Browsing by Subject "Data transfer"

In the finite element simulation of problems with contact there arises

the need to change the mesh and continue the simulation on a new mesh.

This is encountered when the mesh has to be changed because the original mesh experiences severe distortion or the mesh is adapted to minimize errors in the solution. In such instances a crucial component is the transfer of data from the old mesh to the new one.

This work proposes a strategy by which such remeshing can be accomplished in the presence of mortar-discretized contact,

focusing in particular on the remapping of contact variables which must occur to make the method robust and efficient.

By splitting the contact stress into normal and tangential components and transferring the normal component as a scalar and the tangential component by parallel transporting on the contact surface an accurate and consistent transfer scheme is obtained. Penalty and augmented Lagrangian formulations are considered. The approach is demonstrated by a number of two and three dimensional numerical examples.

This dissertation addresses interface problems simulated with the finite element method (FEM) with mesh adaptivity. More specifically, we concentrate on the strategies that adaptively modify the mesh and the associated data transfer issues.

In finite element simulations there often arises the need to change the mesh and continue the simulation on a new mesh. Analysts encounter such an issue when they adaptively refine the mesh to reduce the computational cost, smooth distorted elements to improve system conditioning, or introduce new surfaces and change the domain in simulations of fracture problems. In such circumstances, the transfer of data from the old mesh to the new one is of crucial importance, especially for nonlinear problems. We are concerned in this work with contact problems with adaptive re-meshing and fracture problems modeled with the eXtended finite element method (X-FEM). For the former ones, the transfer of surface data is built upon the technique of parallel transport, and the error of such a transfer strategy is investigated through classic benchmark tests. A transfer scheme based on a least squares problem is also proposed to transfer the bulk data when nearly incompressible hyperelastic materials are employed. For the latter type of problems, we facilitate the transfer of internal variables by making partial elements utilize the same quadrature points from the uncut parent elements and meanwhile adjusting the quadrature weights via the solution of moment fitting equations. The proposed scheme helps avoid the complicated remapping procedure of internal variables between two different sets of quadrature points. A number of numerical examples are presented to demonstrate the robustness and accuracy of our proposed approaches.

Another renowned technique to simulate fracture problems is based upon the phase-field formulation, where a set of coupled mechanics and phase-field equations are solved via FEM without modeling crack geometries. However, losing the ability to model distinct surfaces in the phase-field formulation has drawbacks, such as difficulties simulating contact on crack surfaces and poorly-conditioned stiffness matrices. On the other hand, using the pure X-FEM in fracture simulations mandates the calculation of the direction and increment of crack surfaces at each step, introducing intricacies of tracing crack evolution. Thus, we propose combining phase-field and X-FEM approaches to utilize their individual benefits based on a novel medial-axis algorithm. Consequently, we can still capture complex crack geometries while having crack surfaces explicitly modeled by modifying the mesh with the X-FEM.