational framework for the dimensional reduction of discrete, high-fidelity, nonlinear, finite element structural dynamics models is presented. It is based on the pre-computation of solution snapshots, their compression into a reduced-order basis, and the Galerkin projection of the given discrete high-dimensional model onto this basis. To this effect, this framework distinguishes between vector-valued displacements and manifold-valued finite rotations. To minimize computational complexity, it also differentiates between the cases of constant and configuration-dependent mass matrices. Like most projection-based nonlinear model reduction methods, however, its computational efficiency hinges not only on the ability of the constructed reduced-order basis to capture the dominant features of the solution of interest but also on the ability of this framework to compute fast and accurate approximations of the projection onto a subspace of tangent matrices and/or force vectors. The computation of the latter approximations is often referred to in the literature as hyper reduction. Hence, this paper also presents the energy-conserving sampling and weighting (ECSW) hyper reduction method for discrete (or semi-discrete), nonlinear, finite element structural dynamics models. Based on mesh sampling and the principle of virtual work, ECSW is natural for finite element computations and preserves an important energetic aspect of the high-dimensional finite element model to be reduced. Equipped with this hyper reduction procedure, the aforementioned Galerkin projection framework is first demonstrated for several academic but challenging problems. Then, its potential for the effective solution of real problems is highlighted with the realistic simulation of the transient response of a vehicle to an underbody blast event. For this problem, the proposed nonlinear model reduction framework reduces the CPU time required by a typical high-dimensional model by up to four orders of magnitude while maintaining a good level of accuracy. Copyright © 2014 John Wiley & Sons, Ltd.

This paper is concerned with the numerical calculation of stress intensity factors in two-dimensional linear fracture problems by Petrov–Galerkin natural element method, for which the Voronoi polygon-based Laplace interpolation functions and constant strain finite element basis functions are taken for the trial and test functions, respectively. A local element patch recovery technique is employed to obtain more accurate smoothed strain and stress fields, and the stress intensity factors of edge and angled center cracks are calculated by both the *J*-integral and interaction integral methods. The influence of the grid density, integral domain size, and weighting function type on the numerical accuracy is investigated through the numerical experiments. In addition, the present method is compared with the hybrid crack elements in combination with extended FEM and the scaled boundary FEM. It is confirmed that Petrov–Galerkin natural element method provides the numerical accuracy similar to these recent direct methods. Also, it is found that the accuracy of the *J*-integral is affected by the grid density but not by the integral domain size. In the case of the interaction integral, the numerical accuracy is influenced by both the type of weighting function and the integral domain size. Copyright © 2014 John Wiley & Sons, Ltd.

In the numerical analysis of 2‒D bimodular materials, strain discontinuity is problematic, and the traditional iterative algorithm is frequently unstable. This paper develops a stable algorithm for the large‒displacement and small‒strain analyses of 2‒D bimodular materials and structures. Geometrically nonlinear formulations are based on the co‒rotational approach. Using the parametric variational principle (PVP), a unified constitutive equation is created to resolve the problem induced by strain discontinuity in the local coordinate system. Because the traditional stress iteration is not required, the local linear stiffness matrix does not need to be updated when computing the global stiffness matrix and the nodal internal force vector. The nonlinear problem is ultimately transformed into a complementarity problem that is simply solved by combing the Newton–Raphson scheme and the mature quadratic programming algorithm. Numerical examples demonstrate that the PVP algorithm presents better convergence behavior than the traditional iterative algorithm. By incorporating the concept of material modification, the new algorithm is also be successfully extended to the wrinkling analysis of thin membranes. Copyright © 2014 John Wiley & Sons, Ltd.

