Selected Publications

Pfefferkorn, R., Betsch, P.: Hourglassing- and locking-free mesh distortion insensitive Petrov-Galerkin EAS element for large deformation solid mechanics. Int J Numer Methods Eng., 2022, DOI

Ströhle, T., Betsch, P.: A simultaneous space-time discretization approach to the inverse dynamics of geometrically exact strings. Int J Numer Methods Eng. 123(11), 2573-2609, 2022, DOI

Betsch, P., Schneider, S.: Conservation of Generalized Momentum Maps in the Optimal Control of Constrained Mechanical Systems. IFAC PapersOnLine, 54(9), 615-619, 2021, DOI

Pfefferkorn, R., Betsch, P.: Mesh distortion insensitive and locking-free Petrov-Galerkin low-order EAS elements for linear elasticity. Int J Numer Methods Eng. 122(23), 6924-6954, 2021, DOI

Schiebl, M., Betsch, P.: Structure‐preserving space‐time discretization of large‐strain thermo‐viscoelasticity in the framework of GENERIC. Int J Numer Methods Eng. 122(14), 3448-3488, 2021, DOI

Yang, Y., Betsch, P., Zhang, W.: Numerical integration for the inverse dynamics of a large class of cranes. Multibody Syst. Dyn., Vol. 48(1), pp 1-40, 2020, DOI

Pfefferkorn, R., Betsch, P.: Extension of the enhanced assumed strain method based on the structure of polyconvex strain-energy functions. Int J Numer Methods Eng.,121(8), 1695-1737, 2020, DOI

Betsch, P., Schiebl, M.: GENERIC-based formulation and discretization of initial boundary value problems for finite strain thermoelasticity, Comput. Mech., 65:503-531, 2020, DOI

Janz, A., Betsch, P., Franke, M.: Structure-preserving space-time discretization of a mixed formulation for quasi-incompressible large strain elasticity in principal stretches. Int J Numer Methods Eng., 120(13), 1381-1410, 2019, DOI

Pfefferkorn, R., Betsch, P.: On transformation and shape functions for enhanced assumed strain elements. Int J Numer Methods Eng., 120(2), 231-261, 2019, DOI

Betsch, P., Schiebl, M.: Energy-Momentum-Entropy consistent numerical methods for large strain thermoelasticity relying on the GENERIC formalism. Int J Numer Methods Eng., 119(12), 1216-1244, 2019, DOI

Betsch P.: Computational Dynamics. In: Altenbach H., Öchsner A. (eds) Encyclopedia of Continuum Mechanics. Springer, 1-11, 2018, DOI

Ortigosa, R., Franke, M., Janz, A., Gil, A.J., Betsch, P.: An energy-momentum time integration scheme based on a convex multi-variable framework for non-linear electro-elastodynamics. Comput. Methods Appl. Mech. Eng., 339, 1-35, 2018, DOI

Franke, M., Janz, A., Schiebl, M., Betsch, P.: An energy-momentum consistent integration scheme using a polyconvexity-based framework for non-linear thermo-elastodynamics. Int J Numer Methods Eng., 115(5), 549-577, 2018, DOI

Betsch, P., Janz, A., Hesch, C.: A mixed variational framework for the design of energy-momentum schemes inspired by the structure of polyconvex stored energy functions. Comput. Methods Appl. Mech. Eng., 335, 660-696, 2018, DOI

Groß, M., Bartelt, M., Betsch, P.: Structure-preserving time integration of non-isothermal finite viscoelastic continua related to variational formulations of continuum dynamics. Comput. Mech. (2017), 1-28, DOI

Betsch, P., Becker, C.: Conservation of generalized momentum maps in mechanical optimal control problems with symmetry. Int J Numer Methods Eng., 111(2), 144-175, 2017, DOI

Hesch, C., Gil, A.J., Ortigosa, R., Dittmann, M., Bilgen, C., Betsch, P., Franke, M., Janz, A., Weinberg, K.: A framework for polyconvex large strain phase-field methods to fracture. Comput. Methods Appl. Mech. Eng., Vol. 317, 649-683, 2017, DOI

Roller, M., Betsch, P., Gallrein, A., Linn, J.: An enhanced tire model for dynamic simulation based on geometrically exact shells. Archive of Mechanical Engineering 63(2), 277-295, 2016, DOI

Betsch, P.: Energy-momentum integrators for elastic Cosserat points, ridig bodies and multibody systems. In: Structure-preserving integrators in nonlinear structural dynamics and multibody dynamics, Series: CISM Courses and Lectures, Betsch, P. (Ed.), Vol. 565 (31-89), Springer Verlag, 2016

