Energy–entropy–momentum integration schemes for general discrete non‐smooth dissipative problems in thermomechanics

[1]  O. Gonzalez Time integration and discrete Hamiltonian systems , 1996 .

[2]  J. C. Simo,et al.  The discrete energy-momentum method. Conserving algorithms for nonlinear elastodynamics , 1992 .

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

[4]  J. C. Simo,et al.  A new energy and momentum conserving algorithm for the non‐linear dynamics of shells , 1994 .

[5]  Ignacio Romero,et al.  A thermodynamically consistent numerical method for a phase field model of solidification , 2014, Commun. Nonlinear Sci. Numer. Simul..

[6]  Peter Betsch,et al.  A temperature-based thermodynamically consistent integration scheme for discrete thermo-elastodynamics , 2016, Commun. Nonlinear Sci. Numer. Simul..

[7]  J. C. Simo,et al.  Conserving algorithms for the dynamics of Hamiltonian systems on lie groups , 1994 .

[8]  F. Armero,et al.  Formulation and analysis of conserving algorithms for frictionless dynamic contact/impact problems , 1998 .

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

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

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

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

[13]  Ignacio Romero,et al.  An analysis of the stress formula for energy-momentum methods in nonlinear elastodynamics , 2012 .

[14]  J. Marsden,et al.  Variational Integrators and the Newmark Algorithm for Conservative and Dissipative Mechanical Systems , 2000 .

[15]  Ignacio Romero,et al.  Energy-Entropy-Momentum integration of discrete thermo-visco-elastic dynamics , 2012 .

[16]  Ignacio Romero,et al.  An objective finite element approximation of the kinematics of geometrically exact rods and its use in the formulation of an energy–momentum conserving scheme in dynamics , 2002 .

[17]  Christian Hesch,et al.  Thermodynamically consistent algorithms for a finite‐deformation phase‐field approach to fracture , 2014 .

[19]  Philip J. Morrison,et al.  A paradigm for jointed Hamiltonian and dissipative systems , 1986 .

[20]  Jerrold E. Marsden,et al.  The Hamiltonian structure of nonlinear elasticity: The material and convective representations of solids, rods, and plates , 1988 .

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

[22]  Jerrold E. Marsden,et al.  Nonsmooth Lagrangian Mechanics and Variational Collision Integrators , 2003, SIAM J. Appl. Dyn. Syst..

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

[24]  G. Quispel,et al.  Geometric integration using discrete gradients , 1999, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[25]  Elena Celledoni,et al.  Preserving energy resp. dissipation in numerical PDEs using the "Average Vector Field" method , 2012, J. Comput. Phys..

[26]  M. Crisfield,et al.  Energy‐conserving and decaying Algorithms in non‐linear structural dynamics , 1999 .

[27]  Donald Greenspan,et al.  Energy and momentum conserving methods of arbitrary order for the numerical integration of equations of motion , 1975 .

[28]  Francisco Armero,et al.  Volume-preserving energy–momentum schemes for isochoric multiplicative plasticity , 2007 .

[29]  Alberto Cardona,et al.  A nonlinear beam element formulation in the framework of an energy preserving time integration scheme for constrained multibody systems dynamics , 2008 .

[30]  T. Laursen,et al.  Energy consistent algorithms for dynamic finite deformation plasticity , 2002 .

[31]  Peter Betsch,et al.  Energy-momentum conserving integration of multibody dynamics , 2007 .

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

[33]  Ignacio Romero,et al.  Energy-consistent time integration for nonlinear viscoelasticity , 2014 .

[34]  Ignacio Romero,et al.  A Characterization of Conserved Quantities in Non-Equilibrium Thermodynamics , 2013, Entropy.

[35]  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 .

[36]  T. Laursen,et al.  DESIGN OF ENERGY CONSERVING ALGORITHMS FOR FRICTIONLESS DYNAMIC CONTACT PROBLEMS , 1997 .

[37]  Ignacio Romero,et al.  Algorithms for coupled problems that preserve symmetries and the laws of thermodynamics Part II: fractional step methods , 2010 .

[38]  M. A. Crisfield,et al.  An energy‐conserving co‐rotational procedure for the dynamics of shell structures , 1998 .