Benchmark Collection SPP 1748:

J. Schröder, T. Wick, S. Reese, P. Wriggers, R. Müller, S.
Kollmannsberger, M. Kästner, A. Schwarz, M. Igelbüscher, N. Viebahn, H.
R. Bayat, S. Wulfinghoff, K. Mang, E. Rank, T. Bog, D. d'Angella, M.
Elhaddad, P. Hennig, A. Düster, W. Garhuom, S. Hubrich, M. Walloth, W.
Wollner, Ch. Kuhn, T. Heister;
A selection of benchmark problems in solid mechanics and applied mathematics,
Archives of Computational Methods in Engineering (ARCO), Aug 2020, accepted

Hybrid discretizations in solid mechanics for non-linear and non-smooth problems

2020:

H. R. Bayat, S. Rezaei, A. Rajaei Harandi, T. Brepols, S. Reese,
About the influence of neglecting locking effects on the failure behavior at the interface.
PAMM, Submitted June 26, 2020, 2020.

H. R. Bayat,
other contributors: S. Reese, S. Wulfinghoff, L. Noels.
Failure modeling of interfaces and sheet metals.
Rheinisch-Westfälische Technische Hochschule Aachen, Dissertation, Aachen, 2020.

H. R. Bayat, S. Rezaei, T. Brepols, S. Reese.
Locking-free interface failure modeling by a cohesive discontinuous Galerkin method for matching and nonmatching meshes.
International Journal for Numerical Methods in Engineering, Vol. 121, No. 8, pages 1762–1790, 2020.

U. Khristenko, A. Constantinescu, P. L. Tallec, J T. Oden, B. Wohlmuth.
A statistical framework for generating microstructures of two-phase random materials: application to fatigue analysis.
Multiscale Modeling & Simulation, Vol. 18, No. 1, pages 21–43, 2020.

M. Dittmann, S. Schuß, B. Wohlmuth, C. Hesch.
Crosspoint modification for multi-patch isogeometric analysis.
Computer Methods in Applied Mechanics and Engineering, Vol. 360, pages 112768, 2020.

2019:

S. Schuß, M. Dittmann, B. Wohlmuth, S. Klinkel, C. Hesch.
Multi-patch isogeometric analysis for Kirchhoff–Love shell elements.
Computer Methods in Applied Mechanics and Engineering, Vol. 349, pages 91–116, 2019.

M. Dittmann, S. Schuß, B. Wohlmuth, C. Hesch.
Weak C^n coupling for multipatch isogeometric analysis in solid mechanics.
International Journal for Numerical Methods in Engineering, Vol. 118, No. 11, pages 678–699, 2019.

L. Wunderlich, A. Seitz, M. D. Alaydin, B. Wohlmuth, A. Popp.
Biorthogonal splines for optimal weak patch-coupling in isogeometric analysis with applications to finite deformation elasticity.
Computer Methods in Applied Mechanics and Engineering, Vol. 346, pages 197–215, 2019.

T. Horger, A. Reali, B. Wohlmuth, L. Wunderlich.
A hybrid isogeometric approach on multi-patches with applications to Kirchhoff plates and eigenvalue problems.
Computer Methods in Applied Mechanics and Engineering, Vol. 348, pages 396–408, 2019.

2018:

A. Alipour, S. Wulfinghoff, H. R. Bayat, S. Reese, B. Svendsen.
The concept of control points in hybrid discontinuous Galerkin methods—Application to geometrically nonlinear crystal plasticity.
International Journal for Numerical Methods in Engineering, Vol. 114, No. 5, pages 557–579, 2018.

2017:

A. Alipour, S. Wulfinghoff, B. Svendsen, S. Reese.
Geometrically nonlinear single crystal viscoplasticity implemented into a hybrid discontinuous Galerkin framework.
Proceedings of the 7th GACM Colloquium on Computational Mechanics, 2017.

A. Alipour, S. Wulfinghoff, H. R. Bayat, S. Reese.
Geometrically nonlinear crystal plasticity implemented into a discontinuous Galerkin element formulation.
PAMM, Vol. 17, No. 1, pages 753–754, 2017.

Structure Preserving Adaptive Enriched Galerkin Methods for Pressure-Driven 3D Fracture Phase-Field Models

2020:

Wick, T. Multiphysics Phase-Field Fracture. Berlin, Boston: De Gruyter. 2020. doi: https://doi.org/10.1515/9783110497397

S. Basava, K. Mang, M. Walloth, T. Wick, W. Wollner.
Adaptive and Pressure-Robust Discretization of Incompressible Pressure-Driven Phase-Field Fracture.
arXiv, Preprint, 2020.

K. Mang, M. Walloth, T. Wick, W. Wollner.
Adaptive Numerical Simulation of a Phase-field Fracture Model in Mixed Form tested on an L-shaped Specimen with High Poisson Ratios.
arXiv, Preprint, 2020.

K. Mang, T. Wick, W. Wollner.
A Phase-Field Model for Fractures in Incompressible Solids.
Comput. Mech., Vol. 65, No. 1, pages 61–78, 2020.

M. F. Wheeler, T. Wick, S. Lee.
IPACS: Integrated Phase-Field Advanced Crack Propagation Simulator. An adaptive, parallel, physics-based-discretization phase-field framework for fracture propagation in porous media.
Computer Methods in Applied Mechanics and Engineering, Vol. 367, pages 113124, 2020.

M. Kirkesaether Brun, T. Wick, I. Berre, J. M. Nordbotten, F. A. Radu.
An iterative staggered scheme for phase field brittle fracture propagation with stabilizing parameters.
Computer Methods in Applied Mechanics and Engineering, Vol. 361, pages 112752, 2020.

F. Aldakheel, N. Noii, T. Wick, P. Wriggers.
A global-local approach for hydraulic phase-field fracture in poroelastic media.
arXiv, 2020.

2019:

K. Mang, M. Walloth, T. Wick, W. Wollner.
Mesh adaptivity for quasi-static phase-field fractures based on a residual-type a posteriori error estimator.
GAMM Mitteilungen, Early-Access, Vol. 43, No. 1, 2019.

A. Mikelić, M. F. Wheeler, T. Wick.
Phase-field modeling through iterative splitting of hydraulic fractures in a poroelastic medium.
GEM - International Journal on Geomathematics, Vol. 10, No. 1, 20 Jan 2019.

N. Noii, F. Aldakheel, T. Wick, P. Wriggers.
An adaptive global-local approach for phase-field modeling of anisotropic brittle fracture.
Computer Methods in Applied Mechanics and Engineering, pages 112744, 2019.

M. Fan, Y. Jin, T. Wick.
A phase-field model for mixed-mode fracture.
Hannover : Institutionelles Repositorium der Leibniz Universität Hannover, 40 S., 2019.

N. Noii, T. Wick.
A phase-field description for pressurized and non-isothermal propagating fractures.
Computer Methods in Applied Mechanics and Engineering, Vol. 351, pages 860–890, 2019.

