Premium
Adaptive isogeometric discretizations for diffuse modeling of discontinuities
Author(s) -
Hennig Paul,
Maier Roland,
Peterseim Daniel,
Kästner Markus
Publication year - 2019
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201900421
Subject(s) - classification of discontinuities , homogenization (climate) , discretization , isogeometric analysis , polygon mesh , computer science , kinematics , compatibility (geochemistry) , interface (matter) , mathematics , finite element method , materials science , mathematical analysis , structural engineering , physics , classical mechanics , engineering , composite material , parallel computing , biodiversity , ecology , computer graphics (images) , bubble , maximum bubble pressure method , biology
In this contribution, we discuss the modeling of discontinuities using non‐conforming meshes. For weak discontinuities we propose to regularize the sharp material interface over a characteristic length scale. To define the material properties in the transition region, homogenization assumptions are used that fulfill the kinematic compatibility across the interface and the static equilibrium at the interface. For strong discontinuities we use a phase‐field model that is able to account for failure of adhesive interfaces and extend it to general heterogeneous materials. To improve the efficiency of the approach, adaptive isogeometric analysis is used to discretize the computational domain.