Gradient damage models can be acknowledged as a unified framework of dynamic brittle fracture. As a phase-field approach to fracture, they are gaining popularity over the last few years in the computational mechanics community. This paper concentrates on a better understanding of these models. We will highlight their properties during the initiation and propagation phases of defect evolution. The variational ingredients of the dynamic gradient damage model are recalled. Temporal discretization based on the Newmark- $$\beta $$ β scheme is performed. Several energy release rates in gradient damage models are introduced to bridge the link from damage to fracture. An antiplane tearing numerical experiment is considered. It is found that the phase-field crack tip is governed by the asymptotic Griffith’s law. In the absence of unstable crack propagation, the dynamic gradient damage model converges to the quasi-static one. The defect evolution is in quantitative accordance with the linear elastic fracture mechanics predictions. These numerical experiments provide a justification of the dynamic gradient damage model along with its current implementation, when it is used as a phase-field model for complex real-world dynamic fracture problems.

In this paper we present a family of gradient-enhanced continuum damage models which can be viewed as a regularization of the variational approach to fracture capable of predicting in a unified framework the onset and space-time dynamic propagation (growth, kinking, branching, arrest) of complex cracks in quasi-brittle materials under severe dynamic loading. The dynamic evolution problem for a general class of such damage models is formulated as a variational inequality involving the action integral of a generalized Lagrangian and its physical interpretation is given. Finite-element based implementation is then detailed and mathematical optimization methods are directly used at the structural scale exploiting fully the variational nature of the formulation. Finally, the link with the classical dynamic Griffith theory and with the original quasi-static model as well as various dynamic fracture phenomena are illustrated by representative numerical examples in quantitative accordance with theoretical or experimental results.

The main objective of this paper is to numerically investigate the use of fiber-dependent viscosity models in injection molding simulations of short fiber reinforced thermoplastics with latest commercial software. We propose to use the homogenization-based anisotropic rheological model to take into account flow-fiber coupling effects. The 4th-order viscosity tensor is approximated by an optimal scalar model and then implemented in the Moldflow Insight API framework. Numerical simulations are performed for a test-case rectangular plate with three fiber orientation models. The resulting coupled flow kinematics and fiber evolutions are then compared to the standard uncoupled simulations. Interpretations are given based on detailed post-processing of the field results. Certain deformation conditions are expected to be better taken into account, which may also in return lead to an improved fiber orientation prediction. Preliminary confrontation between flow-fiber coupled simulations and existing experimental data is then presented at the end of the paper.