An isogeometric analysis Bézier interface element for mechanical and poromechanical fracture problems

Abstract

SUMMARYInterface elements are a powerful tool for modelling discontinuities. Herein, we develop an interface element that is based on the isogeometric analysis concept. Through Bézier extraction the novel interface element can be cast in the same format as conventional interface elements. Consequently, the isogeometric interface element can be implemented in a straightforward manner in existing finite element software by a mere redefinition of the shape functions. The interface elements share the advantages of isogeometric continuum elements in that they can exactly model the geometry. On the other hand, they inherit the simplicity of conventional interface elements, but also some deficiencies, like the occurrence of traction oscillations when a high interface stiffness is used. The extension towards poroelasticity is rather straightforward, and in this situation the smoother flow profiles and the ensuing preservation of local mass balance are additional advantages. These are demonstrated at the hand of some example problems.

Image-based goal-oriented adaptive isogeometric analysis with application to the micro-mechanical modeling of trabecular bone

“…Finite element data structures have been developed to facilitate the implementation of the isogeometric analysis paradigm in existing finite element codes, see e.g. [5][6][7].…”

Isogeometric analysis of fluid‐saturated porous media including flow in the cracks

“…[34,35] for details to build the jump operator M u ), while N p contains the shape functions related to the interpolation of the pressure field. From Equation (17a), the strains in the body can be derived by standard differentiation of the isogeometric shape functions so that…”

“…We note that, because in the present contribution we are only considering stationary discontinuities, we can exploit isogeometric interface elements. However, as noticed in [34], such interface elements can suffer from traction oscillations. An indepth analysis has been made in [35] for the purely mechanical case, which will herein be extended to poromechanics.…”

A classification of poromechanical interface elements

“…Likewise, it is naturally embedded in interface elements with a double pressure node because of the −1 continuity in the pressure field at the interface [19,20]. It is finally noted that (pressurecontinuous) poroelastic interface elements have also been developed within the context of isogeometric analysis [22], including the possibility of fluid flow and storage in the discontinuity [23].…”