An energy momentum consistent integration scheme using a polyconvexity‐based framework for nonlinear thermo‐elastodynamics

[1]  Michael Groß,et al.  Variational-based energy–momentum schemes of higher-order for elastic fiber-reinforced continua , 2017 .

[2]  Oscar Gonzalez,et al.  Exact energy and momentum conserving algorithms for general models in nonlinear elasticity , 2000 .

[3]  Ignacio Romero,et al.  Algorithms for coupled problems that preserve symmetries and the laws of thermodynamics: Part I: Monolithic integrators and their application to finite strain thermoelasticity , 2010 .

[4]  S. C. Martín.  Energy-entropy-momentum time integration methods for coupled smooth dissipative problems , 2016 .

[5]  H. C. Öttinger.  Beyond Equilibrium Thermodynamics: Öttinger/Beyond , 2005 .

[6]  Rogelio Ortigosa,et al.  A computational framework for polyconvex large strain elasticity for geometrically exact beam theory , 2015, Computational Mechanics.

[7]  Peter Betsch,et al.  An energy–momentum time integration scheme based on a convex multi-variable framework for non-linear electro-elastodynamics , 2018, Computer Methods in Applied Mechanics and Engineering.

[8]  Jörg Schröder,et al.  Poly-, quasi- and rank-one convexity in applied mechanics , 2010 .

[9]  Peter Betsch,et al.  A mixed variational framework for the design of energy–momentum schemes inspired by the structure of polyconvex stored energy functions , 2018, Computer Methods in Applied Mechanics and Engineering.

[10]  Gerhard A. Holzapfel,et al.  Entropy elasticity of isotropic rubber-like solids at finite strains , 1996 .

[11]  Peter Betsch,et al.  Galerkin-based energy-momentum consistent time-stepping algorithms for classical nonlinear thermo-elastodynamics , 2011, Math. Comput. Simul..

[12]  Peter Betsch,et al.  Energy–momentum consistent finite element discretization of dynamic finite viscoelasticity , 2010 .

[13]  Rogelio Ortigosa,et al.  On a tensor cross product based formulation of large strain solid mechanics , 2016 .

[14]  Christian Miehe,et al.  Entropic thermoelasticity at finite strains. Aspects of the formulation and numerical implementation , 1995 .

[15]  Andrew M. Stuart,et al.  A First Course in Continuum Mechanics: Bibliography , 2008 .

[16]  Marlon Franke,et al.  Isogeometric Analysis and thermomechanical Mortar contact problems , 2014 .

[17]  R. de Boer,et al.  Theory of Porous Media , 2020, Encyclopedia of Continuum Mechanics.

[18]  R. L. Harder,et al.  A proposed standard set of problems to test finite element accuracy , 1985 .

[19]  Peter Betsch,et al.  Energy-momentum consistent algorithms for dynamic thermomechanical problems—Application to mortar domain decomposition problems , 2011 .

[20]  A. Lion,et al.  A physically based method to represent the thermo-mechanical behaviour of elastomers , 1997 .

[21]  Peter Betsch,et al.  A framework for polyconvex large strain phase-field methods to fracture , 2017 .

[22]  J. Ball.  Convexity conditions and existence theorems in nonlinear elasticity , 1976 .

[23]  Peter Betsch,et al.  An energy‐entropy‐consistent time stepping scheme for nonlinear thermo‐viscoelastic continua , 2016 .

[24]  Melanie Krüger.  Energie-Entropie-konsistente Zeitintegratoren für die nichtlineare Thermoviskoelastodynamik , 2013 .

[25]  Ignacio Romero,et al.  Thermodynamically consistent time‐stepping algorithms for non‐linear thermomechanical systems , 2009 .

[26]  Peter Betsch,et al.  An energy–momentum consistent method for transient simulations with mixed finite elements developed in the framework of geometrically exact shells , 2016 .

[27]  Alexander Mielke,et al.  Formulation of thermoelastic dissipative material behavior using GENERIC , 2011 .

[28]  Miroslav Grmela,et al.  Dynamics and thermodynamics of complex fluids. I. Development of a general formalism , 1997 .

[29]  Peter Wriggers,et al.  A new Mixed Finite Element based on Different Approximations of the Minors of Deformation Tensors , 2011 .

[30]  Peter Betsch,et al.  Structure-preserving integrators in nonlinear structural dynamics and flexible multibody dynamics , 2016 .

[31]  M. Hütter,et al.  On the Formulation of Continuum Thermodynamic Models for Solids as General Equations for Non-equilibrium Reversible-Irreversible Coupling , 2011 .

[32]  Stefan Hartmann,et al.  A monolithic finite element approach using high-order schemes in time and space applied to finite strain thermo-viscoelasticity , 2015, Comput. Math. Appl..

[33]  J. C. Simo,et al.  A CLASS OF MIXED ASSUMED STRAIN METHODS AND THE METHOD OF INCOMPATIBLE MODES , 1990 .

[34]  D. Greenspan.  Conservative numerical methods for ẍ = f(x) , 1984 .

[35]  Miroslav Grmela,et al.  Dynamics and thermodynamics of complex fluids. II. Illustrations of a general formalism , 1997 .

[36]  Stefanie Reese,et al.  Theoretical and Numerical Aspects in the Thermo-Viscoelastic Material Behaviour of Rubber-Like Polymers , 1997 .