Energy-Entropy-Momentum integration of discrete thermo-visco-elastic dynamics

A novel time integration scheme is presented for the numerical solution of the dynamics of discrete systems consisting of point masses and thermo-visco-elastic springs. Even considering fully coupled constitutive laws for the elements, the obtained solutions strictly preserve the two laws of thermodynamics and the symmetries of the continuum evolution equations. Moreover, the unconditional control over the energy and the entropy growth have the effect of stabilizing the numerical solution, allowing the use of larger time steps than those suitable for comparable implicit algorithms. Proofs for these claims are provided in the article as well as numerical examples that illustrate the performance of the method.

► We study the dynamics of nonlinear viscoelastic elements with temperature effects.
► Numerical solution with standard integrators does not comply with thermodynamics.
► Novel Energy-Entropy-Momentum method consistent with thermodynamics and symmetries.
► Numerical examples show accuracy and robustness.
► Proposed method is starting point of the infinite dimensional case under development.