Composite network materials: constitutive behavior and structure-properties relations

Abstract

Composite network materials are heterogeneous and fibrous solids in which a stochastic discrete fiber network forms a load bearing skeleton while a second phase—a surrounding matrix and/or embedded inclusions, shares load and constrains deformation. Many examples of such materials can be found in the biological world: the intracellular cytoskeleton embeds the cellular organelle and the nucleus, the extracellular matrix embeds cells, while implants are developed from reconstituted collagen reinforced with particles. Connective tissue is made from collagen networks embedded in a viscoelastic environment composed of water and various macromolecules (e.g. proteoglycans). Mechanical response of such network composites is controlled not only by constituent stiffness, but by network connectivity, non-affinity, and local compatibility constraints which make the classical particulate composite theory unreliable. This research addresses this unreliability by investigating structure-property relations of the two phases of these network composites to create design criteria where the classical theories are applicable with modifications, introduces their novel constitutive behavior and underlying reasons. This is useful information for design and manufacturing of engineered network composites, and prediction of their stiffness, strength, deformation and damage characteristics. To demonstrate that, an integrated experimental-computational methodology is developed, with collaboration, to study the mechanical behavior of underlying networks with and without embedded inclusion. Therefore, the objective of this work is to develop an understanding of the effect of such additions (matrix and reinforcing fillers) on the mechanical behavior of the network. An application of this research can be the development of more performant collagen-based implants for connective tissue repair. Composite network material models for networks embedded in a continuum matrix make the assumption of no interactions between network and matrix. This research has quantitatively shown that this classical parallel model is valid in some parameter ranges but the network-matrix interaction remains a major influencing factor that controls the composite mechanical behavior in linear and nonlinear deformations. Therefore, a coupled network-matrix model is developed which accounts for the network matrix interaction and explains the underlying parameters that affect such network composite deformation mechanics. The coupled results show that local matrix-network interactions can qualitatively reshape the composite response. The matrix suppresses the local volumetric changes needed for network fiber reorganization, delaying and reducing strain stiffening. In the opposite extreme, an auxetic matrix promotes transverse expansion that counteracts network contraction and can eliminate strain stiffening, producing an extended quasi-linear regime and revealing a kinematic design lever for synthetic fibrous composites. Reinforcement of networks by the addition of inclusions is widely used in application. Therefore, inclusion reinforcement is investigated in composite network materials with variations in network and inclusion parameters. The effects of filler volume fraction and size on small-strain stiffness, nonlinear deformation, damage accumulation, and ultimate strength are quantified across networks of different design parameters. The results show that, relative to the unfilled networks, non-affine networks are more reinforceable in stiffness with increasing filler content, while strength decreases with increasing filler volume fraction; this reduction is linked to increase in inclusion-induced non-affinity and enhanced localization of damage near the inclusion at higher filler volume fraction. A collaborative, integrated computational–experimental effort is developed for the design and manufacturing of nanofiber networks and network composites. The objective is to manufacture networks with controlled structural parameters designed computationally, enabling direct comparison between computational predictions and manufactured specimen responses. Controlled fabrication (e.g., near-field electrospinning) addresses the long-standing barrier of microstructural uncertainty in experiments, while matched computational models enable systematic structure–property evaluation of stiffness, strength, ductility, and toughness. The same framework supports extension to inclusion-embedded networks, providing an essential route for validating field-level predictions relevant to inclusion-driven perturbations in network composites. Finally, a field-based methodology is introduced to quantify inclusion-induced strain perturbations in composite networks. Discrete nodal displacements are mapped onto a fixed continuum triangulation using carefully chosen and accurate interpolation, then converted to strain via a constant-strain-triangle operator to obtain directly comparable strain fields for inclusion embedded network composites and its counterpart without inclusion. The perturbation field is sampled along circular contours and expanded in an angular Fourier fitting; the resulting mode amplitudes provide a compact “spectral footprint” of the perturbation, including dominant quadrupolar symmetry and systematic radial decay. These metrics enable consistent comparison across network architectures and support validation against experimentally manufactured inclusion-embedded networks.