On the effective behavior of nonlinear inelastic composites: II A second-order procedure

Noël Lahellec (1) , Pierre Suquet (1)

1 LMA - Laboratoire de Mécanique et d'Acoustique [Marseille]

A new method for determining the overall behavior of composite materials comprising nonlinear viscoelastic and elasto-viscoplastic constituents is presented. Part I of this work showed that upon use of an implicit time-discretization scheme, the evolution equations describing the constitutive behavior of the phases can be reduced to the minimization of an incremental energy function. This minimization problem is rigorously equivalent to a nonlinear thermoelastic problem with a transformation strain which is a nonuniform field (not even uniform within the phases). In part I of this paper the nonlinearity was handled using a variational (or secant) technique. In this second part of the study, a proper modification of the second-order procedure of Ponte Castañeda is proposed and leads to replacing, at each time-step, the actual nonlinear viscoelastic composite by a linear viscoelastic one. The linearized problem is even further simplified by using an “effective internal variable” in each individual phase. The resulting predictions are in good agreement with exact results and improve on the predictions of the secant model proposed in part I of this paper.

Mots clés: Homogenization; Nonlinear viscoelasticity; Elasto-viscoplasticity; Second-order method; Hashin–Shtrikman estimates

Domaines: Matériaux et structures en mécanique [physics.class-ph]; Matériaux et structures en mécanique [physics.class-ph]

Noël Lahellec, Pierre Suquet. On the effective behavior of nonlinear inelastic composites: II A second-order procedure. Journal of the Mechanics and Physics of Solids, 2007, 55 (9), pp.1964-1992. ⟨10.1016/j.jmps.2007.02.004⟩. ⟨hal-00214215⟩