The finite element method (FEM) is a well established tool for solving a wide range of different engineering problems. However in recent years different methods like the virtual element method (VEM) were introduced as tools that brings some new features to the numerical solution of problems in solid and fluid mechanics.
The virtual element method is a competitive discretization scheme for meshes with highly irregular shaped elements and arbitrary number of nodes. VEM can use convex and non-convex polygons/polyhedra to mesh both two and three-dimensional solids. In VEM, the potential density is formulated in terms of suitable polynomial functions, instead of computing the unknown shape functions for complicated element geometries. This results in a rank-deficient structure, therefore it is necessary to add a stabilization term to the formulation. Herein, a robust stabilization technique for VEM will be introduced.
At IKM, latest developments related to the virtual element scheme will be investigated using the software tool AceGen program in the numerical implementation to compute the unknown fields. Of particular interest are problems related to contact mechanics, finite strain elasto-plasticity, thermo-mechanics, crack initiation and propagation and phase-field modeling of brittle and ductile fracture.
Virtual Elements For Engineering Appications
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Virtual Element Method for 3D ContactContact plays a very important role in engineering problems, where two or more bodies interact with each other through their surfaces. Many techniques were developed in the past, to formulate the contact constraint at the contact interface between two bodies. Nevertheless, VEM provides efficient and robust properties to enforce the contact constraint through the contact interface. Investigations in 2D have been done so far. This work aims an extensions of VEM to 3D contact problems.Leitung: F. Aldakheel, B. Hudobivnik, P. WriggersTeam:Jahr: 2020
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Virtual Element Method for Dynamic ApplicationsThe Virtual Element Method is a recent developed discretization method, which can be seen as an extension of the classical Galerkin finite element method. It has been applied to various engineering fields, such as elasto-plasticity, multiphysics, damage and fracture mechanics. This project focuses on the extension of VEM towards dynamic applications. In the first part the appropriate computation of the Massmatrix regarding the vitual element ansatzspace will be done. In future works, VEM will be applied to engineering problems, considering the dynamic behavior.Leitung: F. Aldakheel, B. Hudobivnik, P. WriggersTeam:Jahr: 2019
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2D VEM for crack-propagationLeitung: F. Aldakheel, B. Hudobivnik, P. WriggersTeam:Jahr: 2018Förderung: IRTG 1627
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Virtual element method (VEM) for phase-field modeling of brittle and ductile fractureLeitung: F. Aldakheel, B. Hudobivnik, P. WriggersJahr: 2018Förderung: DFG SPP 1748
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PROJECT COORDINATORS
30823 Garbsen
30823 Garbsen
30823 Garbsen
