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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. In particular, although occasionally used conjecturally, the notion of fiber entanglements in athermal networks is not well defined, nor it is clear what role entanglements play in athermal network mechanics. The primary contribution of this work is the introduction of a measure of the degree of entanglement of a system of random athermal fibers, and the definition of its relationship with the mechanical behavior of the network. Entanglements confine the fibers during tensile loading, reduce the auxetic effect in mat-like networks, and maintain the inter-fiber contact density. In the absence of this contribution, reduction of the contact density during tensile loading due to auxeticity results in stress reduction. Entanglements stabilize the network via a tensegrity mechanism similar to that operating in woven materials and lead to network stiffening. The relation between the proposed measure of entanglements and the fiber volume fraction is defined. The effect of inter-fiber friction on the mechanics of entangled mat-like non-crosslinked fiber networks is also evaluated.

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. The size effect is more pronounced in non-affine than in affine networks and decreases slowly when the model size increases. In order to eliminate this effect, models lager than can be effectively solved with current computers have to be considered. To address this issue, we propose a method that allows using relatively small models, while accurately predicting the small and large strain behaviors of the network. The method is based on the generalized boundary conditions introduced in (Glüge 2013, Computational Materials Science 79, 408–416), which are being adapted here to the requirements imposed by fibrous materials.

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. At smaller distances, the nonlocal nature of fiber interactions modifies the solution.

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. We conclude that the network strength scales linearly with the cross-link number density and with the cross-link strength for a broad range of network parameters, and for both types of networks considered. Network strength is independent of fiber material properties and of fiber tortuosity. This information can be used to design fiber networks for specified strength and, generally, to understand the mechanical behavior of fibrous materials.

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. It is observed that once the stress is normalized by the strength measured in uniaxial tension, the failure surface becomes approximately independent of network parameters. This extends the relation between strength and network parameters previously established in (S. Deogekar, M. R. Islam, R. C. Picu, Parameters controlling the strength of stochastic fibrous materials, Int. J. Solids Struct., 2019, 168, 194–202) to the multiaxial case. The failure surface depends on both first two invariants of the stress. Strongly non-affine networks behave somewhat different from the affine networks under loadings close to the hydrostatic and pure shear loading modes, while the difference disappears in the first quadrant of the principal stress space. The results are compared with experimental data from the literature.

We study the effect of inter-fiber adhesion on the mechanical behavior of cross-linked ran- dom fiber networks in two dimensions. To this end, we consider networks with connectiv- ity number, z , below, at, and above the isostaticity limit of the structure without adhesion, z c . Fibers store energy in the axial and bending deformation mode and the cross-links are of freely rotating type. Adhesive forces lead to fiber bundling and to a reduction of the total volume of the network. The degree of shrinkage is determined as a function of the strength of adhesion and network parameters. The mechanical response of these struc- tures is further studied in uniaxial tension and compression. The stress-strain curves of networks without inter-fiber adhesion exhibit an initial linear regime, followed by strain stiffening in tension and strain softening and strain localization in compression. In pres- ence of adhesion, the response becomes more complex. The initial linear regime persists, with the effective modulus decreasing and increasing with increasing adhesion in cases with z > z c and z z c subjected to tension strain-stiffen at rates that depend on the adhesion strength, but eventually enter a large strain/stress regime in which the response is independent of this parameter. Networks with z z c case, increasing the adhe- sion strength reduces the linear elastic modulus and significantly increases the range of the linear regime, delaying strain localization. This first investigation of the mechanics of cross-linked random networks with inter-fiber adhesion opens the door to the design of soft materials with novel properties.

