Residual stresses in metal deposition modeling: Discretizations of higher order

Abstract

This article addresses the research question if and how the finite cell method, an embedded domain finite element method of high order, may be used in the simulation of metal deposition to harvest its computational efficiency. This application demands for the solution of a coupled thermo-elasto-plastic problem on transient meshes within which history variables need to be managed dynamically on non-boundary conforming discretizations. To this end, we propose to combine the multi-level hp-method and the finite cell method. The former was specifically designed to treat high-order finite element discretizations on transient meshes, while the latter offers a remedy to retain high-order convergence rates also in cases where the physical boundary does not coincide with the boundary of the discretization. We investigate the performance of the method at two analytical and one experimental benchmark.

The hierarchical finite cell method for nonlinear problems: Moment fitting quadratures, basis function removel, and remeshing

“…Since its introduction, the FCM has been successfully applied in various fields, e.g. applications to elastic and plastic problems in small and large strain [19,20,[23][24][25][26][27][28][29][30][31][32][33], homogenization of heterogeneous and cellular materials as well as foams [34][35][36][37][38][39][40], topology optimization [41,42], problems including material interfaces [43][44][45][46][47], contact problems [40,[48][49][50][51][52][53][54], multi-physic problems [55][56][57][58][59][60][61][62], fracture simulation [63,64], or simulation of wave propagation [65][66][67]…”

Modeling and experimental validation of an immersed thermo-mechanical part-scale analysis for laser powder bed fusion processes

“…However, due to its multi-scale nature in both space and time, numerical simulations of LPBF processes are extremely challenging from a modeling as well as from a numerical point of view. For detailed reviews on the state of the art of LPBF AM process simulations we refer to [24]. In particular, we can distinguish three main groups of physical models which dier in the spatial and temporal scale they aim at solving [5]: powder, micro-structural, and part-scale models.…”

“…In particular, the Finite Cell Method (FCM) [22] has already been applied to simulate thermal [23] and thermo-mechanical [24] In Section 5, we present and discuss our numerical results, comparing them with the experimental measurements, while we draw conclusions and provide an outlook in Section 6.…”

“…processes. Further details on the implementation of an FCM-based thermomechanical problem solver can be found in[31].…”

Finite Cell Method for functionally graded materials based onV-models and homogenized microstructures

“…The FCM [24] uses besides the embedded domain approach also high-order finite elements, deploying hierarchical Legendre, spectral, or B-Spline shape functions [43,69]. Initially developed for 2D and 3D linear elasticity, it was extended to various fields of applications, such as topology optimization [34,11], local enrichment for material interfaces [41], elastodynamics and wave propagation [43,22], or additive manufacturing [63]. Further investigations include efficient integration techniques [30,42], or homogenization [46].…”