A regularized XFEM model for the transition from continuous to discontinuous displacements

This work focuses on the modelling through the extended finite element method of structural problems characterized by discontinuous displacement. As a model problem, an elastic isotropic domain characterized by a displacement discontinuity across a surface is studied. A regularization of the displac...

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Bibliographic Details
Published in:International journal for numerical methods in engineering 2008-05, Vol.74 (6), p.911-944
Main Authors: Benvenuti, E., Tralli, A., Ventura, G.
Format: Article
Language:English
Subjects:
Computational techniques
discontinuous displacement
Exact sciences and technology
extended finite element method
Fundamental areas of phenomenology (including applications)
Mathematical methods in physics
numerical quadrature
Physics
Solid mechanics
Static elasticity (thermoelasticity...)
Structural and continuum mechanics
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Summary:This work focuses on the modelling through the extended finite element method of structural problems characterized by discontinuous displacement. As a model problem, an elastic isotropic domain characterized by a displacement discontinuity across a surface is studied. A regularization of the displacement field is introduced depending on a scalar parameter. The regularized solution is defined in a layer. The emerging strain and stress fields are independently modelled using specific constitutive assumptions. In particular, it is shown that the mechanical work spent within the regularization layer can be interpreted as an interface work provided that a spring‐like constitutive law is adopted. The accuracy of the integration procedures adopted for the stiffness matrix is assessed, as highly non‐linear terms appear. Standard Gauss quadrature is compared with adaptive quadrature and with a new technique, based on an equivalent polynomial approach. One‐ and two‐dimensional results are reported for varying discretization size, regularization parameter, and constitutive parameters. Copyright © 2007 John Wiley & Sons, Ltd.
ISSN:0029-5981
1097-0207
DOI:10.1002/nme.2196