Ch. Engwer, S. I. Pop, T. Wick.
Dynamic and weighted stabilizations of the L-scheme applied to a phase-field model for fracture propagation.
arXiv, 2019.

2018:

M. Walloth.
Residual-type A Posteriori Estimators for a Singularly Perturbed Reaction-Diffusion Variational Inequality – Reliability, Efficiency and Robustness.
arXiv, 2018.

T. Heister, T. Wick.
Parallel solution, adaptivity, computational convergence, and open-source code of 2d and 3d pressurized phase-field fracture problems.
PAMM, Vol. 18, No. 1, 2018.

Robust and Efficient Finite Element Discretizations for Higher-Order Gradient Formulations

2020:

J. Riesselmann and J. Ketteler and M. Schedensack and D. Balzani,
Rot-free finite elements for gradient-enhanced formulations at finite strains,
PAMM Proc. Appl. Math. Mech., V. Bach and H. Fassbender, 2020, Submitted for publication.

J. Riesselmann, J. Ketteler, M. Schedensack, D. Balzani.
Rot-free mixed finite elements for gradient elasticity at finite strains.
2020. Submitted.

D. Gallistl, M. Schedensack.
A Robust Discretization of the Reissner-Mindlin Plate with Arbitrary Polynomial Degree.
J. Comput. Math., Vol. 38, pages 1–13, 2020.

2019:

Riesselmann, J. and Ketteler, J.W. and Schedensack, M. and Balzani, D.
C0 continuous finite elements for gradient elasticity at finite strains,
Proc. of 8th GACM Colloq. on Comp. Mech., pages 27-30, 2019.

J. Riesselmann, J. Ketteler, M. Schedensack, D. Balzani.
Three-field mixed finite element formulations for gradient elasticity at finite strains.
GAMM-Mitteilungen, 2019.

D. Gallistl., M. Schedensack.
Taylor–Hood discretization of the Reissner–Mindlin plate.
Submitted for publication

J. Hu, M. Schedensack.
Two low-order nonconforming finite element methods for the Stokes flow in 3D.
IMA J. Numer. Anal., Vol. 39, No. 3, pages 1447–1470, 2019.

J. Riesselmann, J. Ketteler, M. Schedensack, D. Balzani.
A New C0-Continuous FE-Formulation for Finite Gradient Elasticity.
PAMM Proc. Appl. Math. Mech., editors: V. Bach and H. Fassbender, Vol. 19, No. 1, 2019.

J. Riesselmann, J. Ketteler. M. Schedensack, D. Balzani.
Rot-free finite elements for gradient-enhanced formulations at finite strains.
PAMM Proc. Appl. Math. Mech., editors: V. Bach and H. Fassbender, 2019.
Submitted for publication.

Adaptive isogeometric modeling of propagating strong discontinuities in heterogeneous materials

2020:

A. Caiazzo, and R. Maier, and D. Peterseim,
Reconstruction of quasi-local numerical effective models from low-resolution measurements,
J. Sci. Comput., 2020.

R. Maier,
A high-order approach to elliptic multiscale problems with general unstructured coefficients,
ArXiv Preprint, 2009.01226, 2020.

P. Henning, D. Peterseim.
Sobolev gradient flow for the Gross-Pitaevskii eigenvalue problem: global convergence and computational efficiency.
SIAM Journal on Numerical Analysis, Vol. 58, No. 3, pages 1744-1772, 2020.

R. Altmann, P. Henning, D. Peterseim.
Quantitative Anderson localization of Schrödinger eigenstates under disorder potentials.
M3AS Math. Mod. Meth. Appl. S., Mathematical Models & Methods in Applied Sciences, Vol. 30, No. 5, pages 917-955, 2020.

R. Maier.
Computational Multiscale Methods in Unstructured Heterogeneous Media.
University of Augsburg, 2020.

2019:

P. Hennig, R. Maier, D. Peterseim, D. Schillinger, B. Verfürth, M. Kästner.
A diffuse modeling approach for embedded interfaces in linear elasticity.
GAMM-Mitteilungen, pages 1-16, 2019.

R. Maier, D. Peterseim.
Explicit computational wave propagation in micro-heterogeneous media.
BIT Numerical Mathematics, Vol. 59, No. 2, pages 443-462, 2019.

A. C. Hansen-Dörr, F. Damma, R. de Borst, M. Kästner.
Phase-Field Modeling of Crack Branching and Deflection in Heterogeneous Media.
ArXiv e-prints, Vol. 1910.08277, 2019.

A. C. Hansen-Dörr, R. de Borst, P. Hennig, M. Kästner.
Phase-field modelling of interface failure in brittle materials.
Computer Methods in Applied Mechanics and Engineering, Vol. 346, pages 25-42, 2019.

C. J. Paulus, R. Maier, D. Peterseim, S. Cotin.
An Immersed Boundary Method for Detail-Preserving Soft Tissue Simulation from Medical Images.
Computational Biomechanics for Medicine, MICCAI 2017, pages 55-67, Springer, Cham, 2019.

2018:

R. Maier, D. Peterseim.
Fast time-explicit micro-heterogeneous wave propagation.
Proceedings in Applied Mathematics and Mechanics, Vol. 18, No. 1, pages 1-2, 2018.

P. Hennig, M. Ambati, L. De Lorenzis, M. Kästner.
Projection and transfer operators in adaptive isogeometric analysis with hierarchical B-splines.
Computer Methods in Applied Mechanics and Engineering, Vol. 334, pages 313-336, 2018.

2017:

D. Peterseim, M. Schedensack.
Relaxing the CFL condition for the wave equation on adaptive meshes.
Journal of Scientific Computing, Vol. 72, No. 3, pages 1196-1213, 2017.

D. Gallistl, P. Huber, D. Peterseim.
On the stability of Raleigh- Ritz method for eigenvalues.
Numerische Mathematik, pages 1–13, 2017.

P. Morgenstern.
Mesh Refinement Strategies for the Adaptive Isogeometric Method. PhD thesis.
Rheinische Friedrich-Wilhelms-Universität Bonn, 2017.

T. Linse, P. Hennig, M. Kästner, R. De Borst.
An analysis of convergence in phase-field models for brittle fracture.
submitted to: International Journal of Solids and Structures, 2017.

A. C. Hansen-Dörr, P. Hennig, M. Kästner, K. Weinberg.
A numerical analysis of the fracture toughness in phase-field modelling of adhesive fracture.
submitted to: Proceedings in Applied Mathematics and Mechanics.

P. Hennig , M. Kästner, P. Morgenstern, D. Peterseim.
Adaptive mesh refinement strategies in isogeometric analysis – A computational comparison.
Computer Methods in Applied Mechanics and Engineering, Vol. 316, pages 424-448, 2017.

D. Gallistl, D. Peterseim.
Computation of local and quasi-local effective diffusion tensors and connections to the mathematical theory of homogenization.
SIAM Multiscale Modeling & Simulation, Vol. 15, No. 4, pages 1530-1552, 2017.

