International Journal for Numerical Methods in Engineering最新文献

We present an efficient approach to quantify the uncertainties associated with the numerical simulations of the laser-based powder bed fusion of metals processes. Our study focuses on a thermomechanical model of an Inconel 625 cantilever beam, based on the AMBench2018-01 benchmark proposed by the National Institute of Standards and Technology (NIST). The proposed approach consists of a forward uncertainty quantification analysis of the residual strains of the cantilever beam given the uncertainty in some of the parameters of the numerical simulation, namely the powder convection coefficient and the activation temperature. The uncertainty on such parameters is modelled by a data-informed probability density function obtained by a Bayesian inversion procedure, based on the displacement experimental data provided by NIST. To overcome the computational challenges of both the Bayesian inversion and the forward uncertainty quantification analysis we employ a multi-fidelity surrogate modelling technique, specifically the multi-index stochastic collocation method. The proposed approach allows us to achieve a 33% reduction in the uncertainties on the prediction of residual strains compared with what we would get basing the forward UQ analysis on a-priori ranges for the uncertain parameters, and in particular the mode of the probability density function of such quantities (i.e., its “most likely value”, roughly speaking) results to be in good agreement with the experimental data provided by NIST, even though only displacement data were used for the Bayesian inversion procedure.

This paper presents mixed finite element formulations to approximate the hyperelasticity problem using as unknowns the displacements and either stresses or pressure or both. These mixed formulations require either finite element spaces for the unknowns that satisfy the proper inf-sup conditions to guarantee stability or to employ stabilized finite element formulations that provide freedom for the choice of the interpolating spaces. The latter approach is followed in this work, using the Variational Multiscale concept to derive these formulations. Regarding the tackling of the geometry, we consider both infinitesimal and finite strain problems, considering for the latter both an updated Lagrangian and a total Lagrangian description of the governing equations. The combination of the different geometrical descriptions and the mixed formulations employed provides a good number of alternatives that are all reviewed in this paper.

We explore the viability of modeling dynamic problems with a new formulation of an impulse-based Level-Set DEM (LS-DEM). The new formulation is stable, fast, and energy conservative. However, it can be numerically stiff when the assembly has substantial mass differences between particles. We also demonstrate the feasibility of modeling deformable structures in a rigid body framework and propose several enhancements to improve the convergence of collision resolution, including a hybrid time integration scheme to separately handle at rest contacts and dynamic collisions. Finally, we extend the impulse-based LS-DEM to include arbitrarily shaped topographic surfaces and exploit its algorithmic advantages to demonstrate the feasibility of modeling realistic behavior of granular flows. The new formulation significantly improves the performance of dynamic simulations by allowing larger time steps, which is advantageous for observing the full development of physical phenomena such as rock avalanches, which we present as an illustrative example.

The phase field modeling of fracture is able to simulate the nucleation and the propagation of complex crack patterns. However, the relatively small internal lengths that are required usually lead to very fine meshes and high computational costs, especially for three-dimensional applications. In the present work, additional cost also comes from the implicit dynamics regularization of unstable crack propagations which potentially leads to a large variation of time steps when switching from quasi-static to dynamic regimes. To reduce the time to solution in this context, this study proposes a domain decomposition framework and acceleration techniques for the phase field fracture staggered solver. The displacement subproblem and the phase field one are solved with parallel domain decomposition solvers. Dual domain decomposition methods provide low cost preconditioner well adapted to the phase field subproblem. For displacement subproblems undergoing unstable crack propagations, primal domain decomposition methods are preferred to be less sensitive to the treatment of floating substructures. Preconditioners performances are assessed and scalability studies over academic test cases, up to 324 subdomains, are presented. Finally, the robustness of the approach is illustrated on two semi-industrial simulations.

The present article proposes an hybrid equilibrium element (HEE) formulation for the prediction of cohesive fracture formation and propagation with the crack modelled by extrinsic interface embedded at element sides. The hybrid equilibrium element formulation can model high order (quadratic, cubic and quartic) stress fields which strongly satisfy homogeneous equilibrium equations, inter-element and boundary equilibrium equations. The HEE can implicitly model both the initially rigid behaviour of an extrinsic interface and its debonding condition with separation displacement and softening. The extrinsic interface is embedded at the element sides and its behaviour is governed by means of the same degrees of freedom of HEE (generalized stresses), without any additional degree of freedom. The proposed extrinsic cohesive model is developed in the thermodynamic framework of damage mechanics. The proposed crack propagation criterion states that crack grows when the maximum principal stress reaches the tensile strength value, in a direction orthogonal to the principal stress direction. The crack is embedded at an element side and the mesh around crack tip is adapted, by rotation of the element sides, in order to have the interface aligned to the crack growth direction. Three classic two-dimensional problems of fracture propagation are numerically reproduced and the results compared to the experimental data or to the other numerical results.

The solution of large linear systems of equations with sparse matrices is a critical component of finite element analyses. Three linear solvers are investigated here: MUMPS, UMFPACK, and Intel DSS (PARDISO). Often, these solvers are employed as “black boxes.” However, some caveats in their implementation must be observed. For instance, the solvers may yield incorrect results or perform extremely poorly in a multithread environment. These issues are demonstrated, and suggestions to fix them are provided. Some performance benchmarks are also presented with a focus on the multithreaded behavior.

This study presents an alternative boundary element method (BEM) formulation for the cohesive crack propagation modelling in three-dimensional structures. The proposed formulation utilises an initial stress field for representing the mechanical behaviour along the fracture process zone, which leads to a set of self-equilibrated forces named as dipole. Cohesive laws govern the material nonlinear behaviour along the fracture process zone. The proposed dipole-based formulation demonstrates some advantages in comparison to classical BEM approaches in this field. Among them, it is worth citing the requirement of solely three integral equations per collocation point positioned at the fracture process zone. The effectiveness of the dipole-based formulation has been demonstrated by four applications. The results have been compared to numerical, experimental and analytical solutions available in the literature, in which excellent performance has been observed.

Topology optimization (TO) has recently emerged as an advanced design method. To ensure practical reliability in the design process, it is imperative to incorporate considerations of uncertainty. Consequently, performing reliability analysis (RA) during the design phase becomes necessary. However, RA itself constitutes an optimization problem. Combining these two optimization problems can result in inefficiency. To address this challenge, we propose a decoupled approach that integrates deterministic topology optimization (DTO) and RA cycles. The reliability-based stress-constrained TO (RBSCTO) problem is considered in this paper. The DTO constraint is derived based on shifting vectors derived from the previous cycle's RA outcomes, enabling low-reliability constraint shift towards the feasible direction. The DTO is solved based on solid-isotropic-material-with-penalization (SIMP) and augmented Lagrangian method. Meanwhile, the optimization problem in RA is addressed using finite differences and the interior point method. To reduce the errors resulting from linear approximation and optimization in RA when the target reliability is very low, an outlier handling method is employed. Meantime, we utilize a probabilistic neural network to enhance the efficiency of reliability assessment. Comparative studies against traditional methods across four RBSCTO tasks are demonstrated to validate its effectiveness. Monte Carlo simulations are used to validate the reliability of results.