A dispersion of stiff and thin (‘rigid line’) inclusions (RLIs) in a matrix material may result beneficial for stiffening in the elastic range, but might be detrimental to strength, as material instabilities may be triggered by inclusions when the matrix is brought to a viscoplastic-damaging state. This dual role of RLIs is investigated by means of the embedded reinforcement model. Validated against available analytical predictions, this numerical model is employed to assess the roles of RLIs’ orientation, interaction, volume fraction, and distribution, considering up to 1500 inclusions. When the matrix material deforms inelastically, RLIs produce stress concentrations that promote the nucleation of shear bands. These are characterized at collapse for many distributions of RLIs, showing that their effects range from almost negligible to a disrupting alteration of the dominant failure mechanism. In the latter case, it is shown that the dominant shear bands can be fragmented by RLIs into a mosaic of tiny localization bands. These results offer new insights into energy dissipation mechanisms of reinforced materials, as they are promoted or inhibited by the interactions of rigid line inclusions.

Calcium phosphate cements (CPCs) have been widely used during the past decades as biocompatible bone substitution in maxillofacial, oral and orthopedic surgery. CPCs are injectable and are chemically resemblant to the mineral phase of native bone. Nevertheless, their low fracture toughness and high brittleness reduce their clinical applicability to weakly loaded bones. Reinforcement of CPC matrix with polymeric fibers can overcome these mechanical drawbacks and significantly enhance their toughness and strength. Such fiber-reinforced calcium phosphate cements (FRCPCs) have the potential to act as advanced bone substitute in load-bearing anatomical sites. This work achieves integrated experimental and numerical characterization of the mechanical properties of FRCPCs under bending and tensile loading. To this end, a 3-D numerical gradient enhanced damage model combined with a dimensionally-reduced fiber model are employed to develop a computational model for material characterization and to simulate the failure process of fiber-reinforced CPC matrix based on experimental data. In addition, an advanced interfacial constitutive law, derived from micromechanical pull-out tests, is used to represent the interaction between the polymeric fiber and CPC matrix. The presented computational model is successfully validated with the experimental results and offers a firm basis for further investigations on the development of numerical and experimental analysis of fiber-reinforced bone cements.

We propose a computational procedure to assess size effects in nonfunctionalized single-walled carbon nanotube (CNT)-polymer composites. The procedure upscales results obtained with atomistic simulations on a composite unit cell with one CNT to an equivalent continuum composite model with a large number of CNTs. Molecular dynamics simulations demonstrate the formation of an ordered layer of polymer matrix surrounding the nanotube. This layer, known as the interphase, plays a central role in the overall mechanical response of the composite. Due to poor load transfer from the matrix to the CNT, the reinforcement effect attributed to the CNT is negligible; hence the interphase is regarded as the only reinforcement phase in the composite. Consequently, the mechanical properties of the interface and the CNT are not derived since their contribution to the elastic response of the composite is negligible. To derive the elastic properties of the interphase, we employ an intermediate continuum micromechanical model consisting of only the polymer matrix and a three-dimensional fiber representing the interphase. The Young's modulus and Poisson's ratio of the equivalent fiber, and therefore of the interphase, are identified through an optimization procedure based on the comparison between results from atomistic simulations and those obtained from an isogeometric analysis of the intermediate micromechanical model. Finally, the embedded reinforcement method is employed to determine the macroscopic elastic properties of a representative volume element of a composite with various fiber volume fractions and distributions. We then investigate the role of the CNT diameter on the elastic response of a CNT-polymer composite; our simulations predict a size effect on the composite elastic properties, clearly related to the interphase volume fraction.