Gradient damage modeling of brittle fracture in an explicit dynamics context

Abstract

International audienceIn this contribution we propose a dynamic gradient damage model as a phase-field approach for studying brutal fracture phenomena in quasi-brittle materials under impact-type loading conditions. Several existing approaches to account for the tension-compression asymmetry of fracture behavior of materials are reviewed. A better understanding of these models is provided through a uniaxial traction experiment. We then give an efficient numerical implementation of the model in an explicit dynamics context. Simulations results obtained with parallel computing are discussed both from a computational and physical point of view. Different damage constitutive laws and tension-compression asymmetry formulations are compared with respect to their aptitude to approximate brittle fracture

Crack Path Field and Strain Injection Techniques in Dynamic Fracture Simulations

“…The patterns are remarkably symmetric as expected from the imposed boundary conditions and are found in agreement with those provided by different numerical techniques, e.g. phase-field [11] and gradient damage models [15] but at the expense of a mesh discretization which is around two orders of magnitude finer (cf. Figure 9).…”

“…For instance works involving fracture in dynamic problems have been addressed by Falk et al [7], Pandolfi et al [26], Song and Belytschko [35] and Linder and Armero [16], where cracks are inserted between FE (inter-elemental) and inside the FE support (intra-elemental). Other techniques tackle the strain localization phenomena by considering supra-elemental bands such as phase-field modeling [2,11,19] and gradient damage models [15]. Such techniques led to impressive 2D and 3D results but at the cost of extremely fine FE discretizations which can be regarded prohibitive in a dynamic context where a large amount of time steps need to be resolved in order to capture crack growth with a sufficient time resolution.…”

Numerical investigation of dynamic brittle fracture via gradient damage models

“…This is a plausible hypothesis for brittle materials when large rotations are also not expected. Damage and subsequent fracture occur more easily in tension than in compression, thus tension-compression asymmetry formulations in the sense of [10,11] for instance are in general needed. Nevertheless the numerical experiments considered here do not require the use of such formulations.…”

“…In practice it consists of solving numerically the elastic-damage dynamic wave equation (10) coupled with the total energy minimization (11). The irreversibility condition will be automatically enforced during the bound-constrained minimization process.…”

“…The resulting sharp interface fracture model as → 0 remains unclear and inversely the elliptic regularization of the variational approach to fracture that actually accounts for unilateral contact between crack lips is still considered as a difficult task both from the physical and mathematical point of view, see [10]. Nevertheless, these tension-compression asymmetry formulations as summarized for instance in [11] constitute an improvement of the original gradient damage model [6] and can be regarded as an approximation of the actual non-interpenetration condition.…”