Computational Mechanics最新文献

This paper presents a new mixed finite element model for material and geometric non-linear analysis of composite beams in partial interaction taking into account the non-penetration condition between layers. The Hu–Washizu functional with three independent fields is chosen for the developed mixed formulation. The force fields in the connection are chosen as the redundant forces and approximated using interpolation functions. The remaining force fields are obtained from solving equilibrium equations so that the element equlibrium is verified. Nevertheless, the compatibility as well as the constitutive law is satisfied only in a weak sense. The geometric non-linearity is taken into account by adopting the co-rotational approach. In this paper, the contact condition is imposed at the element level. Augmented Lagrangian method with Uzawa iteration algorithm is used to solve the contact problem. It has been shown that the proposed mixed formulation gives a more accurate result with less elements comparing to classical displacement based model. Besides, the buckling behaviour of delaminated two-layered composite columns has been studied by using the developed mixed formulation model. It has been observed that the buckling strength of the composite column can be overestimated if the uplift is not considered in the model.

This study proposes an implicit algorithm applying the primal–dual interior point method (PDIP method) to stabilize the stress update when using a class of the Gurson–Tvergaard–Needleman model (GTN model). The GTN model is widely used to realize the change in void volume fraction that governs ductile fracture in metals, but numerical instabilities arise due to shrinkage of the yield surface and the accelerated void growth. In fact, such shrinkage can lead to misjudgment of yield conditions when using conventional return mapping algorithms, since trial elastic stresses are computed assuming zero incremental plastic strain. In addition, the change in void volume fraction is often approximated in bilinear form to represent the acceleration of void growth, but should be smooth to apply nonlinear solution methods such as the Newton’s method. To avoid such inconvenience in the implicit stress update for the GTN model and ensure numerical stability, we propose an algorithm that replaces the constitutive equations with inequality constraints with an equivalent constrained optimization problem by applying the PDIP method. After verifying the numerical accuracy and convergence of the proposed implicit algorithm using iso-error maps, we demonstrate its capability through several numerical examples that cannot be solved by the conventional return mapping algorithm or the PDIP method applied only to the inequality constraint corresponding to the yield condition.

We present and analyze computationally Geometric MultiGrid (GMG) preconditioning techniques for Generalized Minimal RESidual (GMRES) iterations to space-time finite element methods (STFEMs) for a coupled hyperbolic–parabolic system modeling, for instance, flow in deformable porous media. By using a discontinuous temporal test basis, a time marching scheme is obtained. Higher order approximations that offer the potential to inherit most of the rich structure of solutions to the continuous problem on computationally feasible grids increase the block partitioning dimension of the algebraic systems, comprised of generalized saddle point blocks. Our V-cycle GMG preconditioner uses a local Vanka-type smoother. Its action is defined in an exact mathematical way. Due to nonlocal coupling mechanisms of 348 unknowns, the smoother is applied on patches of elements. This ensures damping of higher order error frequencies. By numerical experiments of increasing complexity, the efficiency of the solver for STFEMs of different polynomial order is illustrated and confirmed. Its parallel scalability is analyzed. Beyond this study of classical performance engineering, the solver’s energy efficiency is investigated as an additional and emerging dimension in the design and tuning of algorithms on the hardware.

Worldwide communication bandwidth growth has largely been driven by (1) multimedia demands, (2) multicommunication-point demands and (3) multicommunication-rate demands, and has increased dramatically over the last two decades due to e-commerce, internet communication and the explosion of cell-phone use, in particular for in-flight services, all of which necessitate broadband use and low latency. In order to accommodate this huge surge in demand, next generation “mega-constellations” of satellites are being proposed combining a mix of heterogeneous unit types in LEO, MEO and GEO orbital shells, in order to provide continuous lower-latency and high-bandwidth service which exploits a wide-range of frequencies for fast internet connections (broadband, which is not possible with single satellite-type orbital shell systems). Accordingly, in this work, we develop a computationally-efficient digital-twin framework for a constellation of satellites around an arbitrary planet (“Planet-X”). The rapid speed of these simulations enables the ability to explore satellite infrastructure parameter combinations, represented by a multicomponent satellite constellation design vector (varvec{Lambda }{mathop {=}limits ^textrm{def}}) (number of satellites, satellite orbital radii, satellite orbital speeds, satellite types), that can deliver desired communication signal or camera coverage on “Planet-X", while simultaneously incorporating satellite infrastructural resource constraints. In order to cast the objective mathematically, we set up the system design as an inverse problem to minimize a cost function via a Genetic Machine Learning Algorithm (G-MLA), which is well-suited for nonconvex optimization. Numerical examples are provided to illustrate the framework.

In this paper, we present a novel adaptive continuous–discontinuous approach for the analysis of phase field fracture. An initial trimmed hexahedral (TH) mesh is created by cutting a hexahedral background grid with the boundary of the solid domain. Octree-based adaptive mesh refinement is performed on the initial TH mesh based on an energy-based criterion to accurately resolve the damage evolution along the phase field crack. Critical damage isosurfaces of the phase field are used to convert fully developed phase field cracks into discontinuous discrete cracks. Mesh coarsening is also performed along the discontinuous discrete cracks to reduce the computational cost. Three-dimensional problems of quasi-brittle fracture are investigated to verify the effectiveness and efficiency of the present adaptive continuous–discontinuous approach for the analysis of phase field fracture.

