Weakly Enforced Boundary Conditions for the NURBS-Based Finite Cell Method

In this paper, we present a variationally consistent formulation for the weak enforcement of essential boundary conditions as an extension to the finite cell method, a fictitious domain method of higher order. The absence of boundary fitted elements in fictitious domain or immersed boundary methods significantly restricts a strong enforcement of essential boundary conditions to models where the boundary of the solution domain coincides with the embedding analysis domain. Penalty methods and Lagrange multiplier methods are adequate means to overcome this limitation but often suffer from various drawbacks with severe consequences for a stable and accurate solution of the governing system of equations. In this contribution, we follow the idea of NITSCHE [29] who developed a stable scheme for the solution of the Laplace problem taking weak boundary conditions into account. An extension to problems from linear elasticity shows an appropriate behavior with regard to numerical stability, accuracy and an adequate convergence behavior. NURBS are chosen as a high-order approximation basis to benefit from their smoothness and flexibility in the process of uniform model refinement

Strip yield modelling of fatigue crack under variable amplitude loading

The results from 'strip yield' approach of the FASTRAN type models of plasticity induced crack closure effects of fatigue cracks subjected to variable amplitude loadings are presented. The strip yield results are compared with authors' finite element (FE) and experimental results. It has been observed that the strip yield model is seen to be fundamentally limited by choice of alpha (constraint factor) and corresponding to treat baseline closure effects. Double overload closure behavior is functionally similar for both strip yield and FE models. Under multiple overloads, an important functional difference is seen between FE and strip yield models. This has been linked to the absence of in-plane constraint in the strip yield model, which is seen to have a distinct decreasing influence on on-going closure effects.Peer reviewedFinal Accepted Versio

A CutFEM method for two-phase flow problems

In this article, we present a cut finite element method for two-phase Navier-Stokes flows. The main feature of the method is the formulation of a unified continuous interior penalty stabilisation approach for, on the one hand, stabilising advection and the pressure-velocity coupling and, on the other hand, stabilising the cut region. The accuracy of the algorithm is enhanced by the development of extended fictitious domains to guarantee a well defined velocity from previous time steps in the current geometry. Finally, the robustness of the moving-interface algorithm is further improved by the introduction of a curvature smoothing technique that reduces spurious velocities. The algorithm is shown to perform remarkably well for low capillary number flows, and is a first step towards flexible and robust CutFEM algorithms for the simulation of microfluidic devices