A micromechanical model of distributed damage due to void growth in general materials and under general deformation histories
We develop a multiscale model of ductile damage by void growth in general materials undergoing arbitrary deformations. The model is formulated in the spirit of multiscale finite element methods (FE 2), that is, the macroscopic behavior of the material is obtained by a simultaneous numerical evaluation of the response of a representative volume element. The representative microscopic model considered in this work consists of a space-filling assemblage of hollow spheres. Accordingly, we refer to the present model as the packed hollow sphere (PHS) model. A Ritz–Galerkin method based on spherical harmonics, specialized quadrature rules, and exact boundary conditions is employed to discretize individual voids at the microscale. This discretization results in material frame indifference, and it exactly preserves all material symmetries. The effective macroscopic behavior is then obtained by recourse to Hill's averaging theorems. The deformation and stress fields of the hollow spheres are globally kinematically and statically admissible regardless of material constitution and deformation history, which leads to exact solutions over the entire representative volume under static conditions. Excellent convergence and scalability properties of the PHS model are demonstrated through convergence analyses and examples of application. We also illustrate the broad range of material behaviors that are captured by the PHS model, including elastic and plastic cavitation and the formation of a vertex in the yield stress of porous metals at low triaxiality. This vertex allows ductile damage to occur under shear-dominated conditions, thus overcoming a well-known deficiency of Gurson's model.
© 2012 John Wiley & Sons, Ltd. Received 5 September 2011; Revised 19 June 2012; Accepted 1 July 2012. Article first published online: 14 Aug. 2012. The support for this study was provided by the Department of Energy National Nuclear Security Administration under Award Number DE-FC52-08NA28613 through Caltech's ASC/PSAAP Center for the Predictive Modeling and Simulation of High Energy Density Dynamic Response of Materials. This work is performed under the auspices of the US Department of Energy by LLNL under Contract DE-AC52-07NA27344.