Mycelium, the root structure of fungi, grows naturally as a biodegradable filamentous material. This unique material has highly heterogeneous microstructure with pronounced spatial variability in density and exhibits strongly non-linear mechanical behavior. In this work we explore the material response in compression, under cyclic deformation, and develop an experimentally-validated multiscale model for its mechanical behavior. The deformation localizes in stochastically distributed sub-domains which eventually percolate to form macroscopic bands of high density material. This is reflected in the stress-strain curve as strain softening. Cycling at fixed macroscopic strain leads to deformation history dependence similar to the Mullins effect. To capture this behavior, we use a two-scale model. At the micro-scale, a random fiber network is used, while at the macroscale the spatial density fluctuations are captured using a stochastic continuum model. The density-dependent local constitutive behavior is defined by the microscale model. An empirical damage model is incorporated to account for the experimentally observed cyclic softening behavior of mycelium. The model is further validated by comparison with a separate set of experimental results. The model can be used to explore the effect of mesoscale density fluctuations on the overall mechanical behavior and to design mycelium-based products with desired mechanical performance. Keywords: Mycelium, Fibrous materials, Mullins effect, Cyclic loading, Constitutive modeling

The development of yarns composed primarily from carbon nanotubes (CNTs) has been pursued recently with the intent of transferring to the yarn the exceptional mechanical and transport properties of individual nanotubes. In this work we study the process of yarn formation by dry stretching buckypaper, and the mechanical behavior of the resulting yarns, function of the CNT length and of the state of the CNT assembly before stretching. The analysis is performed using a coarse grained, bead-spring representation for individual CNTs. It begins with a random buckypaper structure composed from CNTs of diameter 13.5 A. This structure is stretched to form a yarn. This occurs once the stretch ratio becomes larger than a threshold which depends on the CNT length. At the threshold, adhesion stabilizes a highly aligned packing of CNT bundles. Packing defects and pores, reminiscent of the initial structure of the buckypaper, are incorporated in the yarn. The yarn is further tested in uniaxial tension. The defects have little effect on the mechanical behavior of the resulting yarns. However, the behavior depends sensitively on the degree of packing of the CNTs in the sub-bundles forming the yarn. Therefore, the initial structure of the buckypaper has little effect on the performance of the yarn. Increasing the CNT length increases the yarn flow stress and this is associated with the residual tortuosity of the CNTs in the yarn. Decreasing the temperature or increasing the strain rate lead to a small increase of the flow stress. These results have implications for yarn design, which are discussed in the article.

This work investigates the mechanical behavior of mycelium composites reinforced with biodegradable agro-waste particles. In the composite, the mycelium acts as a supportive matrix which binds reinforcing particles within its filamentous network structure. The compressive behavior of mycelium composites is investigated using an integrated experimental and computational approach. The experimental results indicate that the composite mimics the soft elastic response of pure mycelium at small strains and demonstrates marked stiffening at larger strains due to the densification of stiff particles. The composite also exhibits the characteristic stress softening effect and hysteresis under cyclic compression previously observed for pure mycelium. To gain further insight into the composite behavior, a three-dimensional finite element model based on numerical homogenization technique is presented. Model validation is performed by direct comparison with experiments, and a parametric study of the effect of mycelium density and particle size is discussed.

Damage accumulation and failure in random fiber networks is of importance in a variety of applications, from design of synthetic materials, such as paper and non-wovens, to accidental tearing of biological tissues. In this work we study these processes using three-dimensional models of athermal fiber networks, focusing attention on the modes of failure and on the relationship between network strength and network structural parameters. We consider network failure at small and large strains associated with the rupture of inter-fiber bonds. It is observed that the strength increases linearly with the network volume fraction and with the bond strength, while the stretch at peak stress is inversely related to these two parameters. A small fraction of the bonds rupture before peak stress and this fraction increases with increasing failure stretch. Rendering the bond strength stochastic causes a reduction of the network strength. However, heterogeneity retards damage localization and increases the stretch at peak stress, therefore promoting ductility.

The transition from elastic to fully plastic deformation under monotonic loading is studied in heterogeneous materials with stochastic microstructure. The yield stress is defined on the local scale as a random field of specified mean, variance and correlation length, while all other elastic-plastic material parameters are deterministic and constant over the problem domain. The elastic-plastic transition is gradual and the range of strains over which it takes place depends on the yield stress variance (the contrast) and on strain hardening. The plastic heterogeneity leads to fluctuations in the hydrostatic stress and triaxiality fields. Large local triaxiality values result during the transition, particularly for materials with high contrast and low strain hardening. This is expected to favor void nucleation and growth with implications for the subsequent plastic deformation. Reducing the model size in one direction leads to a size effect which becomes pronounced once the respective dimension decreases below ∼10 correlation lengths of the input yield stress field. The elastic-plastic transition is broader and the level of triaxiality is reduced in the thinner samples. Therefore, the effect of heterogeneity is reduced in samples of smaller dimensions. This represents a potential mechanism for the experimentally observed increased ductility of bulk brittle polymers when put in thin fiber form, and for the 3D to 2D crazing transition in thin polymeric films.