T. Linse, P. Hennig, M. Kästner, R. de Borst.
A convergence study of phase-field models for brittle fracture.
Engineering Fracture Mechanics, Vol. 184, pages 307-318, 2017.

A. Målqvist, D. Peterseim.
Generalized finite element methods for quadratic eigenvalue problems.
ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 51, No. 1, pages 147-163, 2017.

P. Henning, D. Peterseim.
Crank-Nicolson Galerkin approximations to nonlinear Schrödinger equations with rough potentials.
M3AS Mathematical Models & Methods in Applied Sciences, Vol. 27, No. 11, pages 2147-2184, 2017.

2016:

D. Gallistl, D. Peterseim, C. Carstensen.
Multiscale petrov-galerkin fem for acoustic scattering.
Proceedings in Applied Mathematics an Mechanics, 2016.

P. Hennig, M. Kästner, P. Morgenstern, D. Peterseim.
Adaptive Mesh Refinement Strategies in Isogeometric Analysis - A Computational Comparison. Computer Methods in Applied Mechanics and Engineering, 2016.

P. Morgenstern.
Globally structured three-dimensional analysis-suitable t- splines: Definition, linear independence and m-graded local refinement.
SIAM Journal on Numerical Analysis, 2016.

M. Kästner, P. Hennig, T. Linse, V. Ulbricht.
Phase-field modelling of damage and fracture – convergence and local mesh refinement.
In: K. Naumenko and M. Assmus (Eds.), Advanced Methods of Continuum Mechanics for Materials and Structures, 2016.

D. Peterseim.
Variational Multiscale Stabilization and the Exponential Decay of Fine-scale Correctors.
In: G.R. Barrenechea, F. Brezzi, A. Cangiani, E.H. Georgoulis (Eds.), Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations, 2016.

P. Hennig, S. Müller, M. Kästner.
Bézier extraction and adaptive refinement of truncated hierarchical NURBS.
Computer Methods in Applied Mechanics and Engineering, 2016.

P. Bringmann, C. Carstensen, D. Gallistl, F. Hellwig, D. Peterseim, S. Puttkammer, H. Rabus, J. Storn.
Towards adaptive discontinuous Petrov-Galerkin methods.
PAMM, Proceedings in Applied Mathematics and Mechanics, Vol. 16, No. 1, pages 741-742, 2016.

A. Buffa, C. Giannelli, P. Morgenstern, D. Peterseim.
Complexity of hierarchical refinement for a class of admissible mesh configurations.
Computer Aided Geometric Design, Vol. 47, pages 83-92, 2016.

D. Gallistl, D. Peterseim, C. Carstensen.
Multiscale Petrov-Galerkin FEM for Acoustic Scattering.
Proceedings in Applied Mathematics and Mechanics, Vol. 16, No. 1, pages 745-746, 2016.

P. Hennig, S. Müller, M. Kästner.
Bézier extraction and adaptive refinement of truncated hierarchical NURBS.
Computer Methods in Applied Mechanics and Engineering, Vol. 305, pages 316–339, 2016.

M. Kästner, P. Hennig, T. Linse, V. Ulbricht.
Phase-Field Modelling of Damage and Fracture–Convergence and Local Mesh Refinement.
Advanced Methods of Continuum Mechanics for Materials and Structures, Springer Singapore, pages 307–324, 2016.

M. Kästner, P. Metsch, R. de Borst.
Isogeometric analysis of the Cahn-Hilliard equation - a convergence study.
Journal of Computational Physics, Vol. 305, pages 360–371, 2016.

2015:

C. Carstensen, D. Peterseim, A. Schröder.
The Norm of a Discretized Gradient in H(div)* for A Posteriori Finite Element Error Analysis.
Numerische Mathematik, Vol. 132, No. 3, pages 519–539, 2015.

P. Morgenstern, D. Peterseim.
Analysis-suitable adaptive T-mesh refinement with linear complexity.
Computer Aided Geometric Design, Vol. 34, pages 50–66, 2015.

Finite element approximation of functions of bounded variation and application to models of damage, fracture and plasticity

2020:

S. Bartels and M. Milicevic and M. Thomas and N. Weber,
Fully discrete approximation of rate-independent damage models with gradient regularization,
WIAS-Preprint 2707, 2020, 10.20347/WIAS.PREPRINT.2707

Bartels, S. and Milicevic, M.,
Efficient iterative solution of finite element discretized nonsmooth minimization problems,
Comput. Math. Appl., Vol. 80:5, 588-603, 2020

Bartels, S. and Milicevic, M.,
Primal-dual gap estimators for a posteriori error analysis of nonsmooth minimization problems,
ESAIM: M2AN, 54 5 (2020) 1635-1660, DOI: https://doi.org/10.1051/m2an/2019074

S. Bartels,
Nonconforming discretizations of convex minimization problems and precise relations to mixed methods,
2020, arXiv:2002.02359, Numerical Analysis (math.NA)

R. Rossi and U. Stefanelli and M. Thomas,
Rate-independent evolution of sets,
Duscrete and Continuous Dynamical Systems Ser. S, published online 2020

2018:

R. Rossi and M. Thomas,
From nonlinear to linear elasticity in a coupled rate-dependent/independent system for brittle delamination,
Proceedings of the INdAM-ISIMM Workshop on Trends on Applications of Mathematics to Mechanics, Rome, Italy, September 2016, Editor: E. Rocca and U. Stefanelli and L. Truskinovsky and A. Visintin, Springer INdAM Series, Vol. 27, Springer International Publishing, Cham., 2018, 127-157, 10.1007/978-3-319-75940-1_7

Bartels, S. and Milicevic, M. and Thomas, M.,
Numerical approach to a model for quasistatic damage with spatial BV-regularization,
Trends in applications of mathematics to mechanics, Springer INdAM Ser., Vol. 27, 179--203, Springer, Cham., 2018

2017:

M. Thomas,
A comparison of delamination models: Modeling, properties, and applications,
Mathematical Analysis of Continuum Mechanics and Industrial Applications II, Proceedings of the International Conference CoMFoS16, Editor: P. van Meurs and M. Kimura and H. Notsu, Mathematics for Industry, Vol. 30, 27-38, Springer, Singapore, 2017

R. Rossi and M. Thomas,
From adhesive to brittle delamination in visco-elastodynamics,
Math. Models Methods Appl. Sci., Vol. 27, 1489-1546, 2017

 R. Rossi and M. Thomas
Coupling rate-independent and rate-dependent processes: Existence results 
SIAM Journal on Mathematical Analysis 2017 49:2, 1419-1494

R. Rossi, M. Thomas.
From nonlinear to linear elasticity in a coupled rate-dependent/rate-independent system for brittle
delamination.
Accepted in INDAM-Springer series: Symposium on Trends in Applications of Mathematics to Mechanics, 2017.

