M.P. Ariza

Flux and traction boundary elements without hypersingular or strongly singular integrals

The present paper deals with a boundary element formulation based on the traction elasticity boundary integral equation (potential derivative for Laplaces problem). The hypersingular and strongly singular integrals appearing in the formulation are analytically transformed to yield line and surface integrals which are at most weakly singular. Regularization and analytical transformation of the boundary integrals is done prior to any boundary discretization. The integration process does not require any change of co-ordinates and the resulting integrals can be numerically evaluated in a simple and efficient way. The formulation presented is completely general and valid for arbitrary shaped open or closed boundaries. Analytical expressions for all the required hypersingular or strongly singular integrals are given in the paper. To fulfil the continuity requirement over the primary density a simple BE discretization strategy is adopted. Continuous elements are used whereas the collocation points are shifted towards the interior of the elements. This paper pretends to contribute to the transformation of hypersingular boundary element formulations as something clear, general and easy to handle similar to in the classical formulation. Copyright

Three-dimensional fracture analysis in transversely isotropic solids

Abstract In this paper a boundary element formulation for three-dimensional crack problems in transversely isotropic bodies is presented. Quarter-point and singular quarter-point elements are implemented in a quadratic isoparametric element context. The point load fundamental solution for transversely isotropic media is implemented. Numerical solutions to several three-dimensional crack problems are obtained. The accuracy and robustness of the present approach for the analysis of fracture mechanics problems in transversely isotropic bodies are shown by comparison of some of the results obtained with existing analytical solutions. The approach is shown to be a simple and useful tool for the evaluation of stress intensity factors in transversely isotropic media.

A singular element for three-dimensional fracture mechanics analysis

Abstract In this article, a singular boundary element for three-dimensional fracture mechanics analysis is presented. It is a nine-node quadratic element with plane geometry. These nodes are located at one quarter of the distance between two opposite sides of the element. Shape functions with a 11 √r singularity at the crack front are used to represent the tractions. The Stress Intensity Factors are computed as system unknowns appearing (except for a constant) as traction nodal values. Special attention is paid to the development of a simple and accurate integration approach for this singular element. The accuracy of the results obtained with the proposed element is demonstrated by solving several crack problems including edge and embedded cracks with different geometries. The element can be easily implemented and incorporated into existing quadratic boundary element codes. In a companion paper the element is formulated and used for fracture mechanics problems in transversely isotropic materials. Extension to other fields for which boundary element formulations exist, is quite simple.

General BE approach for three-dimensional dynamic fracture analysis

Abstract A general mixed boundary element approach for three-dimensional dynamic fracture mechanics problems is presented in this paper. A mixed traction-displacement integral equation formulation in the frequency domain is used. The hypersingular and strongly singular kernels are regularized by analytical transformations yielding an easy to implement BE approach. Nine-node quadrilateral and six-node triangular continuous quadratic elements are used for external boundaries and crack surfaces. The crack front elements have their mid node at one quarter of the element length allowing for a proper representation of the crack surface displacement. The present approach is intended for the frequency domain analysis of fracture mechanics problems of any general 3D geometry; i.e. boundless or bounded regions, single or multiple, surface or internal cracks. Transient dynamic problems are studied using the FFT algorithm. The numerical results presented show the robustness and accuracy of the approach which requires a reasonable number of elements and degrees of freedom.

A direct traction BIE approach for three-dimensional crack problems

A boundary element (BE) approach based on the traction boundary integral equation for the general solution of three-dimensional (3D) crack problems is presented. The hypersingular and strongly singular integrals appearing in the formulation are analytically transformed to yield line and surface integrals which are at most weakly singular. Regularization and analytical transformation of the boundary integrals is done prior to any boundary discretization. The integration process does not require of any change of coordinates and the resulting integrals can be numerically evaluated in a simple and efficient way. In order to show the generality, simplicity and robustness of the proposed approach, different flat and curved crack problems in infinite and finite domains are analyzed. A simple BE discretization strategy is adopted. The results obtained using rather course meshes are very accurate. The emphasis of this paper is on the effective application of the proposed BE approach and it is pretended to contribute to the transformation of hypersingular boundary element formulation in something as clear, general and easy to handle as the classical formulation but much better suited for fracture mechanics problems.