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. The monotonic mechanical behavior of the mycelium is non-linear both in tension and compression. The material exhibits considerable strain hardening before rupture under tension, it mimics the open cell foam behavior under compression and exhibits hysteresis and the Mullins effect when subjected to cyclic loading. Based on our morphological characterization and experimental observations, we develop and validate a multiscale fiber network-based model for the mycelium which reproduces the tensile and compressive behavior of the material.

The mechanical behavior of random fiber networks containing inclusions is studied in this work. Inclusions are considered spherical and of radius comparable to the network mean segment length. Their stiffness is varied in a broad range, from very soft to rigid. It is observed that the presence of inclusions modifies the small strain stiffness of the network but does not change the functional form of the non-linear part of the stress-strain curve which, therefore, remains independent of the inclusion stiffness. Soft, bending-dominated networks can be reinforced more efficiently than the stiffer and more affinely deforming axially dominated networks. The variation of the composite modulus with the stiffness of inclusions does not follow the prediction of continuum homogenization theory. Numerical data that allow predicting the homogenized stiffness are presented.

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. The variation of structural parameters such as the mat thickness and the mean segment length between contacts along given fibers with the strength of adhesion is determined. These systems are largely dissipative in that most of the work performed during deformation is dissipated frictionally and only a small fraction is stored as strain energy. The response of the mats to tensile loading has three regimes: a short elastic regime in which no sliding at contacts is observed, a well-defined sliding regime characterized by strain hardening, and a rapid stiffening regime at larger strains. The third regime is due to the formation of stress paths after the fiber tortuosity is pulled out and is absent in mats of finite length fibers. Networks of finite length fibers lose stability during the second regime of deformation. The scaling of the yield stress, which characterizes the transition between the first and the second regimes, and of the second regime's strain hardening modulus, with system parameters such as the strength of adhesion and friction and the degree of fiber tortuosity are determined. The strength of mats of finite length fibers is also determined as a function of network parameters. These results are expected to become useful in the design of electrospun mats and other planar fibrous non-cross-linked networks.

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. In the presence of inclusions, the small strain modulus increases, while the ability of the network to strain stiffen decreases relative to the unfilled network case. The reinforcement induced by fillers is most pronounced in sparse networks of floppier filaments that deform in the bending-dominated mode in the unfilled state. As the unfilled network density or the bending stiffness of fibers increases, the effect of filling diminishes rapidly. Fillers lead to a transition from the soft, bending-dominated, to the stiffer, stretching-dominated, deformation mode of the network, a transition which is primarily responsible for the observed overall reinforcement. The confinement, i.e., the restriction on network kinematics imposed by fillers, causes this transition. These results provide a justification for the observed difference in reinforcement obtained in sparsely versus densely cross-linked networks at a given filling fraction and provide guidance for the further development of network-based materials.

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. In this study, we investigate the effect of the elastic heterogeneity of the matrix on such toughening mechanisms and observe that increasing the elastic heterogeneity amplifies the effect. The analysis is relevant for bone, which is a highly heterogeneous hierarchical material, in which localized plastic deformation has been recently shown to occur at dilatational bands. Understanding toughening in bone is a subject of current interest in the context of age-related fragility. The heterogeneity-enhanced eigenstrain toughening effect is of interest for a broad range of engineering applications.

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. These are softer than the reference PV networks at the same nominal network parameters such as density, cross-link density, fiber diameter, and connectivity number. Their response is linear elastic over a broad range of strains, unlike PV networks that exhibit a gradual increase of the tangent stiffness starting from small strains. NCV networks exhibit much smaller Poisson contraction than any network of same nominal parameters. Interestingly, the strength of NCV networks increases continuously with an increasing degree of nonconvexity of the cells. These exceptional properties render this class of networks of interest in a variety of applications, such as tissue scaffolds, nonwovens, and protective clothing.