S. Bartels, M. Milicevic.
Alternating direction method of multipliers with variable step sizes.
Preprint, 2017

S. Bartels, M. Milicevic, M. Thomas.
Numerical approach to a model for quasistatic damage with spatial BV-regularization.
Preprint, 2017.

M. Thomas and C. Zanini,
Cohesive zone-type delamination in visco-elasticity,
Discr. Contin. Dyn. Syst. Ser. S, Vol. 10, 1487-1517, 2017
 

2016:

S. Bartels, M. Milicevic.
Iterative solution of a constrained total variation regularized model problem.
Discrete and Continuous Dynamical Systems, 2016.

S. Bartels, M. Milicevic.
Stability and experimental comparison of prototypical iterative schemes for total variation regularized problems.
Computational Methods in Applied Mathematics, 2016.

Foundation and Application of Generalized Mixed FEM Towards Nonlinear Problems in Solid Mechanics

2020:

Bringmann, P.
Adaptive least-squares finite element method with optimal convergence rates
Dissertation, Humboldt-Universität zu Berlin,
Mathematisch-Naturwissenschaftliche Fakultät, 2020

C. Carstensen.
Collective marking for adaptive least-squares finite element methods with optimal rates.
Mathematics of Computation, Vol. 89, No. 321, pages 89–103, 2020.

C. Carstensen, G. Mallik, N. Nataraj.
Nonconforming finite element discretization for semilinear problems with trilinear nonlinearity
IMA Journal of Numerical Analysis, April 2020.

C. Carstensen, A. Ern, S. Puttkammer.
Guaranteed lower bounds on eigenvalues of elliptic operators with a hybrid high-order method.
Submitted, preprint, June 2020.

C. Carstensen, S. Puttkammer.
How to prove the discrete reliability for nonconforming finite element methods.
Journal of Computational Mathematics, Vol. 38, No. 1, pages 142–175, 2020.

2019:

C. Carstensen, G. Mallik, N. Nataraj.
A priori and a posteriori error control of discontinuous Galerkin finite element methods for the von Kármán equations.
IMA Journal of Numerical Analysis, Vol. 39, No. 1, pages 167–200, 2019.

C. Carstensen, D. Gallistl, J. Gedicke.
Residual-based a posteriori error analysis for symmetric mixed Arnold-Winther FEM.
Numerische Mathematik, Vol. 142, No. 2, pages 205–234, 2019.

C. Carstensen, A. K. Dond, H. Rabus.
Quasi-optimality of adaptive mixed FEMs for non-selfadjoint indefinite second-order linear elliptic problems.
Computational Methods in Applied Mathematics, Vol. 19, No. 2, pages 233–250, 2019.

C. Carstensen, D. Liu, J. Alberty.
Convergence of dG(1) in elastoplastic evolution.
Numerische Mathematik, Vol. 141, No. 3, pages 715–742, 2019.

C. Carstensen, N. Nataraj.
Adaptive Morley FEM for the von Kármán equations with optimal convergence rates.
arXiv, 2019.

2018:

Hellwig, F.
Adaptive Discontinuous Petrov-Galerkin Finite-Element-Methods
Dissertation, Humboldt-Universität zu Berlin,
Mathematisch-Naturwissenschaftliche Fakultät, 2018

P. Bringmann, C. Carstensen, G. Starke.
An adaptive least-squares FEM for linear elasticity with optimal convergence rates.
SIAM Journal on Numerical Analysis, Vol. 56, No. 1, pages 428–447, 2018.

C. Carstensen, F. Hellwig.
Constants in Discrete Poincaré and Friedrichs Inequalities and Discrete Quasi-Interpolation.
Comput. Math. Appl., Vol. 18, No. 3, pages 433–450, July 2018.

C. Carstensen, S. Puttkammer.
A low-order discontinuous Petrov-Galerkin method for the Stokes equations.
Numer. Math., Vol. 140, No. 1, pages 1–34, 01 September 2018.

C. Carstensen, P. Bringmann, F. Hellwig, P. Wriggers.
Nonlinear discontinuous Petrov-Galerkin methods.
Numer. Math., Vol. 139, No. 3, pages 529–561, 01 July 2018.

C. Carstensen, F. Hellwig.
Optimal Convergence Rates for Adaptive Lowest-Order Discontinuous Petrov-Galerkin Schemes.
SIAM Journal on Numerical Analysis, Vol. 56, No. 2, pages 1091–1111, 2018.

C. Carstensen, J. Storn.
Asymptotic Exactness of the Least-Squares Finite Element Residual.
SIAM Journal on Numerical Analysis, Vol. 56, No. 4, pages 2008–2028, 2018.

2017:

Carstensen, C. and Köhler, K.
Efficient discrete Lagrange multipliers in three first-order finite element discretizations for the a posteriori error control in an obstacle problem
SIAM J. Numer. Anal., 2017, Vol. 55(1), pp. 349-375

T. Steiner, P. Wriggers.
A primal discontinuous Petrov‐Galerkin finite element method for linear elasticity.
Proc. Appl. Math. Mech., Vol. 17, No. 1, pages 83–86, 2017.

P. Bringmann, C. Carstensen.
An adaptive least-squares FEM for the Stokes equations with optimal convergence rates.
Numerische Mathematik, Vol. 135, No. 2, pages 459–492, 2017.

C. Carstensen, E. J. Park, P. Bringmann.
Convergence of natural adaptive least squares finite element methods.
Numerische Mathematik, Vol. 136, No. 4, pages 1097–1115, 2017.

C. Carstensen, H. Rabus.
Axioms of adaptivity with separate marking for data resolution.
SIAM J. Numer. Anal., Vol. 55, No. 6, pages 2644–2665, 2017.

P. Bringmann, C. Carstensen.
h-adaptive least-squares finite element methods for the 2D Stokes equations of any order with optimal convergence rates.
Computers & Mathematics with Applications. An International Journal, Vol. 74, No. 8, pages 1923–1939, 2017.

2016:

T. Steiner, P. Wriggers, S. Löhnert.
A discontinuous Galerkin Finite Element Method for linear elasticity using a mixed integration scheme to circumvent shear-locking.
Proc. Appl. Math. Mech., Vol. 16, pages 769–770, 2016.

C. Carstensen, D. Peterseim, A.Schröder.
The norm of a discretized gradient in H(div)^* for a posteriori finite element error analysis
Numerische Mathematik, Vol. 132, pages 519–539, 2016.

C. Carstensen, L. Demkowicz, J. Gopalakrishnan.
Breaking spaces and forms for the DPG method and applications including Maxwell equations.
Computers & Mathematics with Applications. An International Journal, Vol. 72, No. 3, pages 494–522, 2016.

P. Bringmann, C. Carstensen, D. Gallistl,  F. Hellwig, D. Peterseim, S. Puttkammer, H. Rabus, J. Storn.
Towards adaptive discontinuous Petrov-Galerkin methods.
PAMM, Vol. 16, No. 1, pages 741–742, 2016.

