Evaluation of the parallel coupling constitutive model for biomaterials using a fully coupled network-matrix model.

In this article we discuss the effective properties of composites containing a crosslinked athermal fiber network embedded in a continuum elastic matrix, which are representative for a broad range of biological materials. The goal is to evaluate the accuracy of the widely used biomechanics parallel coupling model in which the tissue response is defined as the additive superposition of the network and matrix contributions, and the interaction of the two components is neglected. To this end, explicit, fully coupled models are used to evaluate the linear and non-linear response of the composite.

Emergence of an apparent yield phenomenon in the mechanics of stochastic networks with inter-fiber cohesion.

In this work we investigate the contribution of inter-fiber cohesion to defining the mechanical behavior of stochastic crosslinked fiber networks. Fibers are athermal and store energy primarily in their bending and axial deformation modes. Cohesion between fibers is defined by an interaction potential.

Stiffening mechanisms in stochastic athermal fiber networks.

Stochastic athermal networks composed of fibers that deform axially and in bending strain stiffen much faster than thermal networks of axial elements, such as elastomers. Here we investigate the physical origin of stiffening in athermal network materials. To this end, we use models of stochastic networks subjected to uniaxial deformation and identify the emergence of two subnetworks, the stress path subnetwork (SPSN) and the bending support subnetwork (BSSN), which carry most of the axial and bending energies, respectively.

Toughness of Network Materials: Structural Parameters Controlling Damage Accumulation.

Many materials have a network of fibers as their main structural component and are referred to as network materials. Their strength and toughness are important in both engineering and biology. In this work we consider stochastic model fiber networks without pre-existing cracks and study their rupture mechanism.

Random Fiber Network Loaded by a Point Force.

This article presents the displacement field produced by a point force acting on an athermal random fiber network (the Green function for the network). The problem is defined within the limits of linear elasticity, and the field is obtained numerically for nonaffine networks characterized by various parameter sets. The classical Green function solution applies at distances from the point force larger than a threshold which is independent of the network parameters in the range studied.

Probing soft fibrous materials by indentation.

Indentation is often used to measure the stiffness of soft materials whose main structural component is a network of filaments, such as the cellular cytoskeleton, connective tissue, gels, and the extracellular matrix. For elastic materials, the typical procedure requires fitting the experimental force-displacement curve with the Hertz model, which predicts that f=kδ and k is proportional to the reduced modulus of the indented material, E/(1-ν). Here we show using explicit models of fiber networks that the Hertz model applies to indentation in network materials provided the indenter radius is larger than approximately 12l, where l is the mean segment length of the network.

Stress relaxation in network materials: the contribution of the network.

Stress relaxation in network materials with permanent crosslinks is due to the transport of fluid within the network (poroelasticity), the viscoelasticity of the matrix and the viscoelasticity of the network. While relaxation associated with the matrix was studied extensively, the contribution of the network remains unexplored. In this work we consider two and three-dimensional stochastic fiber networks with viscoelastic fibers and explore the dependence of stress relaxation on network structure.

Size Effects in Random Fiber Networks Controlled by the Use of Generalized Boundary Conditions.

Materials with a stochastic fiber network as the main structural constituent are broadly encountered in engineering and in biology. These materials are characterized by multiscale heterogeneity and hence their properties evaluated numerically or experimentally are generally dependent on the size of the sample considered. In this work we evaluate the size effect on the linear and non-linear mechanical response of three-dimensional stochastic fiber networks and determine its dependence on material parameters and on the degree of affinity of network deformation.

Strength of stochastic fibrous materials under multiaxial loading.

Many biological and engineering materials are made from fibers organized in the form of a stochastic crosslinked network, and the mechanics of the network controls the behavior of the material. In this work we investigate the strength of stochastic networks without pre-existing damage which fail due to crosslink rupture. Athermal networks ranging from approximately affine to strongly non-affine are subjected to multiaxial loading and the strength is evaluated using numerical models.

Tensile behavior of non-crosslinked networks of athermal fibers in the presence of entanglements and friction.

Many biological and soft artificial materials contain a random network of non-crosslinked fibers as their main structural component. The excluded volume interactions (contact forces) at fiber contacts control the mechanical behavior of these systems. This physics has been studied extensively in compression, but little is known about the relation between network structure and its mechanical response in tension.

Random Fiber Networks With Superior Properties Through Network Topology Control.

In this work, we study the effect of network architecture on the nonlinear elastic behavior and strength of athermal random fiber networks of cellular type. We introduce a topology modification of Poisson-Voronoi (PV) networks with convex cells, leading to networks with stochastic nonconvex cells. Geometric measures are developed to characterize this new class of nonconvex Voronoi (NCV) networks.

Parameters controlling the strength of stochastic fibrous materials.

Many materials of everyday use are fibrous and their strength is important in most applications. In this work we study the dependence of the strength of random fiber networks on structural parameters such as the network density, cross-link density, fiber tortuosity, and the strength of the inter-fiber cross-links. Athermal networks of cellular and fibrous type are considered.

Random fiber networks with inclusions: The mechanism of reinforcement.