Stacking faults and partial dislocations in graphene

We investigate two mechanisms of crystallographic slip in graphene, corresponding to glide and shuffle generalized stacking faults (GSF), and compute their γ-curves using Sandia National Laboratories Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS). We find evidence of metastable partial dislocations for the glide GSF only. The computed values of the stable and unstable stacking-fault energies are suggestive of a high stability of full dislocations against dissociation and of dislocation dipoles against annihilation.

Finite Temperature Nanovoids Evolution in FCC Metals Using Quasicontinuum Method

Tensile failure of metals often occurs through void nucleation, growth and coalescence. This work is concerned with the study of plastic nanovoid cavitation in face-centeredcubic (FCC) crystals at finite temperature. In particular, the Quasicontinuum (QC) method,suitably extended to finite temperatures, is taken as the basis for the analysis. We specificallyfocus on nanovoids in copper single crystals deforming in uniaxial and triaxial tension. Thecomplex structure of dislocations around the nanovoid and the evolution of stress, deformationand temperature of the sample is described in the present work.

Double kink mechanisms for discrete dislocations in BCC crystals

We present an application of the discrete dislocation theory to the characterization of the energetics of kinks in Mo, Ta and W body-centered cubic (BCC) crystals. The discrete dislocation calculations supply detailed predictions of formation and interaction energies for various double-kink formation and spreading mechanisms as a function of the geometry of the double kinks, including: the dependence of the formation energy of a double kink on its width; the energy of formation of a double kink on a screw dislocation containing a pre-existing double kink; and energy of formation of a double kink on a screw dislocation containing a pre-existing single kink. The computed interaction energies are expected to facilitates the nucleation of double kinks in close proximity to each other and to pre-existing kinks, thus promoting clustering of double kinks on screw segments and of ‘daughter’ double kinks ahead of ‘mother’ kinks. The predictions of the discrete dislocation theory are found to be in good agreement with the full atomistic calculations based on empirical interatomic potentials available in the literature.

A comparative study of nanovoid growth in FCC metals

Abstract Previous HotQC studies of Cu nanovoids undergoing volumetric expansion conducted by the authors have uncovered a quasistatic-to-dynamic transition at a critical strain rate of the order of . At low strain rates nanovoid expansion takes place under essentially isothermal conditions, whereas at high strain rates it happens under essential adiabatic conditions. In this paper, we present a comparative study concerned with two different scenarios, each representing a variation on the reference case presented in [1]: (i) aluminium (Al) nanovoids undergoing volumetric expansion; and (ii) copper (Cu) nanovoids undergoing uniaxial deformation. Scenario (i) addresses material specificity by replacing Cu by Al in the reference case, whereas scenario (ii) addresses the effect of triaxiality by replacing volumetric expansion by uniaxial expansion in the reference case. We find a distinct quasistatic-to-dynamic transition in both scenarios, which suggests that the transition is indeed universal, i.e. material and strain-triaxiality independent. By contrast, the fine structure of the dislocation mechanisms that mediate void growth are strongly material and loading specific.

Acceleration of diffusive molecular dynamics simulations through mean field approximation and subcycling time integration

Diffusive Molecular Dynamics (DMD) is a class of recently developed computational models for the simulation of long-term diffusive mass transport at atomistic length scales. Compared to previous atomistic models, e.g., transition state theory based accelerated molecular dynamics, DMD allows the use of larger time-step sizes, but has a higher computational complexity at each time-step due to the need to solve a nonlinear optimization problem at every time-step. This paper presents two numerical methods to accelerate DMD based simulations. First, we show that when a many-body potential function, e.g., embedded atom method (EAM), is employed, the cost of DMD is dominated by the computation of the mean of the potential function and its derivatives, which are high-dimensional random variables. To reduce the cost, we explore both first- and second-order mean field approximations. Specifically, we show that the first-order approximation, which uses a point estimate to calculate the mean, can reduce the cost by two to three orders of magnitude, but may introduce relatively large error in the solution. We show that adding an approximate second-order correction term can significantly reduce the error without much increase in computational cost. Second, we show that DMD can be significantly accelerated through subcycling time integration, as the cost of integrating the empirical diffusion equation is much lower than that of the optimization solver. To assess the DMD model and the numerical approximation methods, we present two groups of numerical experiments that simulate the diffusion of hydrogen in palladium nanoparticles. In particular, we show that the computational framework is capable of capturing the propagation of an atomically sharp phase boundary over a time window of more than 30 seconds. The effects of the proposed numerical methods on solution accuracy and computation time are also assessed quantitatively.