C. Carstensen, F. Hellwig.
Low-order discontinuous Petrov-Galerkin finite element methods for linear elasticity.
SIAM Journal on Numerical Analysis, Vol. 54, No. 6, pages 3388–3410, 2016.

Carstensen, C., Gallistl, D., Hellwig, F. and Weggler, L.
Low-order dPG-FEM for an elliptic PDE
Comput. Math. Appl., 2014, Vol. 68(11), pp. 1503-1512

High-order immersed-boundary methods in solid mechanics for structures generated by additive processes

2020:

Lothar Banz and Michael Hintermüller and Andreas Schröder.
A posteriori error control for distributed elliptic optimal control problems with control constraints discretized by hp-finite elements.
Computers & Mathematics with Applications, 2020.

W. Garhuom, S. Hubrich, L. Radtke, A. Düster.
A remeshing strategy for large deformations in the finite cell method.
Computers & Mathematics with Applications, 2020.

A. Düster, O. Allix.
Selective enrichment of moment fitting and application to cut finite elements and cells.
Computational Mechanics, Vol. 65, No. 2, pages 429–450, 2020.

A. Düster, S. Hubrich.
Adaptive Integration of Cut Finite Elements and Cells for Nonlinear Structural Analysis.
Modeling in Engineering Using Innovative Numerical Methods for Solids and Fluids, Springer International Publishing, pages 31–73, Cham, 2020.
Editor: Laura De Lorenzis, Alexander Düster.

S. Kollmannsberger, D. D'Angella, E. Rank, W. Garhuom, S. Hubrich, A. Düster, P. di Stolfo, A. Schröder.
Spline- and hp-basis functions of higher differentiability in the finite cell method.
GAMM-Mitteilungen, Vol. 43, No. 1, 2020.

D. D'Angella, A. Reali.
Efficient extraction of hierarchical B-Splines for local refinement and coarsening of Isogeometric Analysis.
Computer Methods in Applied Mechanics and Engineering, Vol. 367, No. 0045-7825, pages 11313–11313, 2020.

L. Coradello, D. D'Angella, M. Carraturo, J. Kiendl, S. Kollmannsberger, E. Rank, A. Reali.
Hierarchically refined isogeometric analysis of trimmed shells.
Computational Mechanics, Vol. 66, pages 431–447, 2020.

M. Carraturo, J. Jomo, S. Kollmannsberger A. Reali, F. Auricchio and E. Rank,
Modeling and experimental validation of an immersed thermo-mechanical part-scale analysis for laser powder bed fusion processes,
Additive Manufacturing, Vol. 36, 101498, 2020.

2019:

Di Stolfo, Paolo and Rademacher, Andreas and Schröder, Andreas.
Dual weighted residual error estimation for the finite cell method.
Journal of Numerical Mathematics, Vol. 27(2), pages 101--122, 2019.

Banz, Lothar and Petsche, Jan and Schröder, Andreas.
Explicit and Implicit Reconstructions of the Potential in Dual Mixed hp-Finite Element Methods.
In Advanced Finite Element Methods with Applications: Selected Papers from the 30th Chemnitz Finite Element Symposium 2017. editors: Apel, Thomas and Langer, Ulrich and Meyer, Arnd and Steinbach, Olaf, Springer International Publishing, pages 17--40, 2019.

S. Hubrich, A. Düster.
Numerical integration for nonlinear problems of the finite cell method using an adaptive scheme based on moment fitting.
Computers & Mathematics with Applications, Vol. 77, No. 7, pages 1983–1997, 2019.

A. Abedian, A. Düster.
Equivalent Legendre polynomials: Numerical integration of discontinuous functions in the finite element methods.
Computer Methods in Applied Mechanics and Engineering, Vol. 343, pages 690–720, 2019.

S. Kollmannsberger, M. Carraturo, A. Reali, F. Auricchio.
Accurate prediction of melt pool shapes in laser powder bed fusion by the non-linear temperature equation including phase changes.
Integrating Materials and Manufacturing Innovation, Vol. 8, pages 167–177, 2019.
 

2018:

Hubrich, S. and Düster, A.,
Adaptive numerical integration of broken finite cells based on moment fitting applied to finite strain problems.
Proc. Appl. Math. Mech., 18: e201800089. doi:10.1002/pamm.201800089, 2018

D. D'Angella, S. Kollmannsberger, E. Rank, A. Reali.
Multi-level Bézier extraction for hierarchical local refinement of Isogeometric Analysis.
Computer Methods in Applied Mechanics and Engineering, Vol. 328, pages 147–174, 2018.

A. Özcan, S. Kollmannsberger, J.  Jomo, L. De Lorenzis, E. Rank.
Residual stresses in metal deposition modeling: discretizations of higher order.
Computers and  Mathematics with Applications, 2018.

S. Nagaraja, M. Elhaddad, M. Ambati, S. Kollmannsberger, L. De Lorenzis, E. Rank.
Phase-field modeling of brittle fracture with multi-level hp-FEM and the finite cell method.
Computational Mechanics, Vol. 63, pages 1283–1300, 30 Oct 2018.

2017:

A. Düster, E. Rank, B. Szabo.
The p-Version of the Finite Element and Finite Cell Methods.
Encyclopedia of Computational Mechanics, volume 2, pages 1–35, 2017.

S. Kollmannsberger, A. Özcan, M.Carraturo, N. Zander, E. Rank.
A hierarchical computational model for moving thermal loads and phase changes with applications to Selective Laser Melting.
Preprint, 2017.

J. Jomo, N. Zander, M. Elhaddad, A. Özcan, S. Kollmannsberger, R-P. Mundani, E. Rank.
Parallelization of the multi-level hp-adaptive finite cell method.
Computers and Mathematics with Applications, 2017.

D. D'Angella, S. Kollmannsberger, E. Rank, A. Reali.
Multi-level Bézier extraction for hierarchical local refinement of Isogeometric Analysis.
Computers Methods in Applied Mechanics and Engineering, 2017.

S. Hubrich, P. Di Stolfo, L. Kudela, S. Kollmannsberger, E. Rank, A. Schröder.
Numerical integration of discontinuous functions: moment fitting and smart octree.
Computational Mechanics, 2017.

2016:

D. D'Angella, N. Zander, S. Kollmannsberger, F. Frischmann, E. Rank, A. Schröder, A. Reali.
Multi-Level hp-Adaptivity and Explicit Error Estimation.
Advanced Modeling and Simulation in Engineering Sciences, pp. 1–18, Springer, 2016.

C. Carstensen, D. Peterseim, A. Schröder.
The norm of a discretized gradient in H(div)∗ for a posteriori finite element error analysis.
Numerische Mathematik, 2016.

M. Joulaian, S. Hubrich, A. Düster.
Numerical integration of discontinuities on arbitrary domains based on moment fitting.
Computational Mechanics, 2016.