We report that the mechanical behavior of Twinning-Induced Plasticity steel deformed at different strain rates depends on the scale of observation. Slower-deformed samples have a higher twin density, which leads to larger flow stress measured in a macroscopic uniaxial test. When probed at the nanoscale by nano-indentation, samples pre-deformed at smaller strain rates exhibit systematically smaller hardness than samples pre-deformed at higher rates. The hardness-based nanoscale strain rate sensitivity is positive. The strain rate sensitivity measured by micro-hardness shifts to negative values as the indenter size and the probed volume increase. The effect is linked to the dislocation-twin interaction mechanism. (C) 2016 Elsevier B.V. All rights reserved.

This article presents a numerical study of the mechanical behavior of particulate composites with stochastic composition. Two types of such materials are considered: composites with homogeneous elastic–plastic matrix and randomly distributed inclusions of stiffness sampled from a distribution function, and composites with matrix having spatially varying elastic–plastic material parameters with no inclusions as well as with randomly distributed identical inclusions. We observe that the presence of fluctuations in either inclusions or matrix material properties leads to smaller effective modulus, smaller strain hardening and a reduction of the yield stress of the composite. Fluctuations of the yield stress of the matrix leads to a significant reduction of the mean yield stress of the composite. Fluctuations of the elastic modulus and of the strain hardening are associated with the reduction of the mean of the distributions of elastic modulus and strain hardening of the composite. For the range of parameters considered, fluctuations lead to maximum principal stress fields with narrow distribution of values, which implies enhanced resistance to damage initiation. Increasing the variance of the distribution functions from which local material properties are sampled, while keeping the mean constant, renders these effects more pronounced. This study is motivated by the growing interest in additive manufacturing technologies which open new possibilities for designing composite materials.

In this work we study the response of AA5182 to rolling, with emphasis on the effect of severe plastic deformation followed by heat treatment on the strain rate sensitivity of the material. Three rolling techniques are compared namely symmetric rolling, continuous and reversed asymmetric rolling and the subsequent heat treatment is performed at 195 °C for times ranging from 30 to 120 mins. The strain rate sensitivity is unaffected by rolling for rolling reductions smaller than 50%. For larger reductions it increases gradually, but remains negative even for reductions as high as 90%. The schedule of the heat treatment makes a difference only for samples with 90% reduction. In these cases the yield stress of symmetrically rolled samples decreases with increasing annealing time, while that of asymmetrically rolled samples increases under the same conditions. Microstructural observations indicate that the grain size decreases continuously, being more pronounced for reductions larger than 50%. Rolling introduces low angle grain boundaries at reductions below 50%, which transform in high angle boundaries at higher reductions. Nanoscale grains are obtained with all rolling methods at 90% reduction. Several mechanisms that may cause the increase of the strain rate sensitivity parameter for reductions larger than 50% are discussed. Keywords: Aluminum alloys, Asymmetric rolling, Severe plastic deformation, Strain rate sensitivity, Heat treatment, Microstructure

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. Here we study bundles in which filaments do not break, while bundle rupture happens by the failure of inter-filament crosslinks, followed by pull-out. In all cases, the crosslinks are randomly distributed along interfaces. The strength of such bundles depends on material parameters of the filaments and crosslinks, such as their stiffness and strength, and on the cross-link density. We focus on the dependence of the bundle strength on two parameters: filament waviness and filament staggering. Bundles with regular staggering are stronger than those with stochastic staggering. We identify the optimal regular staggering that maximizes the strength. Filament waviness increases the strength of stochastically staggered bundles at constant crosslink density but decreases the strength of regularly staggered bundles. Results for bundles with permanent crosslinks, which never reform once they break, as well as transient crosslinks capable of reforming during deformation are presented, and it is shown that the general trends are independent of the nature of the crosslinks. The results are discussed in the context of collagen and carbon nanotube bundles.

