Please cite this article as: Czarnota, C., Kowalczyk-Gajewska, K., Salahouelhadj, A., Martiny, M., Mercier, S., Modeling of the cyclic behavior of elastic-viscoplastic composites by the additive tangent Mori-Tanaka approach and validation by Finite Element calculations, International Journal of Solids and Structures (2014), doi: http:// dx.Abstract This work deals with the prediction of the macroscopic behavior of two-phase composites, based on the Mori-Tanaka scheme combined with an additive/sequential interaction rule and tangent linearization of viscoplastic response. Cyclic tension compression loadings are considered to further validate the approach. The composite is made of spherical inclusions dispersed in a matrix. Both materials have an elastic-visco-plastic behavior. In a second part, finite element calculations are performed using ABAQUS/STANDARD software in order to validate the proposed homogenization technique. A representative volume element is analyzed with 30 randomly distributed inclusions. Comparisons between the additive tangent Mori-Tanaka scheme and finite element calculations are made for different volume fractions of inclusions, different contrasts in elastic and viscous properties and different strain rates and strain amplitudes. These comparisons demonstrate the efficiency of the proposed homogenization scheme. The effect of isotropization of the viscoplastic tangent stiffness is also investigated. It is concluded that quality of predictions does not benefit from such simplification, contrary to the known result for elastic-plastic case.

In this paper extensive research on the polyurethane shape memory polymer (PU-SMP) is reported, including its structure analysis, our experimental investigation of its thermomechanical properties and its modelling. The influence of the effects of thermomechanical couplings on the SMP behaviour during tension at room temperature is studied using a fast and sensitive infrared camera. It is shown that the thermomechanical behaviour of the SMP significantly depends on the strain rate: at a higher strain rate higher stress and temperature values are obtained. This indicates that an increase of the strain rate leads to activation of different deformation mechanisms at the micro-scale, along with reorientation and alignment of the molecular chains. Furthermore, influence of temperature on the SMP’s mechanical behaviour is studied. It is observed during the loading in a thermal chamber that at the temperature 20 °C below the glass transition temperature (Tg) the PU-SMP strengthens about six times compared to the material above Tg but does not exhibit the shape recovery. A finite-strain constitutive model is formulated, where the SMP is described as a two-phase material composed of a hyperelastic rubbery phase and elastic-viscoplastic glassy phase. The volume content of phases is governed by the current temperature. Finally, model predictions are compared with the experimental results.

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The paper addresses the problem of suitable approximation of the interaction between phases in heterogeneous materials that exhibit both viscous and elastic properties. A novel approach is proposed in which linearized subproblems for an inhomogeneity-matrix system with viscous or elastic interaction rules are solved sequentially within one incremental step. It is demonstrated that in the case of a self-consistent averaging scheme, an additional accommodation subproblem, besides purely viscous and elastic subproblems, is to be solved in order to estimate the material response satisfactorily. By examples of an isotropic two-phase material it is shown that the proposed approach provides acceptable predictions in comparison with the existing models.

This paper presents experimental and modeling results of the effects of thermomechanical couplings occurring in a polyurethane shape memory polymer (SMP) subjected to tension at various strain rates within large strains. The SMP mechanical curves, recorded using a testing machine, and the related temperature changes, measured in a contactless manner using an IR camera, were used to investigate the polymer deformation process at various loading stages. The effects of thermomechanical couplings allowed the determination of the material yield point in the initial loading stage, the investigation of nucleation and development of the strain localization at larger strains and the estimation of the effects of thermoelastic behavior during the unloading process. The obtained stress-strain and thermal characteristics, the results of the dynamic mechanical analysis and estimated values of the shape fixity and shape recovery parameters confirmed that the shape memory polymer (T g = 45 °C) is characterized by good mechanical and shape memory properties, as well as high sensitivity to the strain rate. The mechanical response of the SMP subjected to tension was simulated using the finite element method and applying the large strain, two-phase model. Strain localization observed in the experiment was well reproduced in simulations and the temperature spots were correlated with the accumulated viscoplastic deformation of the SMP glassy phase.