Exact evaluation of dissipation for elastic-damage model dynamics Original Research Article

Some considerations about the finite strains dynamic of dissipative elasto-damage models are presented here. The dynamics of the system are treated taking care of the conservative character of the applied time-stepping algorithm in the sense of preserving the continuum balance equations. These are the linear and angular momentum laws and the expanded power of stress in respect of the Clausius-Duhem inequality. The generalised mid-point rule for time integration and the use of a particular algorithmic form of the symmetric Piola-Kirchhoff stress tensor ensure the exact evaluation of the rate of the Helmoltz free-energy. This algorithm is known as energy-momentum method. The presented constitutive model is suited to describe polymers in finite deformations and with some accomodations appears as a way to investigate strain localization problems. Some simple examples, processed using an object-oriented f.e.m. software, show the effectiveness of the algorithm in this last sense and the character of the constitutive model.