N. Zander, T. Bog, M. Elhaddad, F. Frischmann, S. Kollmannsberger, E. Rank.
The multi-level hp-method for three-dimensional problems: Dynamically changing high-order mesh refinement with arbitrary hanging nodes.
Comput. Methods Appl. Mech. Engrg, 2016.

N. Zander, M. Ruess, T. Bog, S. Kollmannsberger, E. Rank.
Multi-Level hp- Adaptivity for Cohesive Fracture Modelling.
International Journal for Numerical Methods in Engineering, 2016.

P. Di Stolfo, A. Schröder, N. Zander, S. Kollmannsberger.
An easy treatment of hanging nodes in hp-finite elements.
Finite Elements in Analysis and Design, 2016.

Hubrich, S., Joulaian, M., Di Stolfo, P., Schröder, A. and Düster, A.,
Efficient numerical integration of arbitrarily broken cells using the moment fitting approach.
Proc. Appl. Math. Mech., 16: 201-202. doi:10.1002/pamm.201610089, 2016

2015:

A. Rademacher, A. Schröder.
Dual Weighted Residual Error Control for Frictional Contact Problems.
Computational Methods in Applied Mathematics, 2015

Hubrich, S. and Joulaian, M. and Düster, A.,
Numerical integration in the finite cell method based on moment-fitting,
Proceedings of 3rd ECCOMAS Young Investigators Conference, 6th GACM Colloquium, pages 1-4, 2015

Hybrid discontinuous Galerkin methods in solid mechanics

2018:

H. R. Bayat, S. Wulfinghoff, S. Kastian, S. Reese.
On the use of reduced integration in combination with discontinuous Galerkin discretization: application to volumetric and shear locking problems.
Advanced Modeling and Simulation in Engineering Sciences, Vol. 5, No. 1, pages 10, 2018.

H. R. Bayat, J. Krämer, L. Wunderlich, S. Wulfinghoff, S. Reese, B. Wohlmuth, C. Wieners.
Numerical evaluation of discontinuous and nonconforming finite element methods in nonlinear solid mechanics.
Computational Mechanics, Vol. 62, No. 6, pages 1413–1427, 2018.

2017:

A. Matei, S. Sitzmann, K. Willner, B. Wohlmuth.
A mixed variational formulation for a class of contact problems in viscoelasticity.
Submitted, 2017.

H. R. Bayat, S. Kastian, S. Wulfinghoff, S. Reese,
Discontinuous Galerkin (DG) method in 3D linear elasticity with application in problems with locking.
PAMM, Vol. 17, No. 1, pages 19–22, 2017.

S. Wulfinghoff, H. R. Bayat, A. Alipour, S. Reese.
Investigation of a locking-free hybrid discontinuous Galerkin element that is very easy to implement into FE-codes.
PAMM, Vol. 17, No. 1, pages 87–90, 2017.

S. Wulfinghoff , H. R. Bayat , A. Alipour, S. Reese.
A low-order locking-free hybrid discontinuous Galerkin element formulation for large deformations.
Computer Methods in Applied Mechanics and Engineering, 2017.

S. Reese, H. R. Bayat, S. Wulfinghoff.
On an equivalence between a discontinuous Galerkin method and reduced integration with hourglass stabilization for finite elasticity.
Computer Methods in Applied Mechanics and Engineering, Vol. 325, No. Supplement C, pages 175–197, 2017.

2016:

H. R. Bayat, S. Wulfinghoff, S. Reese.
Discontinuous Galerkin method with reduced integration scheme for the boundary terms in almost incompressible linear elasticity.
Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering, 2016.

H. R. Bayat, S. Wulfinghoff, S. Reese.
The discontinuous Galerkin method with reduced integration scheme for the boundary terms in almost incompressible linear elasticity.
Proceedings in Applied Mathematics and Mechanics, 2016.

J. Krämer, C. Wieners, B. Wohlmuth, L. Wunderlich.
A hybrid weakly nonconforming discretization for linear elasticity.
Proceedings in Applied Mathematics and Mechanics, 2016.

T. Horger, B. Wohlmuth, L. Wunderlich.
Reduced basis isogeometric mortar approximations for eigenvalue problems
in vibroacoustics.
Model Reduction for Parametrized, 2016.

T. Horger, A. Reali, B. Wohlmuth, L. Wunderlich.
Improved approximation of eigenvalues in isogeometric methods for
multi-patch geometries and Neumann boundaries.
Cornell University Library, 2016.

A. Seitz, P. Farrah, J. Kremheller, B. Wohlmuth, W. Wall, A. Popp.
Isogeometric dual mortar methods for computational contact mechanics.
Computer Methods in Applied Mechanics and Engineering, Vol. 301, pages 259–280, 2016.

2015:

H. R. Bayat, S. Wulfinghoff, S. Reese.
Application of the discontinuous Galerkin finite element method in small deformation regimes.
Proceedings in Applied Mathematics and Mechanics, 2015.

H. R. Bayat, S. Wulfinghoff, S. Reese.
Discontinuous Galerkin analysis of displacement discontinuities for linear elasticity.
Proceedings of the 3rd ECCOMAS Young Investigators Conference on Computational Methods in Applied Sciences and 6th GACM Colloquium on Computational Mechanics, 2015.

E. Brivadis, A. Buffa, B. Wohlmuth, L. Wunderlich.
The Influence of Quadrature Errors on Isogeometric Mortar Methods.
Isogeometric Analysis and Applications 2014. Springer, 2015.

E. Brivadis, A. Buffa, B. Wohlmuth, L. Wunderlich.
Isogeometric mortar methods.
Computer Methods in Applied Mechanics and Engineering, 2015.

O. Steinbach, B. Wohlmuth, L.Wunderlich.
Trace and flux a priori error estimates in finite element approximations of Signorini-type problems.
IMA Journal of Numerical Analysis, 2015.

Isogeometric and stochastic collocation methods for nonlinear probabilistic multiscale problems in solid mechanics

2020:

F. Fahrendorf, S. Morganti, A. Reali, T. J.R. Hughes, L. De Lorenzis.
Mixed stress-displacement isogeometric collocation for nearly incompressible elasticity and elastoplasticity.
Computer Methods in Applied Mechanics and Engineering, Vol. 369, 2020.

2019:

E. Marino, J. Kiendl, L. De Lorenzis.
Explicit isogeometric collocation for the dynamics of three-dimensional beams undergoing finite motions.
Computer Methods in Applied Mechanics and Engineering, Vol. 343, pages 530–549, 2019.

E. Marino, J. Kiendl, L. De Lorenzis.
Isogeometric collocation for implicit dynamics of three-dimensional beams undergoing finite motions.
Computer Methods in Applied Mechanics and Engineering, Vol. 356, pages 548–570, 2019.

2018:

F. Fahrendorf, L. De Lorenzis, H. Gomez.
Reduced integration at superconvergent points in isogeometric analysis.
Computer Methods in Applied Mechanics and Engineering, Vol. 328, pages 390–410, 2018.