A new finite element tool is presented, which utilises the extended FEM (XFEM) to model leaks through cracks. Heat flux and pressure boundary conditions are imposed on the crack in the form of jump terms. Enrichments are chosen to model either strong or weak discontinuities across the crack, as well as singularities at the crack tips. Excellent convergence rates are achieved for both the thermal and mechanical models, where errors are calculated relative to analytical solutions derived for this specific problem. A more general temperature approximation is also presented, which makes no assumptions about the continuity of temperature or heat flux across the crack. Results indicate that this is a robust way of modelling the temperature of a plate containing a crack with or without a leaking fluid. Thermomechanical simulations were then carried out to demonstrate the applicability of the FEM for analysing leak rates in nuclear reactor primary pipework. A two-phase flow model based on the Henry–Fauske model is chosen for the fluid aspect, and this is coupled to the structure through a convection law. Crack closure is shown to reduce the leak rate by up to 40%. Copyright © 2014 John Wiley & Sons, Ltd.

Procedures to couple reservoir and geomechanical models are reviewed. The focus is on immiscible compressible non-compositional reservoir–geomechanical models. Such models require the solution to: coupled stress, pressure, saturation and temperature equations. Although the couplings between saturation and temperature with stress and fluid pressure are ‘weak’ and can be adequately captured thru staggered (fixed point) iterations, the couplings between stress and pressure are ‘strong’ and require special procedures for accurate integration. As shown and discussed in detail in our previous works, two-way coupling (i.e., simultaneous integration) of pressure and stress equations is required if poromechanical effects are to be captured accurately. In our previous work, a Galerkin implementation of both pressure and stress equations was used with equal order interpolants.

However, most (if not all) reservoir simulators use a finite volume implementation of the pressure equation. Therefore, there remain important unanswered questions related to the interface between a Galerkin vertex-centered geomechanical model with a reservoir finite volume model as such an implementation has never been attempted before. We address those issues in the following by studying the interface with both a cell-centered and a vertex-centered finite volume implementation of the pressure equation. Central to the success of the implementation is the computation of the Jacobian matrix. The elemental contribution to the coupling Jacobian matrix is computed through numerical finite differencing of the residuals. The procedure is detailed herein. In the following, in order to attempt to clear confusion, the simplest case of an isothermal fully saturated, slightly compressible system is presented in detail, and the various solution strategies, simplifications and shortcomings are identified. Copyright © 2014 John Wiley & Sons, Ltd.

The elastic multi-body system dynamics is studied from the prospect of modal reduction. The bodies are seen as stiff, close to rigid, subjected to non-smooth contact interactions, such as collisions and dry friction. The finite element degrees of freedom of the bodies are represented either through the method of a floating frame of reference or the classical small deformation method in the global frame. The numerical modal reduction strategy based on Craig–Bampton representation of the current degrees of freedom is suggested. The method is general and may be applied to both quasi-static and dynamic simulations. The key modeling assumption for the method is that the neglected modes have constant response in time. Numerical experiments, where the method is examined and compared with modally full floating frame approach, show satisfying accuracy while achieving significant computational savings. Copyright © 2014 John Wiley & Sons, Ltd.

A new finite heterogeneous element consisting of sliced microstructures (FHES) is applied in a multi‒scale technique. The FHES represents a heterogeneous material with microscopic constituents without homogenization or microscopic finite element analysis. A representative volume element extracted from a heterogeneous structure is thinly sliced. Each slice is modeled as a combined spring to calculate properties of the FHES. Each FHES has the same number of nodes as an ordinary finite element, and the macroscopic analysis cost is the same as that for ordinary finite element analysis. However, the FHES retains information about the microscopic material layout (i.e., the distribution of a material's property) in itself that is lost during homogenization. In the proposed approach, materials are not homogenized. The FHES does not have a constant (homogenized) material property and can ‘change stiffness’ depending on its deformation behavior. This reduces error due to coarse‒graining and allows us to calculate the macroscopic deformation behavior with sufficient accuracy even if a large gradient of strain is generated in the macroscopic field. The novelty of the research is the development of rational heterogeneous finite elements. The paper presents the theory behind the FHES and its practical application to a linear elastic problem. Copyright © 2014 John Wiley & Sons, Ltd.

