1,056 research outputs found
A phase-field model for fractures in incompressible solids
Within this work, we develop a phase-field description for simulating
fractures in incompressible materials. Standard formulations are subject to
volume-locking when the solid is (nearly) incompressible. We propose an
approach that builds on a mixed form of the displacement equation with two
unknowns: a displacement field and a hydro-static pressure variable.
Corresponding function spaces have to be chosen properly. On the discrete
level, stable Taylor-Hood elements are employed for the displacement-pressure
system. Two additional variables describe the phase-field solution and the
crack irreversibility constraint. Therefore, the final system contains four
variables: displacements, pressure, phase-field, and a Lagrange multiplier. The
resulting discrete system is nonlinear and solved monolithically with a
Newton-type method. Our proposed model is demonstrated by means of several
numerical studies based on two numerical tests. First, different finite element
choices are compared in order to investigate the influence of higher-order
elements in the proposed settings. Further, numerical results including spatial
mesh refinement studies and variations in Poisson's ratio approaching the
incompressible limit, are presented
Adaptive Finite Elements for Monolithic Fluid-StructureInteraction on a Prolongated Domain: Applied to an Heart Valve Simulation
In this work, we apply a fluid-structure interaction method to a long axis heart valve simulation. Our method of choice is based on a monolithic coupling scheme for fluid-structure interaction, where the fluid equations are rewritten in the arbitrary Lagrangian Eulerian' framework. To prevent back-flow of waves in the structure due to its hyperbolic nature, a damped structure equation is solved on an artificial layer that prolongates the computational domain. This coupling is stable on the continuous level. To reduce the increased computational cost in presence of the artificial layer, we refine the mesh only regions of interest. To this end, a stationary version of goal-oriented mesh refinement is part of our numerical tests. The results show that heart valve dynamics can be simulated with our proposed model
Solving Monolithic Fluid-Structure Interaction Problems in Arbitrary Lagrangian Eulerian Coordinates with the deal.II Library
We briefly describe a setting of a non-linear fluid-structure interaction problem and its solution in the finite element software package deal.II. The fluid equations are transformed via the ALE map (Arbitrary Lagrangian Eulerian framework) to a reference configuration. The mapping is constructed using the biharmonic operator. The coupled problem is defined in a monolithic framework and serves for unsteady (or quasi-stationary) configurations. Different types of time stepping schemes are implemented. The non-linear system is solved by a Newton method. Here, the Jacobian matrix is build up by exact computation of the directional derivatives. The implementation serves for the computation of the fluid-structure benchmark configurations proposed by J. Hron and S. Turek
Sergey I. Repin, Stefan A. Sauter: “Accuracy of Mathematical Models” : EMS, 2020, 317 pp.
[no abstract available
Modeling, Discretization, Optimization, and Simulation of Multiphysics Problems (IIT Indore)
The goal of this winter school is to give an introduction to numerical modeling
of multiphysics problems. These are nonstationary, nonlinear, coupled partial
differential equations. The philosophy of this school is to
provide a mixture of very basic techniques that are immediately applied
to `complicated' practical and/or current research problems
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