2017:

O. Weeger, B. Narayanan, L. De Lorenzis, J. Kiendl, M. L. Dunn.
An isogeometric collocation method for frictionless contact of Cosserat rods.
Computer Methods in Applied Mechanics and Engineering, 2017.

O. Weeger, S.-K. Yeung, M. L. Dunn.
Isogeometric collocation methods for Cosserat rods and rod structures.
Computer Methods in Applied Mechanics and Engineering, Vol. 316, pages 100–122, 2017.

J. Kiendl, E. Marino, L. De Lorenzis.
Isogeometric collocation for the Reissner–Mindlin shell problem.
Computer Methods in Applied Mechanics and Engineering, Vol. 325, pages 645–665, 2017.

2016:

H. Gomez, L. De Lorenzis.
The variational collocation method.
Computer Methods in Applied Mechanics and Engineering, Vol. 309, pages 152–181, 2016.

2015:

R. Kruse, N. Nguyen-Thanh, L. De Lorenzis, T.J.R. Hughes.
Isogeometric collocation for large deformation elasticity and frictional contact problems.
Computer Methods in Applied Mechanics and Engineering, Vol. 296, pages 73–112, 2015

First-order system least squares finite elements for finite elasto-plasticity

2018:

M. Igelbüscher, A. Schwarz, K. Steeger, and J. Schröder.
Modified mixed least-squares finite element formulations for small and finite strain plasticity.
International Journal for Numerical Methods in Engineering, 117:141-160, 2018.

A. Schwarz, K. Steeger, M. Igelbüscher, and J. Schröder.
Different approaches for mixed LSFEMs in hyperelasticity: Application of logarithmic deformation measures.
International Journal for Numerical Methods in Engineering, 115:1138-1153, 2018.

2017:

M. Igelbüscher, A. Schwarz, K. Steeger, and J. Schröder.
Remarks on a modified mixed least-squares finite element formulation for small strain elasto-plasticity.
Proceedings in Applied Mathematics and Mechanics, 17:311-312, 2017.

F. Bertrand, M. Moldenhauer, G. Starke.
A Posteriori Error Estimation for Planar Linear Elasticity by Stress Reconstruction.
SIAM Journal on Numerical Analysis, submitted.

J. Schröder, M. Igelbüscher, A. Schwarz,  G. Starke.
A Prange-Hellinger-Reissner type finite element formulation for small strain elasto-plasticity.
Computer Methods in Applied Mechanics and Engineering, 317:400–418, 2017.

2016:

A. Schwarz, K. Steeger, M. Igelbüscher, and J. Schröder.
Comparison of different least-squares mixed finite element formulations for hyperelasticity.
Proceedings in Applied Mathematics and Mechanics, 16:239–240, 2016.

M. Igelbüscher, J. Schröder,  A. Schwarz.
On the performance of the Prange- Hellinger-Reissner finite element formulation for elasto-plasticity at small strains.
Proceedings in Applied Mathematics and Mechanics, 16:203–204, 2016.

R. Krause, B. Müller, G. Starke.
An adaptive least-squares mixed finite element method for the Signorini problem.
Numerical Methods for Partial Differential Equations, 2016.

Advanced Finite Element Modeling of 3D Crack Propagation by a Phase Field Approach

2020:

T. Noll, C. Kuhn, D. Olesch, R. Müller.
3D phase field simulations of ductile fracture.
GAMM‐Mitteilungen. 2020; 43:e202000008.

2018:

T. Noll, C. Kuhn, R. Müller.
Modeling of Ductile Fracture by a Phase Field Approach,
Proc. Appl. Math. Mech., 18: e201800376. doi:10.1002/pamm.201800376

2017:

T. Noll, C. Kuhn, R. Müller.
A Monolithic Solution Scheme for a Phase Field Model of Ductile Fracture.
Submitted to:  Proceedings in Applied Mathematics and Mechanics, 2017.

2016:

T. Noll, C. Kuhn, R. Müller.
Investigation of a Phase Field Model for Elasto-plastic Fracture.
Proceedings in Applied Mathematics and Mechanics, 2016.

C. Kuhn, T. Noll, R. Müller.
On phase field modeling of ductile fracture.
GAMM- Mitteilungen, 2016.

C. Kuhn, R. Müller.
A discussion of fracture mechanisms in heterogeneous materials by means of configurational forces in a phase field fracture model.
Computer Methods in Applied Mechanics and Engeneering, 2016.

Novel finite element technologies for anisotropic media

2019:

Aldakheel, F. and Hudobivnik, B. and Wriggers, P. Virtual elements for finite thermo-plasticity problems.
Computational Mechanics, Vol. 64, pp. 1347--1360, 2019.

Aldakheel, F. and Hudobivnik, B. and Wriggers, P. Virtual element formulation for phase-field modeling of ductile fracture.
International Journal for Multiscale Computational Engineering, Vol. 17, pp. 181--200, 2019.

Hussein, A. and Aldakheel, F. and Hudobivnik, B. and Wriggers, P. and Guidault, P.-A. and Allix, O. A Computational framework for brittle crack propagation based on an efficient virtual element method. Finite Elements in Analysis and Design, Vol. 159, pp. 15--32, 2019.

Viebahn, N., Schröder, J. & Wriggers, P. An extension of assumed stress finite elements to a general hyperelastic framework. Adv. Model. and Simul. in Eng. Sci. 6, 9 (2019). https://doi.org/10.1186/s40323-019-0133-z

2018:

B. Hudobivnik and F. Aldakheel and  P. Wriggers. Low order 3D virtual element formulation for finite elasto-plastic deformations. Computational Mechanics, Vol. 63, pp. 253--269, 2018.

F. Aldakheel and   B. Hudobivnik and A. Hussein and P. Wriggers. Phase-Field Modeling of Brittle Fracture Using an Efficient Virtual Element Scheme, Computer Methods in Applied Mechanics and Engineering, Vol. 341, pp. 443--466, 2018

Viebahn, N., Steeger, K. and Schröder, J., (2018), "A simple and efficient Hellinger-Reissner type mixed finite element for nearly incompressible elasticity", Computer Methods in Applied Mechanics and Engineering. Vol. 340, pp. 278-295.

Viebahn, N., Steeger, K. and Schröder, J., (2018), "On the construction of a triangular Mixed Finite Element based on the principle of Hellinger-Reissner", Proceedings in Applied Mathematics and Mechanics. Vol. 18.

2017:

P. Wriggers and B. Hudobivnik. A low order virtual element formulation for finite elasto-plastic deformations, Computer Methods in Applied Mechanics and Engineering, Vol. 327, pp. 459--477, 2017.

J. Schröder, N. Viebahn, P. Wriggers, F. Auricchio, K. Steeger.
On the stability analysis of hyperelastic boundary value problems using three- and two-field mixed finite element formulations.
accepted for publication in Computational Mechanics 2017.

