Space-time adaptive ALM simulation

 

 

Manufacturing the Yorkshire Pudding

Simulation of additive layer manufacturing by direct energy deposition using CutFEM

 

 

S. Claus, S. Bigot and P. Kerfriden, CutFEM Method for Stefan--Signorini Problems with Application in Pulsed Laser Ablation, SIAM J. Sci. Comput., 40(5), 2018
 

https://doi.org/10.1137/18M1185697

Additive Layer Manufacturing simulations (metal deposition) with CutFEM

CutFEM: 1D fibrous reinforcements embedded in 3D structures

P Kerfriden, S Claus, I Mihai, A mixed-dimensional CutFEM methodology for the simulation of fibre-reinforced composites, Advanced Modeling and Simulation in Engineering Science, 2020 

 

 

We develop a novel unfitted finite element solver for composite materials with quasi-1D fibrous reinforcements. The method belongs to the class of mixed-dimensional non-conforming finite element solvers. The fibres are treated as 1D structural elements that may intersect the mesh of the embedding structure in an arbitrary manner. No meshing of the unidimensional elements is required. Instead, fibre solution fields are described using the trace of the background mesh. A regularised “cut” finite element formulation is carefully designed to ensure that analyses using such non-conforming finite element descriptions are stable. We also design a dedicated primal/dual operator splitting scheme to resolve the coupling between structure and fibrous reinforcements efficiently. The novel computational strategy is applied to the solution of stiff computational models whereby fibrous reinforcements may lose their bond to the embedding material above a certain level of stress. It is shown that the primal-dual 1D/3D CutFEM scheme is convergent and well-behaved in variety of scenarios involving such highly nonlinear structural computations.

CutFEM method to simulate composite fracture

Phase-field in the bulk, zero-thickness cohesive elements with friction contact at the matrix/inclusions interface

Laser ablation: micro-cavity

We have developed a cut finite element method for one-phase Stefan problems, with applications in laser manufacturing. The geometry of the workpiece is represented implicitly via a level set function. Material above the melting/vaporisation temperature is represented by a fictitious gas phase. The moving interface between the workpiece and the fictitious gas phase may cut arbitrarily through the elements of the finite element mesh, which remains fixed throughout the simulation, thereby circumventing the need for cumbersome remeshing operations. The primal/dual formulation of the linear one-phase Stefan problem is recast into a primal non-linear formulation using a Nitsche-type approach, which avoids the difficulty of constructing inf-sup stable primal/dual pairs. Through the careful derivation of stabilisation terms, we show that the proposed Stefan-Signorini-Nitsche CutFEM method remains stable independently of the cut location. In addition, we obtain optimal convergence with respect to space and time refinement. Several 2D and 3D examples are proposed, highlighting the robustness and flexibility of the algorithm, together with its relevance to the field of micro-manufacturing.

 

Simulations by S. Claus, S. Bigot and P. Kerfriden in the FEniCS library CutFEM.

S. Claus, S. Bigot and P. Kerfriden, CutFEM Method for Stefan--Signorini Problems with Application in Pulsed Laser Ablation, SIAM J. Sci. Comput., 40(5), 2018
Funding: Sêr Cymru National Research Network

Eddy, Cardiff sliding Dinosaur

Eddy is held by the tails and gravity acts in direction [1 -1] in the plane of the picture. The dinosaur will either slip or stumble forward depending on the roughness of the contact between its feet and the support.

Eddy is not meshed. Instead, the .stl file that describes its boundary is converted into a continuous level-set, whose negative values indicate eddies spatial occupancy. The zero isoline can cut arbitrarily through the elements.

The simulations were performed using the CutFEM FEniCS library.
 
S. Claus & P. Kerfriden, A stable and optimally convergent LaTIn-Cut Finite Element Method for multiple unilateral contact problems, IJNME, 2017
https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.5694

Burman, E., Claus, S., Hansbo, P., Larson, M. G., and Massing, A. (2015) CutFEM: Discretizing geometry and partial differential equations. Int. J. Numer. Meth. Engng, 104: 472–501. doi: 10.1002/nme.4823.

The 3D dinosaur model was created by ThinkerThing: http://www.thingiverse.com/thing:343924

Thermal ablation simulation over a fixed background mesh

Quasi-static simulation of a thermal ablation manufacturing process by pulse laser using the CutFEM technology. Modelling and simulation by Dr Claus & Dr Kerfriden in collaboration with Dr Bigot

Dynamics of shells over background meshes

Preliminary result from the work of Susanne Claus and Pierre Kerfriden.

The shell intersects a regular background mesh in an arbitrary manner, thereby avoiding the need for complex meshing operations. To alleviate the well-known problem of instability due to the existence of "bad cuts", we make use of a regularised penalty approach. The implementation is performed within the FEniCS CutFEM library developed by Dr Claus together with André Massing and Erik Burman.

Harmonic Dirichlet boundary conditions

Free vibration modes

Multiple crack propagation with XFEM

Work of Dr Sutula, P. Kerfriden and S. Bordas, in collaboration with Soitec. 

 

D Sutula, P Kerfriden, T van Dam, SPA Bordas, Minimum energy multiple crack propagation. Part I: Theory and state of the art review, Engineering Fracture Mechanics 191, 205-224, 2018

D Sutula, P Kerfriden, T van Dam, SPA Bordas, Minimum energy multiple crack propagation. Part-II: Discrete solution with XFEM, Engineering Fracture Mechanics 191, 225-256, 2018