An affine formulation for the self-consistent modeling of elasto-viscoplastic heterogeneous materials based on the translated field method

Abstract

is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. AbstractThe modeling of heterogeneous materials with an elasto-viscoplastic behavior is generally complex because of the differential nature of the local constitutive law. Indeed, the resolution of the heterogeneous problem involves space-time couplings which are generally difficult to estimate. In the present paper, a new homogenization model based on an affine linearization of the viscoplastic flow rule is proposed. First, the heterogeneous problem is written in the form of an integral equation. The purely thermoelastic and purely viscoplastic heterogeneous problems are solved independently using the self-consistent approximation. Using translated field techniques, the solutions of the above problems are combined to obtain the final self-consistent formulation. Then, some applications concerning two-phase fibre-reinforced composites and polycrystalline materials are presented. When compared to the reference solutions obtained from a FFT spectral method, a good description of the overall response of heterogeneous materials is obtained with the proposed model even when the viscoplastic flow rule is highly non-linear. Thanks to this approach, which is entirely formulated in the real-time space, the present model can be used for studying the response of heterogeneous materials submitted to complex thermo-mechanical loading paths with a good numerical efficiency.

A comparison between different numerical methods for the modeling of polycrystalline materials with an elastic–viscoplastic behavior

“…[12,13,15,16]). In the present work, the self-consistent model recently developed by Mareau and Berbenni [20] is considered. This model is based upon an affine linearization procedure of the viscoplastic flow rule:ε…”

“…In the model of Mareau and Berbenni [20], a specific form of the integral equation is derived by introducing fluctuations (δc and δb) for both the elastic and viscoplastic moduli:…”

“…In the approach of Mareau and Berbenni [20], the self-consistent solutions obtained for the purely elastic and purely viscoplastic heterogeneous problems are combined using translated field techniques to deduce the final strain rate localization rule: …”

“…The self-consistent problem can then be solved in the Laplace-Carson space before proceeding to the inversion of the solution to the real time space. On the other hand, interval variable models are entirely formulated in the real-time space [13,14,15,16,17,18,19,20]. They are based on a set of internal variables whose introduction allows accounting for the interactions associated with the space-time couplings.…”

Mechanical behaviors of irradiated FCC polycrystals with nanotwins

“…In comparison, the EVPSC method is suitable for predicting the effective macroscopic behaviors of heterogeneous materials, and has been widely used to model the elastic-viscoplastic behaviors of polycrystals (Berbenni et al, 2004;Mercier and Molinari, 2009;Mareau and Berbenni, 2015). For instance, based on an affine linearization of the viscoplastic flow rule, Mareau and Berbenni (2015) recently proposed a homogenization model, which has been verified suitable to study the behavior of heterogeneous materials under complex thermo-mechanical loading conditions. Here, the EVPSC method (Paquin et al, 1999;Sabar et al, 2002) is applied to predict the macroscopic behaviors of irradiated polycrystals with nanotwins.…”