Fiber-based materials are prevalent around us. While microscopically these systems resemble a discrete assembly of randomly interconnected fibers, the network architecture varies from one system to another. To identify the role of the network architecture, we study here cellular and fibrous random networks in tension and compression, and in the context of large strain elasticity. We observe that, compared to cellular networks of same global parameter set, fibrous networks exhibit in tension reduced strain stiffening, reduced fiber alignment, and reduced Poisson's contraction in uniaxial tension. These effects are due to the larger number of kinematic constraints in the form of cross-links per fiber in the fibrous case. The dependence of the small strain modulus on network density is cubic in the fibrous case and quadratic in the cellular case. This difference persists when the number of cross-links per fiber in the fibrous case is rendered equal to that of the cellular case, which indicates that the different scaling is due to the higher structural disorder of the fibrous networks. The behavior of the two network types in compression is similar, although softening induced by fiber buckling and strain localization is less pronounced in the fibrous case. The contribution of transient interfiber contacts is weak in tension and important in compression.

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. The range of system parameters leading to each of these states is identified. The network of bundles is subisostatic and is stabilized by prestressed triangular features forming at bundle-to-bundle nodes, similar to the situation in foams. Interfiber friction promotes locking and expands the parametric range of nonevolving systems.

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. The system of fibers self-organizes in one of three types of structures: locked networks, in which fibers remain in the as-deposited state, cellular networks, in which fibers form bundles and these organize into a larger scale network, and disintegrated networks, in which the network of bundles becomes disconnected. We determine the parametric space corresponding to each of these structures. Further, we identify a triangular structure of bundles, similar to the Plateau triangle occurring in foams, which stabilizes the network of bundles and study in detail the stabilization mechanism. The analysis provides design guidelines and a physical picture of the stability and structure of random fiber networks with adhesion.

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. The objective of the present work is to provide additional insight into this relationship. To this end, results from models of random collagen networks are compared with experimental data on reconstructed collagen gels, mouse skin dermis, and the human amnion. Attention is devoted to the mechanism leading to the large Poisson's effect observed in experiments. The results indicate that the incremental Poisson's contraction is directly related to preferential collagen orientation. The experimentally observed downturn of the incremental Poisson's ratio at larger strains is associated with the confining effect of fibers transverse to the loading direction and contributing little to load bearing. The rate of collagen orientation increases at small strains, reaches a maximum, and decreases at larger strains. The peak in this curve is associated with the transition of the network deformation from bending dominated, at small strains, to axially dominated, at larger strains. The effect of fiber tortuosity on network mechanics is also discussed, and a comparison of biaxial and uniaxial loading responses is performed.

The classical approach to linking lattice dynamics properties to continuum equations of motion, the "method of long waves," is extended to include higher order terms. The additional terms account for non-local and non-linear effects. In the first part of the article, the derivation is made within the harmonic approximation for the perfect lattice response. Higher order terms are included in the continuum equation of motion to account for non-linear dispersion effects. Wave propagation coefficients as well as fourth order dispersion coefficients are obtained. In the second part, the lattice anharmonicity is considered and nonlinear macroscopic equations of motion are obtained within the local approximation. Both continuum solutions are particularized to the one-dimensional case and are compared with the lattice response in order to establish the accuracy of the approximation.

In this work we develop anisotropic first and second order displacement gradient linear elastic continuum models for two-dimensional random fiber networks. The continuum constitutive parameters are evaluated based on the response of the explicit representation of the network in which each fiber is a beam and the fibers are connected at crossing points with welded joints. The scaling of the first and second order moduli with the network parameters, such as the network density and the ratio of the fiber bending to axial stiffness, is determined. We observe that the dependence of the second gradient moduli on these two parameters is similar to the dependence of the classical moduli on the same parameters. The internal length scales associated with the gradient terms of the constitutive equation are also defined in terms of the network parameters. The influence of the model size on the elastic constants is discussed. We observe that if the model size is large enough for the classical moduli to be size effect free. However, there is still a strong size dependency of the computed internal lengths associated to second order gradient effects.