P. Wriggers, B.D. Reddy, W. Rust, B. Hudobivnik.
Efficient virtual element formulations for compressible and incompressible finite deformations.
Computational Mechanics, 2017

P. Wriggers, B. Hudobivnik, J. Schröder.
Finite and virtual element formulations for large strain anisotropic material with inextensive fibers.
in Multiscale Modeling of Heterogeneous Structures, eds. J. Soric and P. Wriggers, Lecture Notes in Applied and Computational Mechanics, Springer, 2017.

P. Wriggers, B. Hudobivnik, J. Korelc.
Efficient Low Order Virtual Elements for Anisotropic Materials at Finite Strains.
in Advances in Computational Plasticity, 2017.

N. Viebahn, J. Schröder, P. Wriggers, F. Auricchio
Challenges of stability analysis using mixed FEM
Proceedings in Applied Mathematics and Mechanics, submitted

2016:

N. Viebahn, P.M. Pimenta, J. Schröder.
A Simple triangular finite element for nonlinear thin shells - Statics, Dynamics and Anisotropy. Computational Mechanics, DOI: 10.1007/s00466-016-1343-6, 2016

P. Wriggers, W. Rust, B.D. Reddy.
A virutual element method for contact.
Computational Mechanics, 2016

J. Schröder, N. Viebahn, D. Balzani, P. Wriggers.
A novel mixed finite element for finite anisotropic elasticity; the SKA-element Simplified Kinematics for Anisotropy.
Computer Methods in Applied Mechanics and Engineering, 2016.

N. Viebahn, J. Schröder, P. Wriggers, D. Balzani.
Notes on a novel finite element for anisotropy at large strains.
Proceedings in Applied Mathematics and Mechanics, 2016

P. Wriggers, J. Schröder, F. Auricchio.
Finite element formulations for large strain anisotropic material with inextensive fibers.
Advanced Modeling and Simulation in Engineering Sciences, 2016.

Large-scale simulation of pneumatic and hydraulic fracture with a phase-field approach

2017:

C. Bilgen, A. Kopanicakova, R. Krause, K. Weinberg.
A phase-field approach to conchoidal fracture.
Under review at Meccanica, 2017.

T. Dally, K. Weinberg, C. Bilgen.
Cohesive elements or phase-field fracture: Which method is better for reliable analyses in dynamic fracture?
Submitted to: Engineering Fracture Mechanics, 2017.

C. Bilgen, A. Kopanicakova, R. Krause, K. Weinberg.
A phase-field approach to pneumatic fracture.
submitted to: Proceedings in Applied Mathematics and Mechanics, 2017.

K. Weinberg.
A phase-field approach to material degradation.
14th Joint European Thermodynamics Conference, 2017.

C. Hesch, A. J. Gil, R. Ortigosa, M. Dittmann, C. Bilgen, P. Betsch, M. Franke, A. Janz, K. Weinberg.
A framework for polyconvex large strain phase-field methods to fracture.
Comput. Methods Appl. Mech. Engrg., 2017.

M. Thomas, C. Bilgen, K. Weinberg.
Analysis and Simulations for a Phase Field Fracture Model at Finite Strains.
Preprint, 2017.

2016:

C. Bilgen, C. Hesch, K. Weinberg.
A polyconvex strain-energy split for a high-order phase-field approach to fracture.
Proceedings in Applied Mathematics and Mechanics, 2016.

C. Hesch, S. Schuß, M. Dittmann, M. Franke and K. Weinberg.
Isogeometric analysis and hierarchical refinement for higher-order phase-field models.
Comput. Methods Appl. Mech. Engrg, 2016.

C. Hesch, M. Franke, M. Dittmann and I. Temizer.
Hierarchical NURBS and a higher-order phase-field approach to fracture for finite-deformation contact problems.
Comput. Methods Appl. Mech. Engrg, 2016

K. Weinberg, T. Dally, S. Schuß, M. Werner and C. Bilgen.
Modeling and numerical simulation of crack growth and damage with a phase-field approach.
GAMM-Mitteilungen, 2016.

A novel smooth discretization approach for elasto-plastic contact of bulky and thin structures

2018:

C. Meier, M. J. Grill, W. A. Wall, A. Popp.
Geometrically exact beam elements and smooth contact schemes for the modeling of fiber-based materials and structures.
International Journal of Solids and Structures, Vol. 154, pages 124–146, 2018.

A. Seitz, W. A. Wall, A. Popp.
A computational approach for thermo-elasto-plastic frictional contact based on a monolithic formulation using non-smooth nonlinear complementarity functions.
Advanced Modeling and Simulation in Engineering Sciences, Vol. 5, No. 1, page 5, 2018.

2017:

A. Seitz, W.A. Wall, A. Popp.
A computational approach for thermo-elasto-plastic frictional contact based on a monolithic formulation employing non-smooth nonlinear complementarity functions.
submitted to: Advanced Modeling and Simulation in Engineering Sciences, 2017.

C. Meier, M.J. Grill, W.A. Wall, A. Popp.
Geometrically exact beam elements and smooth contact schemes for the modeling of fiber-based materials and structures.
submitted to: International Journal of Solids and Structures, 2017.

2016:

A. Seitz, P. Farah, J. Kremheller, B. Wohlmuth, W. Wall, A. Popp.
Isogeometric dual mortar methods for computational contact mechanics.
Computer Methods in Applied Mechanics and Engineering, 2016.

2015:

A. Seitz, A. Popp, W. Wall.
A semi-smooth Newton method for orthotropic plasticity and frictional contact at finite strains.
Computer Methods in Applied Mechanics and Engineering, Vol. 285, pages 228–254, 2015.

Approximation and reconstruction of stresses in the deformed configuration for hyperelastic material models

2020:

Bertrand, F., Moldenhauer, M. and Starke, G. (2020),
Weakly symmetric stress equilibration for hyperelastic material models.
GAMM‐Mitteilungen, 43: e202000007. doi:10.1002/gamm.202000007

F. Bertrand and D. Boffi and G. G. de Diego.
Convergence analysis of the scaled boundary finite element method for the Laplace equation.
eprint 2005.02287, arXiv, Numerical Analysis, 2020.

2019:

Bertrand , B. Kober,  M. Moldenhauer and G. Starke.
Weakly symmetric stress equilibration and a posteriori error estimation for linear elasticity.
eprint 1808.02655, arXiv, Numerical Analysis, 2019.

F. Bertrand and D. Boffi.
The Prager-Synge theorem in reconstruction based a posteriori error estimation.
eprint 1907.00440, arXiv, Numerical Analysis, 2019.

M. Igelbüscher and J. Schrörder.
On the relaxation of continuity conditions for finite elements schemes based on a least-squares approach.
Proceedings in Applied Mathematics and Mechanics, 2019.

M. Igelbüscher, J. Schröder, and A. Schwarz.
A mixed least-squares finite element formulation with explicit consideration of the balance of moment of momentum, a numerical study. GAMM Mitteilungen, 2019.