Finite strain micromechanical analysis for thermoelastoplastic multiphase materials

Abstract

A micromechanical model that is based on the homogenization technique for periodic composites is developed for the prediction of the response of multiphase materials undergoing large deformations. Every one of the constituents is supposed to be either a rate-independent thermoelastoplastic material or a thermoelastic one, both of which are formulated in the framework of finite strains. Hyperelastic constituents are obtained as a special case. The resulting macroscopic (global) constitutive equations of the composite involve the instantaneous mechanical and thermal tangent tensors. The reliability of the prediction is examined by comparisons with the composite cylinder assemblage model, which is formulated for a finite strain rate-independent thermoplasticity and is valid under axisymmetric loading. Applications are given for a system of a rubber-like matrix reinforced by metallic fibers. In addition, the behavior of rate-independent elastoplastic laminated materials undergoing large deformations and subjected to in-plane loading is investigated. Finally, the response of an elastoplastic auxetic metallic material, which is capable of generating a negative Poisson's ratio at any stage of a finite strain loading is examined by employing the proposed micromechanical model.

The Effect of Evolving Damage on the Finite Strain Response of Inelastic and Viscoelastic Composites

“…The Lie derivative of ${\mathrm{bold-italicB}}^e$ can be expressed in the form [13] $\begin{array}{c}trueright{L}_v\left[{\mathit{B}}^e\right]=\mathrm{bold-italicF}{\dot{\mathrm{bold-italicC}}}^{p-1}{\mathrm{bold-italicF}}^T\end{array}$ It is worth mentioning that the flow rule (10) is identical to the one used in the book by Bonet and Wood [26], and the von Mises plasticity is readily obtained from Equation 8 by setting $D=0$. The finite strain plastic flow rule of Simo and Hughes [13] that was employed by Aboudi [27] however is given, apart from a numerical coefficient, by Equation 10 but with ${\left[{\mathrm{bold-italicB}}^e\right]}^{-1}$ on the left-hand-side replaced by ${\left(trace\left[{\mathrm{bold-italicB}}^e\right]\right)}^{-1}$. It is worth mentioning that both the present and Simo and Hughes [13] flow rules provide almost identical responses of the ductile material that is specified in the following when it is subjected to uniaxial stress loading.…”

“…The finite strain HFGMC micromechanical model predictions were assessed verified by comparison with analytical and numerical large deformation solutions by Aboudi and Pindera [ 29 ], Aboudi [ 27 ] and Aboudi [ 2 ] for elastic, elastoplastic and elastic composite in which the Mullins damage effect is incorporated with the hyperelastic constituents, respectively.…”