A new method to compute numerically efficient closed-form representation of matrix exponential and its derivative is developed for 3 × 3 matrices with real eigenvalues. The matrix exponential is obtained by automatic differentiation of an appropriate scalar generating function in a general case, and highly accurate asymptotic expansions are derived for special cases in which the general formulation exhibits ill-conditioning, for instance, for almost equal eigenvalues. Accuracy and numerical efficiency of the closed-form matrix exponential as compared with the truncated series approximation are studied. The application of the closed-form matrix exponential in the finite-strain elastoplasticity is also presented. To this end, several time-discrete evolution laws employing the exponential map are discussed for *J*_{2} plasticity with isotropic hardening and nonlinear kinematic hardening of Armstrong–Frederick type. The discussion is restricted to the case of elastic isotropy and implicit time integration schemes. In this part, the focus is on a general automatic differentiation-based formulation of finite-strain plasticity models. Numerical efficiency of the corresponding incremental schemes is studied in the context of the FEM. Copyright © 2014 John Wiley & Sons, Ltd.

A Discontinuous Galerkin (DG)-based approach is proposed for computing the scattered field from an elastic bounded object immersed in an infinite homogeneous fluid medium. The proposed method possesses two distinctive features. First, it employs higher-order polynomial-shape functions needed to address the high-frequency propagation regime. Second, it is equipped with curved boundary edges to provide an accurate representation of the fluid–structure interface. The most salient benefits resulting from the latter feature, as demonstrated by the numerical investigation, are the following: (i) an improvement by—at least—two orders of magnitude on the relative error and (ii) the disappearance of spurious resonance frequencies in the surrounding fluid medium. In addition, the reported numerical results reveal that when using cubic polynomials with less than three elements per wavelength, the proposed DG method computes the scattered field with a relative error below 1% for an elastic scatterer of about 30 wavelengths. This observation highlights the potential of the proposed solution methodology for efficiently solving mid-frequency to high-frequency elasto-acoustic scattering problems. Copyright © 2014 John Wiley & Sons, Ltd.

We compare a family of mixed interpolations on triangles with straight edges as applied to limit analysis. The aim of this paper is to prove theoretically that the approximate collapse factors obtained with these finite elements always comply with certain inequalities that exist among them. Two of these interpolations are used in limit analysis for the first time in this article. The inequalities in the proposition are also demonstrated via numerical applications. To this end, the most frequently used benchmark problems in limit analysis are revisited and discussed with respect to the results computed with these finite elements. Copyright © 2014 John Wiley & Sons, Ltd.

We employ the linked interpolation concept to develop two higher-order nine-node quadrilateral plate finite elements with curved sides that pass the constant bending patch test for arbitrary node positions. The linked interpolation for the plate displacements is expanded with three bubble parameters to get polynomial completeness necessary to satisfy the patch test. In contrast to some other techniques, the elements developed in this way retain a symmetric stiffness matrix at a marginal computational expense at the element level. The new elements generated using this concept are tested on several examples with curved sides or some other kind of geometric distortion. Copyright © 2014 John Wiley & Sons, Ltd.

A modified Green operator is proposed as an improvement of Fourier-based numerical schemes commonly used for computing the electrical or thermal response of heterogeneous media. Contrary to other methods, the number of iterations necessary to achieve convergence tends to a finite value when the contrast of properties between the phases becomes infinite. Furthermore, it is shown that the method produces much more accurate local fields inside highly conducting and quasi-insulating phases, as well as in the vicinity of phase boundaries. These good properties stem from the discretization of Green's function, which is consistent with the pixel grid while retaining the local nature of the operator that acts on the polarization field. Finally, a fast implementation of the ‘direct scheme’ of Moulinec *et al.* (1994) that allows for parsimonious memory use is proposed. Copyright © 2014 John Wiley & Sons, Ltd.

The hybrid taxonomy — a means of characterizing different atomistic-continuum methods on the basis of the type of information exchanged between the atomistic and the continuum solver — is introduced. The formulation of the taxonomy raises a new hybrid possibility, called a ‘hybrid-hybrid’ method. Some examples of hybrid-hybrid simulations for dense fluids are discussed and validated against full molecular dynamics results. Copyright © 2014 John Wiley & Sons, Ltd.