Bauchau, O., Betsch, P., Cardona, A., Gerstmayr, J., Jonker, B., Masarati, P., Sonneville, V.: Validation of flexible multibody dynamics beam formulations using benchmark problems. Multibody System Dynamics 37(1), 29-48, 2016, DOI

Betsch, P., Altmann, R., Yang, Y.: Numerical integration of underactuated mechanical systems subjected to mixed holonomic and servo constraints. Multibody Dynamics: Computational Methods and Applications, Series: Computational Methods in Applied Sciences, Vol. 42, 1-18, Font-Llagunes, J.M (Ed.), Springer Verlag, 2016, DOI

Betsch, P., Janz, A.: An energy-momentum consistent method for transient simulations with mixed finite elements developed in the framework of geometrically exact shells. Int. J. Numer. Meth. Engng 108(5), 423-455, 2016, DOI

Krüger, M., Groß, M., Betsch, P.: An energy-entropy-consistent time stepping scheme for nonlinear thermo-viscoelastic continua. Z. Angew. Math. Mech. (ZAMM) 96(2), 141-178, 2016, DOI 

Conde Martín, S., Betsch, P., García Orden, J.C.: A temperature-based thermodynamically consistent integration scheme for discrete thermo-elastodynamics. Commun. Nonlinear Sci. Numer. Simulat., Vol. 32 (63-80), 2016, DOI

Altmann, R., Betsch, P., Yang, Y.: Index reduction by minimal extension for the inverse dynamics simulation of cranes. Multibody System Dynamics 36(3), 295-321, 2016, DOI

Roller, M., Betsch, P., Gallrein, A. and Linn, J.: On the Use of Geometrically Exact Shells for Dynamic Tyre Simulation. In: Multibody Dynamics: Computational Methods and Applications, Series: Computational Methods in Applied Sciences, Terze, Z. (Ed.), Vol. 35 (205-236), Springer Verlag, 2014, Springer Webpage

Becker, C. and Betsch, P.: Application of a gyrostatic rigid body formulation in the context of a direct transcription method for optimal control in multibody dynamics. In: Multibody Dynamics: Computational Methods and Applications, Series: Computational Methods in Applied Sciences, Terze, Z. (Ed.), Vol. 35 (237-254), Springer Verlag, 2014, Springer Webpage 

Eugster, S.R., Hesch, C., Betsch, P. and Glocker, Ch.: Director-based beam finite elements relying on the geometrically exact beam theory formulated in skew coordinates, Int. J. Numer. Meth. Engng 97(2), 111-129, 2014, DOI

Sinclair, A.J., Hurtado, J.E., Berinato, C., Betsch, P.: On Noether's theorem and the various integrals of the damped linear oscillator. J. of Astronaut. Sci. (2013), Vol. 60 (396-407), DOI

Hesch, C., Betsch, P.: Continuum mechanical considerations for rigid bodies and fluid-structure interaction problems, Archive of Mechanical Engineering, 2013, DOI, PDF

Franke, M., Hesch, C. and Betsch, P.: An augmentation technique for large deformation frictional contact problems, Int. J. Numer. Meth. Engng 94(5), 513-534, 2013, DOI

Betsch, P. and Sänger, N.: On the consistent formulation of torques in a rotationless framework for multibody dynamics, Computers and Structures 127, 29-38, 2013, DOI

Hesch, C. and Betsch, P.: Isogeometric analysis and domain decomposition methods, Comput. Methods Appl. Mech. Engng, 213-216: 104-112, 2012, DOI

Betsch, P., Siebert, R., and Sänger, N.: Natural coordinates in the optimal control of multibody systems, J. Comput. Nonlinear Dynam., 7(1):011009/1-011009/8, 2012, DOI

Groß, M. and Betsch, P.: Galerkin-based energy-momentum consistent time-stepping algorithms for classical nonlinear thermo-elastodynamics, Mathematics and Computers in Simulation, 82(4), 718-770, 2011, DOI

Hesch, C., and Betsch, P.: Transient three-dimensional contact problems: mortar method. Mixed methods and conserving integration, Computational Mechanics, 48(4), 461-475, 2011, DOI

Hesch, C., and Betsch, P.: Transient 3d contact problems--NTS method: mixed methods and conserving integration, Computational Mechanics, 48(4), 437-449, 2011, DOI

