A diffuse modeling approach for embedded interfaces in linear elasticity

DOI10.1002/gamm.202000001OpenAlexW2969468574MaRDI QIDQ6067378

Daniel Peterseim, Dominik Schillinger, Paul Hennig, Markus Kästner, Roland Maier, Barbara Verfürth

Publication date: 14 December 2023

Published in: GAMM-Mitteilungen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/gamm.202000001

zbMATH Keywords

homogenizationlocal refinementisogeometric analysisdiffuse interface representationembedded interface problems

Mathematics Subject Classification ID

Mechanics of deformable solids (74-XX) Numerical and other methods in solid mechanics (74Sxx) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx)

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Cites Work

• Unnamed Item
• The finite cell method: a review in the context of higher-order structural analysis of CAD and image-based geometric models
• An isogeometric design-through-analysis methodology based on adaptive hierarchical refinement of NURBS, immersed boundary methods, and T-spline CAD surfaces
• The finite cell method for linear thermoelasticity
• Local enrichment of the finite cell method for problems with material interfaces
• THB-splines: The truncated basis for hierarchical splines
• Weak coupling for isogeometric analysis of non-matching and trimmed multi-patch geometries
• An unfitted hp-adaptive finite element method based on hierarchical B-splines for interface problems of complex geometry
• Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement
• A novel homogenization method for phase field approaches based on partial rank-one relaxation
• The finite cell method for three-dimensional problems of solid mechanics
• Finite cell method. \(h\)- and \(p\)-extension for embedded domain problems in solid mechanics
• Solving PDEs in complex geometries: a diffuse domain approach
• Complexity of hierarchical refinement for a class of admissible mesh configurations
• An unfitted finite element method, based on Nitsche's method, for elliptic interface problems.
• Variationally consistent isogeometric analysis of trimmed thin shells at finite deformations, based on the STEP exchange format
• Phase-field modelling of interface failure in brittle materials
• The non-symmetric Nitsche method for the parameter-free imposition of weak boundary and coupling conditions in immersed finite elements
• Adaptive mesh refinement strategies in isogeometric analysis -- a computational comparison
• A diffuse interface method for the Navier-Stokes/Darcy equations: perfusion profile for a patient-specific human liver based on MRI scans
• A multiscale method for linear elasticity reducing Poisson locking
• The multi-level \(hp\)-method for three-dimensional problems: dynamically changing high-order mesh refinement with arbitrary hanging nodes
• Projection and transfer operators in adaptive isogeometric analysis with hierarchical B-splines
• Phase-field elasticity model based on mechanical jump conditions
• On the stability of the Rayleigh-Ritz method for eigenvalues
• Analysis-suitable adaptive T-mesh refinement with linear complexity
• Bézier extraction and adaptive refinement of truncated hierarchical NURBS
• Multi phase field model for solid state transformation with elastic strain
• Combining phase field approach and homogenization methods for modelling phase transformation in elastoplastic media
• Isogeometric finite element data structures based on Bézier extraction of NURBS
• The hp-d -adaptive finite cell method for geometrically nonlinear problems of solid mechanics
• Higher-order extended FEM for weak discontinuities - level set representation, quadrature and application to magneto-mechanical problems
• Numerical analysis of Lamb waves using the finite and spectral cell methods
• CutFEM: Discretizing geometry and partial differential equations
• The extended/generalized finite element method: An overview of the method and its applications
• Imposing Dirichlet boundary conditions with Nitsche's method and spline-based finite elements
• Localization of elliptic multiscale problems
• Composite finite elements for elliptic interface problems
• p-convergent finite element approximations in fracture mechanics
• Finite Elements for Elliptic Problems with Highly Varying, Nonperiodic Diffusion Matrix
• Modeling wave propagation in realistic heart geometries using the phase-field method
• Globally Structured Three-Dimensional Analysis-Suitable T-Splines: Definition, Linear Independence and $m$-graded local refinement
• Modeling holes and inclusions by level sets in the extended finite element method

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