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. Here, we propose a new three-dimensional ultrastructure volume element model showing the formation of nanoscale dilatational bands based on stress-induced non-collagenous protein denaturation and quantify the total energy released through this mechanism in the vicinity of a propagating crack. Under tensile deformation, large hydrostatic stress develops at the nanoscale as a result of local confinement. This tensile hydrostatic stress supports the denaturation of non-collagenous proteins at organic–inorganic interfaces, which leads to energy dissipation. Our model provides new fundamental understanding of the mechanism of dilatational bands formation and its contribution to bone toughness.

The effect of correlations of the spatial distribution of inclusions in a two-phase composite is studied numerically in this work. Microstructures with fractal distribution of inclusions, characterized by long-range power law correlations, are compared with random inclusion distributions of same volume fraction. The elastic–plastic response of composites with stiff elastic inclusions and elastic–plastic matrix is studied, and it is concluded that fractal microstructures always lead to stiffer composites, with higher strain hardening rates, compared with the equivalent composites with randomly distributed inclusions. Composites with filler distributions characterized by shorter range, exponential correlations exhibit behavior intermediate between that of random and power law-correlated microstructures. Larger variability from replica to replica is observed in the fractal case. The pressure in inclusions is larger in the case of fractal microstructures, indicating that these are expected to be advantageous in applications such as toughening of thermoset polymers which takes place via the cavitation mechanism. The effect of the spatial distribution of inclusions on the effective damping of the composite is also investigated. The matrix is considered elastic and non-dissipative, while inclusions dissipate energy. The composite with fractal microstructure provides more damping than the random microstructure of same filler volume fraction, and the effect increases with increasing fractal dimension. When damping is introduced only in the interfaces between matrix and inclusions, the spatial distribution of fillers becomes inconsequential for the overall composite behavior. These results are relevant for the design of composites with hierarchical multiscale structure.

Bonded random fiber networks are heterogeneous on multiple scales. This leads to a pronounced size effect on their mechanical behavior. In this study we quantify the size effect and determine the minimum model size required to eliminate the size effect for given set of system parameters. These include the network density, the fiber length and the fiber bending and axial stiffness. The results may guide the definition of models and the selection of the size of representative volume elements in sequential multiscale models of fiber networks. To underline the origins of the size effect, we characterize the network heterogeneity by analyzing the geometry of the network (density distribution), the strain field and the strain energy distribution. The dependence of the heterogeneity on the scale of observation and system parameters is discussed.

Slip asymmetry is a common occurrence in some monatomic crystals where it is due to complex core structures or specific packing of slip planes. Here we present another mechanism, based on molecular steric hindrance, which leads to asymmetric dislocation motion in cyclotrimethylenetrinitramine (RDX) molecular crystal. Dislocations move at different critical stresses when shear is applied in the positive and negative directions of the Burgers vector in the slip system that contributes most to plastic deformation.

WOS: 000320831300012, The mechanical properties of commercial dual phase (DP), transformation induced plasticity (TRIP), and high strength low alloy (HSLA-340) steel sheets are investigated and compared at various strain rates ranging from 0.0017 to 0.17 s(-1) at ambient temperature. TRIP steel outperforms the other two materials, having comparable ductility and twice as large strength relative to DP steel. TRIP has larger strength and much larger ductility than HSLA-340. The exceuent ductility of TRIP800 is due to its high strain hardening capability, which promotes stable plastic deformation. It is observed that the strain hardening rate in TRIP800 does not decrease to zero at failure, as common in most materials in which failure is preceded by necking.

The elastic modulus of two-dimensional random fibre networks is determined for structures in which, the degree of cross-linking is varied. The relationship between the network parameters – fibre axial and bending stiffness, fibre density and degree of cross-linking – and the overall elastic modulus is discussed and presented in terms of a master curve. It is shown that master curves for sparsely cross-linked networks with various degrees of cross-linking can be collapsed to a unique curve, which is also valid in case of fully cross-linked network.

A microstructural-based model, describing the plastic behavior of Al-30wt% Zn alloy, is proposed and the effect of solid solution decomposition, Orowan looping, twinning and grain refinement is analyzed. It is assumed that the plastic deformation process is dominated by strain-induced solute diffusion and dislocation motion. To capture the essential physics, a law describing the evolution of the mean free path of dislocations with plastic strain is proposed which reproduces the experimentally observed strain softening.