Krüger, M., Groß, M., and Betsch, P.: A comparison of structure-preserving integrators for discrete thermoelastic systems, Computational Mechanics, 47(6), 701–722, 2011, DOI

Hesch, C., and Betsch, P.: Energy-momentum consistent algorithms for dynamic thermomechanical problems – application to mortar domain decomposition problems, Int. J. Numer. Meth. Engng, 86(11), 1277–1302, 2011, DOI

Hesch, C., and Betsch, P.: Transient three-dimensional domain decomposition problems: Frame-indifferent mortar constraints and conserving integration, Int. J. Numer. Meth. Engng 82(3), 329–358, 2010, DOI

Groß, M., and Betsch, P.: Energy-momentum consistent finite element discretization of dynamic finite viscoelasticity, Int. J. Numer. Meth. Engng 81(11), 1341–1386, 2010, DOI

Uhlar, S., and Betsch, P.: On the derivation of energy consistent time stepping schemes for friction afflicted multibody systems, Computers and Structures 88(11-12), 737–754, 2010, DOI

Betsch, P., Hesch, C., Sänger, N., and Uhlar, S.: Variational integrators and energy-momentum schemes for flexible multibody dynamics, J. Comput. Nonlinear Dynam. 5(3), 031001/1–031001/11, 2010, DOI

Betsch, P., and Siebert, R.: Rigid body dynamics in terms of quaternions: Hamiltonian formulation and conserving numerical integration, Int. J. Numer. Meth. Engng 79(4), 444–473, 2009, DOI

Betsch, P., and Sänger, N.: On the use of geometrically exact shells in a conserving framework for flexible multibody dynamics, Comput. Methods Appl. Mech. Engrg. 198, 1609–1630, 2009, DOI

Hesch, C., and Betsch, P.: A mortar method for energy-momentum conserving schemes in frictionless dynamic contact problems, Int. J. Numer. Meth. Engng 77(10), 1468–1500, 2009, DOI

Uhlar, S., and Betsch, P.: A rotationless formulation of multibody dynamics: Modeling of screw joints and incorporation of control constraints, Multibody System Dynamics 22(1), 69–95, 2009, DOI

Betsch, P., and Sänger, N.: A nonlinear finite element framework for flexible multibody dynamics: Rotationless formulation and energy-momentum conserving discretization, Multibody Dynamics: Computational Methods and Applications, Vol 12, Springer-Verlag, 119–141, Eds: Bottasso, Carlo L., 2009

Uhlar, S., and Betsch, P.: Conserving Integrators for Parallel Manipulators, Parallel Manipulators, I-Tech Education and Publishing, www.books.i-techonline.com, 75–108, Eds: Ryu, J.-H., Vienna, Austria, 2008

Leyendecker, S., Betsch, P., and Steinmann, P.: The discrete null space method for the energy consistent integration of constrained mechanical systems. Part III: Flexible multibody dynamics, Multibody System Dynamics 19(1-2), 45–72, 2008, DOI

Betsch, P., and Hesch, C.: Energy-momentum conserving schemes for frictionless dynamic contact problems. Part I: NTS method, IUTAM Symposium on Computational Methods in Contact Mechanics, vol 3, Springer-Verlag, 77–96, Eds: Wriggers, P., and Nackenhorst, U., 2007, DOI

Betsch, P., and Uhlar, S.: Energy-momentum conserving integration of multibody dynamics, Multibody System Dynamics 17(4), 243–289, 2007, DOI

Hesch, C., and Betsch, P.: A comparison of computational methods for large deformation contact problems of flexible bodies, Z. Angew. Math. Mech. (ZAMM) 86(10), 818–827, 2006, DOI

Leyendecker, S., Betsch, P., and Steinmann, P.: Objective energy-momentum conserving integration for the constrained dynamics of geometrically exact beams, Comput. Methods Appl. Mech. Engrg. 195, 2313–2333, 2006, DOI

Betsch, P.: Energy-consistent numerical integration of mechanical systems with mixed holonomic and nonholonomic constraints, Comput. Methods Appl. Mech. Engrg. 195, 7020–7035, 2006, DOI

Betsch, P., and Leyendecker, S.: The discrete null space method for the energy consistent integration of constrained mechanical systems. Part II: Multibody dynamics, Int. J. Numer. Meth. Engng 67(4), 499–552, 2006, DOI

Betsch, P.: The discrete null space method for the energy consistent integration of constrained mechanical systems. Part I: Holonomic constraints, Comput. Methods Appl. Mech. Engrg. 194(50-52), 5159–5190, 2005, DOI