Abstract

This is Part II of a multipart article on a hyperelastic extended Kirchhoff–Love shell model with out-of-plane normal stress. We introduce an isogeometric discretization method for incompressible materials and present test computations. Accounting for the out-of-plane normal stress distribution in the out-of-plane direction affects the accuracy in calculating the deformed-configuration out-of-plane position, and consequently the nonlinear response of the shell. The return is more than what we get from accounting for the out-of-plane deformation mapping. The traction acting on the shell can be specified on the upper and lower surfaces separately. With that, the model is now free from the “midsurface’ location in terms of specifying the traction. In dealing with incompressible materials, we start with an augmented formulation that includes the pressure as a Lagrange multiplier and then eliminate it by using the geometrical representation of the incompressibility constraint. The resulting model is an extended one, in the Kirchhoff–Love category in the degree-of-freedom count, and encompassing all other extensions in the isogeometric subcategory. We include ordered details as a recipe for making the implementation practical. The implementation has two components that will not be obvious but might be critical in boundary integration. The first one is related to the edge-surface moment created by the Kirchhoff–Love assumption. The second one is related to the pressure/traction integrations over all the surfaces of the finite-thickness geometry. The test computations are for dome-shaped inflation of a flat circular shell, rolling of a rectangular plate, pinching of a cylindrical shell, and uniform hydrostatic pressurization of the pinched cylindrical shell. We compute with neo-Hookean and Mooney–Rivlin material models. To understand the effect of the terms added in the extended model, we compare with models that exclude some of those terms.

In this work, we propose an efficient smoothed particle hydrodynamics (SPH) method for simulating laser powder bed fusion (LPBF). The multi-physics process of LPBF, including the heat transfer and phase change with complex boundaries, is accurately resolved by a novel heat source model and a modified continuous surface force based on a corrected surface delta function. Moreover, we also develop an efficient tensile instability control algorithm for preventing the pressure oscillations. The present method is implemented in a GPU-accelerated framework, and its performance is well demonstrated by simulating the LPBF processes with both single-layer and multi-layer powder beds (with the help of surface reconstruction). The numerical results are compared well with the experimental ones which clearly verify the ability of the present method in capturing the complex physical phenomenon of LPBF.

This study presents an innovative approach for developing a reduced-order model (ROM) tailored specifically for nearly incompressible materials at large deformations. The formulation relies on a three-field variational approach to capture the behavior of these materials. To construct the ROM, the full-scale model is initially solved using the finite element method (FEM), with snapshots of the displacement field being recorded and organized into a snapshot matrix. Subsequently, proper orthogonal decomposition is employed to extract dominant modes, forming a reduced basis for the ROM. Furthermore, we efficiently address the pressure and volumetric deformation fields by employing the k-means algorithm for clustering. A well-known three-field variational principle allows us to incorporate the clustered field variables into the ROM. To assess the performance of our proposed ROM, we conduct a comprehensive comparison of the ROM with and without clustering with the FEM solution. The results highlight the superiority of the ROM with pressure clustering, particularly when considering a limited number of modes, typically fewer than 10 displacement modes. Our findings are validated through two standard examples: one involving a block under compression and another featuring Cook’s membrane. In both cases, we achieve substantial improvements based on the three-field mixed approach. These compelling results underscore the effectiveness of our ROM approach, which accurately captures nearly incompressible material behavior while significantly reducing computational expenses.

This paper presents a novel framework combining proper generalized decomposition (PGD) with the shooting method to determine the steady-state response of nonlinear dynamical systems upon a general periodic input. The proposed PGD approximates the response as a low-rank separated representation of the spatial and temporal dimensions. The Galerkin projection is employed to formulate the subproblem for each dimension, then the fixed-point iteration is applied. The subproblem for the spatial vector can be regarded as computing a set of reduced-order basis vectors, and the shooting problem projected onto the subspace spanned by these basis vectors is defined to obtain the temporal coefficients. From this procedure, the proposed framework replaces the complex nonlinear time integration of the full-order model with the series of solving simple iterative subproblems. The proposed framework is validated through two descriptive numerical examples considering the conventional linear normal mode method for comparison. The results show that the proposed shooting method based on PGD can accurately capture nonlinear characteristics within 10 modes, whereas linear modes cannot easily approximate these behaviors. In terms of computational efficiency, the proposed method enables CPU time savings of about one order of magnitude compared with the conventional shooting methods.

Failure initiation and subsequent crack trajectory in heterogeneous materials, such as functionally graded materials and bones, are yet insufficiently addressed. The AT1 phase field model (PFM) is investigated herein in a 1D setting, imposing challenges and opportunities when discretized by h- and p-finite element (FE) methods. We derive explicit PFM solutions to a heterogeneous bar in tension considering heterogeneous E(x) and (G_{Ic}(x)), necessary for verification of the FE approximations. (G_{Ic}(x)) corrections accounting for the element size at the damage zone in h-FEMs are suggested to account for the peak stress underestimation. p-FEMs do not require any such corrections. We also derive and validate penalty coefficient for heterogeneous domains to enforce damage positivity and irreversibility via penalization. Numerical examples are provided, demonstrating that p-FEMs exhibit faster convergence rates comparing to classical h-FEMs. The new insights are encouraging towards p-FEM discretization in a 3D setting to allow an accurate prediction of failure initiation in human bones.