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. The scaling of the small strain modulus with the network parameters is established. The large strain deformation of these structures is less sensitive to the shape of the cross section.

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 Sr columns located preferentially at twin boundaries. Density functional theory simulations indicate that Sr atoms bind in the Si lattice only along the direction, with preferential positions at first and second nearest neighbors for interstitial and substitutional Sr, respectively. Density functional theory total energy calculations confirm that twin nucleation at Sr columns is energetically favorable. Hence, twins may nucleate in Si precipitates after solidification, which provides a different perspective to the currently accepted mechanism which suggests twin formation during precipitate growth.

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. The effect is due to the fractal nature of the fragmentation process and is not linked to the roughness of individual cracks.

An investigation of the structure and mechanical behavior of melt-spun isotactic polypropylene (iPP) fibers subjected to thermal treatment in an inert atmosphere is described. Two iPP formulations, Basell Pro-fax PH835 and ExxonMobil Achieve 3854, synthesized by the Ziegler-Natta and metallocene catalysts respectively, and spun at take-up velocities of 1000 to 3000 m/min are considered. The evolution of the structure is monitored with WAXS, SAXS, Raman spectroscopy and birefringence measurements. The fibers spun at 1000 m/min are predominantly mesomorphic, while those spun at 3000 m/min are semi-crystalline in the as-spun state. Thermal treatment for 20 min at 145 °C erases the processing history and increases the crystallinity of all samples. It is shown that thermal treatment leads to the formation of a secondary set of kebab lamellae which are thinner than the original ones, separated by thicker lamellae. The spatial variability of the lamellar thickness and of interlamellar spacings is estimated from the SAXS data and it is concluded that the variability is rather pronounced in all samples. Both annealed and non-annealed fibers are subjected to monotonic and cyclic mechanical testing. Large differences are seen in the behavior of non-annealed fibers processed in different conditions. The monotonic mechanical behavior of the annealed fibers is not very much different from that of the corresponding non-annealed fibers. The central difference between annealed and non-annealed samples is observed in the cyclic behavior; annealed samples containing lamellae with bimodal distribution of thickness exhibit bimodal hysteresis curves while this feature is not observed in non-annealed samples.

Cottrell–Stokes-type experiments are performed with AA6022, a heat treatable commercial Al alloy, at different stages of precipitation. It is shown that the ratio of the flow stress at given temperature and that extrapolated to 0 K, measured at given material state, is independent of the strain and of the precipitation state. The ratio depends only on temperature and strain rate. However, when probed using strain rate jump experiments, the Cottrell–Stokes law appears not to be fulfilled in any of these materials, and the strain rate sensitivity parameter depends on the precipitation state. A model based on the interaction of dislocations with populations of obstacles of various types is used to provide an interpretation of the Cottrell–Stokes law. The model indicates that as the dislocation velocity increases, the effective Cottrell–Stokes ratio in systems with various obstacle compositions takes values in a narrow range close to the critical value of 1 (i.e. “microstructure” insensitivity). Conversely, the model suggests that the Cottrell–Stokes ratio should become more sensitive to the microstructure under creep conditions.

A concurrent multiscale method for coupling discrete (atomistic) and continuum models at finite temperatures is presented. Motion of atoms is governed by an inter-atomic potential and is represented by molecular dynamics. A thermo-mechanical continuum defined by standard differential equations of conservation of momentum and heat transport is used. The coupling is performed by an interface region where the two models overlap. The phonon spectrum of the discrete region is divided into a low frequency part which is transferred to the continuum model as mechanical waves, and a high frequency component which is modeled in the continuum as diffusive heat transport. Seamless mechanical coupling is ensured by imposing weak compatibility of displacements in the interface region. The method is implemented in 1D and full bi-directional thermal and mechanical coupling is demonstrated in thermodynamic equilibrium and in non-equilibrium.

