Discontinuous and continuous damage evolution in Ogden-type large-strain elastic materials

摘要

The paper presents an application of continuum damage mechanics to large-strain Ogden-type elastic materials. A Eulerian setting of elasticity with isotropic damage-caused softening effect is discussed exclusively in terms of the Finger tensor as a strain measure. The local damage accumulation is related to two phenomenological variables, the maximum value and the arclength of effective free energy attained during a typical loading process. The frame is specified for a rigorously decoupled volumetric-isochoric response based on a multiplicative split of the Finger tensor into spherical and unimodular parts. In this context, the damage is related to the isochoric part of the deformation only, which is assumed to be governed by an Ogden-type effective free-energy function formulated in terms of the eigenvalues of the unimodular part of the Finger tensor. A constitutive algorithm for the computation of the nominal stresses and nominal tangent moduli for plane problems is developed. Finally, some fundamental finite-element simulations for rubber-like materials are presented.