Groß, M., Betsch, P., and Steinmann, P.: Conservation properties of a time FE method. Part IV: Higher order energy and momentum conserving schemes, Int. J. Numer. Meth. Engng 63, 1849–1897, 2005, DOI

Betsch, P.: A unified approach to the energy-consistent numerical integration of nonholonomic mechanical systems and flexible multibody dynamics, GAMM Mitteilungen 27(1), 66–87, 2004,

Leyendecker, S., Betsch, P., and Steinmann, P.: Energy-conserving integration of constrained Hamiltonian systems - a comparison of approaches, Computational Mechanics 33(3), 174–185, 2004, DOI

Betsch, P., and Steinmann, P.: Constrained dynamics of geometrically exact beams, Computational Mechanics 31, 49–59, 2003, DOI

Betsch, P.: Computational Methods for Flexible Multibody Dynamics, Habilitationsschrift, Lehrstuhl für Technische Mechanik, Universität Kaiserslautern, 2002,

Betsch, P., and Steinmann, P.: Conservation Properties of a Time FE Method. Part III: Mechanical systems with holonomic constraints, Int. J. Numer. Meth. Engng 53, 2271–2304, 2002, DOI

Betsch, P., and Steinmann, P.: Frame-indifferent beam finite elements based upon the geometrically exact beam theory, Int. J. Numer. Meth. Engng 54, 1775–1788, 2002, DOI

Betsch, P., and Steinmann, P.: A DAE approach to flexible multibody dynamics, Multibody System Dynamics 8, 367–391, 2002, DOI

Betsch, P., and Steinmann, P.: Constrained Integration of Rigid Body Dynamics, Comput. Methods Appl. Mech. Engrg. 191, 467–488, 2001, DOI

Betsch, P., and Steinmann, P.: Conservation Properties of a Time FE Method. Part II: Time-Stepping Schemes for Nonlinear Elastodynamics, Int. J. Numer. Meth. Engng 50, 1931–1955, 2001, DOI

Betsch, P., and Steinmann, P.: Derivation of the Fourth-Order Tangent Operator Based on a Generalized Eigenvalue Problem, Int. J. Solids Structures 37, 1615–1628, 2000, DOI

Betsch, P., and Steinmann, P.: Inherently Energy Conserving Time Finite Elements for Classical Mechanics, Journal of Computational Physics 160, 88–116, 2000, DOI

Betsch, P., and Steinmann, P.: Conservation Properties of a Time FE Method. Part I: Time-Stepping Schemes for N-Body Problems, Int. J. Numer. Meth. Engng 49, 599–638, 2000, DOI

Steinmann, P., and Betsch, P.: A Localization Capturing FE-Interface Based on Regularized Strong Discontinuities at Large Inelastic Strains, Int. J. Solids Structures 37, 4061–4082, 2000, DOI

Betsch, P., and Stein, E.: Numerical Implementation of Multiplicative Elasto-Plasticity into Assumed Strain Elements with Application to Shells at Large Strains, Comput. Methods Appl. Mech. Engrg. 179, 215–245, 1999, DOI

Betsch, P., Menzel, A., and Stein, E.: On the Parametrization of Finite Rotations in Computational Mechanics. A Classification of Concepts with Application to Smooth Shells, Comput. Methods Appl. Mech. Engrg. 155, 273–305, 1998, DOI

Steinmann, P., Betsch, P., and Stein, E.: FE Plane Stress Analysis Incorporating Arbitrary 3D Large Strain Constitutive Models, Eng. Comput. 14, 175–201, 1997, DOI

Betsch, P.: Statische und dynamische Berechnungen von Schalen endlicher elastischer Deformationen mit gemischten Finiten Elementen, Dissertation, Bericht-Nr. F 96/4, Institut für Baumechanik und Numerische Mechanik der Universität Hannover, 1996

Betsch, P., Gruttmann, F., and Stein, E.: A 4-Node Finite Shell Element for the Implementation of General Hyperelastic 3D-Elasticity at Finite Strains, Comput. Methods Appl. Mech. Engrg. 130, 57–79, 1996, DOI

Betsch, P., and Stein, E.: A Nonlinear Extensible 4-Node Shell Element Based on Continuum Theory and Assumed Strain Interpolations, J. Nonlinear Sci. 6, 169–199, 1996, DOI

Betsch, P., and Stein, E.: An Assumed Strain Approach Avoiding Artificial Thickness Straining for a Nonlinear 4-Node Shell Element, Commun. Numer. Meth. Engng 11, 899–909, 1995, DOI