WOS: 000283943900012, Mg-rich and Si-rich aluminum alloys from the AA6XXX class are considered to demonstrate that standard heat treatments can be used to produce materials with identical plastic flow (yield stress and strain hardening) and different strain rate sensitivity. The Mg-rich alloy exhibits lower strain rate sensitivity and a different variation of this parameter with the stress (Haasen plot) relative to the Si-rich alloy. This is due to the instantaneous component of the strain rate sensitivity being smaller in the Mg-rich alloy. Hence, the underlying mechanism is not related to the presence of free, fast diffusing Mg atoms, but rather to the different nature of precipitates forming in the two alloys. A simple model is used to demonstrate that it is possible to tailor the strain rate sensitivity while preserving the flow stress by controlling the nature of precipitates and that of the dislocation-precipitate interaction.

The functional form of the equation describing the superposition of contributions to the flow stress due to various strengthening mechanisms is analyzed. Considering that the superposition can be written as a sum to which each mechanism contributes through function f, that the dependence of the critical resolved shear stress on the density of obstacles to dislocation motion is given by function g, and that f and g have the same functional form for all strengthening mechanisms considered, it is shown that these two function are necessarily power functions, and their exponents are related. Furthermore, requiring that the superposition law is valid both at finite temperatures and at 0 K leads to an equivalent expression for the strain rate sensitivity and imposes restrictions on the way in which contributions of various mechanisms to the flow stress are evaluated at finite temperatures.

The mechanical properties of semi-flexible networks have been the subject of intense theoretical and experimental studies concerned primarily with the understanding of the complex behavior of biological systems such as the cell. Here it is shown that the elasticity of these networks, both elastic constants and elastic fields, while fluctuating significantly with position, is long-range correlated and the correlation functions exhibit power law scaling. The correlations are lost when the fiber stiffness is reduced. The range of scales over which correlations are observed is bounded below by the mean fiber segment length and above by the filament persistence length. Therefore, these networks can be regarded as stochastic fractal elastic media over the respective range of scales. This implies that no scale decoupling exists and no representative volume element can be identified on scales below the upper correlation cut-off scale.

The strength of dislocation junctions with segments of unequal length is studied. Such structures are common, while the equivalent symmetric junctions are exceptions. It is shown that varying the length of junction “arms” leads to significant variation of the junction strength and to changes of the failure mechanism. The relative strength of Lomer and glissile junctions may be reversed as the junctions become asymmetric. This increases the variability of the strength of pinning sites a mobile dislocation encounters during glide.

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WOS: 000272119800040, Aluminum-magnesium-silicon (Al-Mg-Si) alloys show medium strength, excellent formability, good corrosion resistance and are widely used in extruded products and automotive body panels. The major advantage of these alloys is their age hardening response during the paint baking process as well as the fact that they exhibit no yield point phenomenon and Ludering. In this study, the mechanical properties of a commercially available AA6061 alloy aged to various levels were studied. Peak-aged conditions were reached in this particular alloy after a 2 h heat treatment at 200 degrees C. The variation of the yield stress, ultimate tensile strength, ductility and strain hardening rate with aging time is measured and discussed in relation to the microstructural changes induced by the heat treatment. (C) 2009 Elsevier Ltd. All rights reserved.

A method for predicting the elastic moduli of a regular network populated by a large number of randomly located defects is presented. The prediction is based exclusively on the stiffness of individual fibers and the location of defects. The method requires a preliminary calibration step in which the eigenstrains associated with “elementary defects” of the regular network are fully characterized. Each type of defect is represented by a superposition of singular point sources in 2D elastostatics producing a field identical to the eigenstrain of the respective defect. The amplitude of the point sources is determined by probing the eigenstrain with a series of path independent integrals. This “spectral decomposition” represents the generalization that allows applying methods developed to account for crack–crack interaction in fracture mechanics to situations in which the interacting sources have eigenstrains obtained by the superposition of multiple types of singularities. Once the representation of each elementary defect is determined, any distribution of defects in the network can be mapped into a distribution of point sources in an equivalent continuum. This allows inferring the elastic behavior of a defective network of any distribution and concentration of defects. The method discussed here provides an efficient way to treat the non-affine deformation of defective regular fiber networks.