Staff

Abstract:
The aim of this study is to analyse the joint effect of reinforcement shape and packing on the effective behaviour of particulate composites. The proposed semi-analytical modelling method combines the Replacement Mori–Tanaka scheme, by means of which the concentration tensors for non-ellipsoidal inhomogeneities are found numerically, and the analytical morphologically representative pattern approach to account for particle packing. Five shapes of inhomogeneities are selected for the analysis: a sphere, a prolate ellipsoid, a sphere with cavities, an oblate spheroid with a cavity as well as an inhomogeneity created by three prolate spheroids crossing at right angles. Semi-analytical estimates are compared with the results of numerical simulations performed using the finite element method and with the outcomes of classical mean-field models based on the Eshelby solution, e.g. the Mori–Tanaka model or the self-consistent scheme.

Keywords:
composite material, micromechanics, computational modelling, packing effect, shape effect

Abstract:
A cluster interaction model has been proposed to account for the spatial distribution and morphology of particles when estimating the effective properties of elastic and thermoelastic composites (Molinari and El Mouden, 1996). In the present paper this approach is extended to elastic-viscoplastic composites. To this end the tangent linearization of the non-linear viscoplastic law and the concept of additive interaction equation are used. Although the extension is formulated for the non-linear case, first applications are considered for linear viscoelastic composites, a situation rich enough to evaluate the interest of the cluster interaction approach. Results of the model are compared to numerical homogenization for periodic
unit cells with two cubic configurations.

Keywords:
homogenization, the cluster interaction model, elastic-viscoplastic composite, spatial configuration of inclusions, interaction between inclusions

Abstract:
The issue of applicability of the Morphologically Representative Pattern (MRP) approach to elastic-plastic composites is addressed. The extension to the regime of non-linear material behaviour is performed by employing the concept of incremental linearization of the material response in two basic variants: tangent and secant. The obtained predictions are evaluated through comparison with the outcomes of numerical analyses. Finite Element simulations are carried out using periodic unit cells with cubic arrangements of spherical particles and representative volume elements (RVE) with 50 randomly placed inclusions. In addition to the analysis of the packing effect in two-phase composites, the size effect is also studied by assuming an interphase between the matrix and inclusions. It is concluded that the MRP approach can be used as an effective predictive alternative to computational homogenization, not only in the case of linear elasticity but also in the case of elastic-plastic composites.

Keywords:
particulate composites, elastoplasticity, micromechanics, size effect, packing effect, morphologically representative pattern

Abstract:
Effects of particle packing and size on the overall elastic properties of particulate random composites are analyzed. In order to account for the two effects the mean-field Morphologically Representative Pattern (MRP) approach is employed and an additional interphase surrounding inclusions (coating) is introduced. The analytical mean-field estimates are compared with the results of computational homogenization performed using the finite element (FE) method. Periodic unit cells with cubic crystal-type arrangements and representative volume elements with random distributions of particles are used for verification purposes. The validity of the MRP estimates with respect to the FE results is assessed.

Keywords:
Composite materials, Elasticity, Micro-mechanics, Packing and size effects

Abstract:
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.

Keywords:
shape memory polyurethane, thermomechanical couplings, infrared camera, temperature change, dynamic mechanical analysis, strain rate, constitutive model

Keywords:
mean-field modelling, numerical homogenization, elasto-plasticity

Abstract:
Different approaches to model packing and size effects are studied to model overall properties of particulate composites of different morphological features of phase distribution. The micromechanical schemes originating in the composite sphere model and its extension by morphologically-based pattern approach are taken as a basis. Analytical predictions are compared with results of computational homogenization performed on the generated representative volume elements of prescribed statistical characteristics.

Keywords:
micromechanics, morphologically representative pattern, computational homogenization, size and scale effect

Abstract:
A constitutive model of SMP, formulated at large strain format, is developed. SMP is described as a two-phase material composed of a soft rubbery phase and a hard glassy phase. The volume fraction of each phase is postulated as a logistic function of temperature. Identification of model parameters has been performed using the experimental tensile loading-unloading tests with different strain rates conducted at thermal chamber at different temperatures.

Keywords:
shape-memory polymers, two-phase model, large strain framework