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.

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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.

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Reinforced composites are used in many industrial and multi-functional applications. The efficiency of the reinforcements depends mainly on the aspect ratio, material properties, and the adhesion between matrix and reinforcement. Particularly, high aspect ratio fillers and inclusions have gained popularity due to their unique material and geometrical features, where a fundamental understanding of composites hierarchical structure and behavior is crucial for the optimal design and performance. There is however a lack of robust numerical modeling frameworks that are able to accurately represent composites with high aspect ratio reinforcements. Ideally the expensive mesh generation of the standard finite element method or the simplifying assumptions adopted by smeared type or mean-field approaches should be avoided.
A group of numerical techniques here referred to as "embedded methods" eliminate mesh conformity restrictions and significantly reduce the computational cost of the standard finite element method, while still benefiting from the advantages of a direct numerical analysis. In formulating the embedded models, enrichment techniques and different element technologies are considered, and physical assumptions are investigated. Limitations of the classical embedded models are highlighted through numerical examples, on the basis of which possible enhancements are discussed. We specifically highlight the important roles of field gradients continuity/discontinuity and the element size, order, and regularity extensions on the smoothness of the solutions.
A computationally efficient embedded model is then applied to the study of failure and inclusion orientation effects in planar composites. A detailed study is also performed for dense fiber-reinforced composites, where homogenized mechanical properties are extracted and various forms of neutrality of thin fibers are demonstrated. In this context, a part of this thesis is dedicated to one-to-one comparisons between results obtained using the standard finite element method and embedded techniques. This led to a range of model and geometry parameters under which predictions of embedded technique are reliable. Comparisons are reported in terms of homogenized properties and local field variables, namely relative displacement between inclusions and matrix (slips).
Finally as a preliminary step towards multi-functional fiber-based structural batteries, an electro-chemical system characterized by composite cathode in a half cell configuration is considered. The main point of difference with common composite batteries is that active material particles are cast in form of high aspect ratio fibers, which are efficiently discretized by use of the embedded technique. A discrete definition of fibers, unlike the case of mean-field approaches, allows to define local fields and interfacial conditions between fibers and electrolyte and is crucial for the accurate modelling of a battery cell with fiber-based electrodes.@en

We report the results of a comparative analysis of mesh independent discrete inclusion models and point out some shortcomings of classical approaches in the approximation of the strain field across an inclusion (artificial continuity) and the slip profile along an inclusion (oscillatory behavior). We also present novel embedded reinforcement models based on partition of unity enrichment strategies, adaptive h-refinement, and order/regularity extensions. These novel models are assessed by means of mesh convergence studies and it is shown that they improve the quality of the solution by significantly decreasing local spurious oscillations in the slip profile along an inclusion.@en

We report numerical evidence for neutrality of thin fibers to a prescribed uniform stress field in a fiber-reinforced composite. Elastic finite element analyses of fiber-reinforced composites are carried out with a conventional fully-resolved model and a novel dimensionally-reduced fiber model.The two modeling approaches are compared in the analysis of mechanical properties and matrix-fiber slip profiles. An analysis of the effectiveness of various fiber orientations with respect to the loading direction shows that the notion of inclusion neutrality, originally formulated for rigid line inclusions by Wang et al. [Journal of Applied Mechanics, 52(4), 814–822, 1985], holds also for linear elastic thin fibers with imperfect interface.@en

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.

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