A micromechanical model of distributed damage due to void growth in general materials and under general deformation histories

Abstract

SUMMARYWe 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. Copyright © 2012 John Wiley & Sons, Ltd.

A massively parallel implementation of the Optimal Transportation Meshfree method for explicit solid dynamics

“…The first example is a typical Taylor bar impact test designed to validate the micromechanical constitutive model of internal damage formation by void growth within ductile materials at high strain rate . A three‐dimensional right circular rod of aluminum alloy 1100‐0 impacting axially against a rigid boundary at velocity between 100 and 300 m/s is simulated using the MPI parallization of OTM described in Section 3.1.…”

“…The model contains 8599 degrees of freedom and 30,448 material points for the 15° slice at the continuum level, shown in Figure (a and b). In the microscopic scale, each material point represents a single hollow sphere . Therefore, the material response at a material point is calculated by solving a boundary value problem using the Finite Element Method.…”

Discrete Averaging Relations for Micro to Macro Transition

“…This approach is capable of dealing with general geometries, materials, and loading conditions, and takes into consideration the evolution of the microstructure. It has been successfully applied to a wide range of problems, including composites (Feyel and Chaboche, 2000;Terada et al, 2000), polycrystalline materials (Miehe et al, 1999(Miehe et al, , 2002Blanco et al, 2014), elastic and plastic porous media (Smit et al, 1998;Reina et al, 2013), quasi-brittle separation laws (Nguyen et al, 2011) and wave propagation in metamaterials (Pham et al, 2013).…”

A Large Strains Finite Element Multiscale Approach

“…However, only a few are dealing with large strains. Thus, there are multiscale approaches dealing with small strains [1,2,3,4,5,6], ductile damage [7], plasticity [8,9,10], quasi-brittle materials [11,12,13,14], laminates [15], filament-wound composites [16], shape memory alloy composites [17],randomly distributed heterogeneities [18], fracture [19,20,21,22,23,24], fracturing reinforced composites based in an embedded cell methodology [25], for the solution of granular materials problems with periodically repeated aggregate configurations [26]. A computational multiscale technique using shells for system of heterogeneous thin sheets with in-plane quadrature points at the macroscale was proposed by [27].…”