The mechanical behavior of athermal random fiber networks embedding particulate inclusions is studied in this work. Composites in which the filler size is comparable with the mean segment length of the network are considered. Inclusions are randomly distributed in the network at various volume fractions, and cases in which fibers are rigidly bonded to fillers and in which no such bonding is imposed are studied separately.

Mechanical behavior of nonwoven non-crosslinked fibrous mats with adhesion and friction.

We present a study of the mechanical behavior of planar fibrous mats stabilized by inter-fiber adhesion. Fibers of various degrees of tortuosity and of infinite and finite length are considered in separate models. Fibers are randomly distributed, are not cross-linked, and interact through adhesion and friction.

Eigenstrain Toughening in Presence of Elastic Heterogeneity with Application to Bone.

Transformation toughening has been used in commercial products for several decades in order to increase the toughness of brittle materials. Composites made from an elastic matrix and elastic-plastic inclusions similarly exhibit increased toughness and R-curve behavior due to the residual stress induced in the wake of the crack tip by the unloaded, plastically deforming fillers. These two mechanisms, in which the eigenstrains in the wake of a major crack lead to toughening, belong to the same class.

Strength of filament bundles - The role of bundle structure stochasticity.

Most biological fibrous materials are hierarchical, in the sense that fibers of finite length assemble in bundles, which then form networks with structural role. Examples include collagen, silk, fibrin and microtubules. Some artificial fiber-based materials share this characteristic, examples including carbon nanotube (CNT) yarns and unidirectional composites.

Filamentary structures that self-organize due to adhesion.

We study the self-organization of random collections of elastic filaments that interact adhesively. The evolution from an initial fully random quasi-two-dimensional state is controlled by filament elasticity, adhesion and interfilament friction, and excluded volume. Three outcomes are possible: the system may remain locked in the initial state, may organize into isolated fiber bundles, or may form a stable, connected network of bundles.

Bone toughening through stress-induced non-collagenous protein denaturation.

Bone toughness emerges from the interaction of several multiscale toughening mechanisms. Recently, the formation of nanoscale dilatational bands and hence the accumulation of submicron diffuse damage were suggested as an important energy dissipation processes in bone. However, a detailed mechanistic understanding of the effect of this submicron toughening mechanism across multiple scales is lacking.

Structural evolution and stability of non-crosslinked fiber networks with inter-fiber adhesion.

Adhesion plays an important role in the mechanics of nanoscale fibers such as various biological filaments, carbon nanotubes and artificial polymeric nanofibers. In this work we study assemblies of non-crosslinked filaments and characterize their adhesion-driven structural evolution and their final stable structure. The key parameters of the problem are the network density, the fiber length, the bending stiffness of fibers and the strength of adhesion.

Publisher Correction: Morphology and mechanics of fungal mycelium.

A correction to this article has been published and is linked from the HTML and PDF versions of this paper. The error has been fixed in the paper.

Poisson's Contraction and Fiber Kinematics in Tissue: Insight From Collagen Network Simulations.

Connective tissue mechanics is highly nonlinear, exhibits a strong Poisson's effect, and is associated with significant collagen fiber re-arrangement. Although the general features of the stress-strain behavior have been discussed extensively, the Poisson's effect received less attention. In general, the relationship between the microscopic fiber network mechanics and the macroscopic experimental observations remains poorly defined.

Morphology and mechanics of fungal mycelium.

We study a unique biomaterial developed from fungal mycelium, the vegetative part and the root structure of fungi. Mycelium has a filamentous network structure with mechanics largely controlled by filament elasticity and branching, and network density. We report the morphological and mechanical characterization of mycelium through an integrated experimental and computational approach.

Structure-properties relation for random networks of fibers with noncircular cross section.

The mechanical behavior of three-dimensional cross-linked random fiber networks composed from fibers of noncircular cross section characterized by two principal moments of inertia is studied in this work. Such fibers store energy in the axial deformation mode and two bending modes of unequal stiffness. We show that the torsional stiffness of fibers becomes important as it determines the relative contribution of the two bending modes to the overall deformation.

Self-organized Sr leads to solid state twinning in nano-scaled eutectic Si phase.

A new mechanism for twin nucleation in the eutectic Al-Si alloy with trace Sr impurities is proposed. Observations made by sub-angstrom resolution scanning transmission electron microscopy and X-ray probing proved the presence of <110> Sr columns located preferentially at twin boundaries. Density functional theory simulations indicate that Sr atoms bind in the Si lattice only along the <110> direction, with preferential positions at first and second nearest neighbors for interstitial and substitutional Sr, respectively.

Interlocking-induced stiffness in stochastically microcracked materials beyond the transport percolation threshold.

We study the mechanical behavior of two-dimensional, stochastically microcracked continua in the range of crack densities close to, and above, the transport percolation threshold. We show that these materials retain stiffness up to crack densities much larger than the transport percolation threshold due to topological interlocking of sample subdomains. Even with a linear constitutive law for the continuum, the mechanical behavior becomes nonlinear in the range of crack densities bounded by the transport and stiffness percolation thresholds.