Failure process of a bundle of plastic fibers

A Static Damage Constitutive Model of Concrete Based on Microscopic Damage Mechanism

In this article, a microscopic constitutive model is established that includes friction, plastic, and spring elements and has clear physical meaning. The friction unit reflects the mutual friction between crack surfaces, the plastic unit reflects the development of concrete plasticity, and the fracture of the spring unit reflects the formation and expansion of interior cracks in concrete. In addition, the integration of the random field theory into this model uncovers the physical underpinnings of the relationship between concrete's nonlinearity and randomness. The multi-scale modeling of the concrete static damage constitutive model is then realized once the parameters of the random field are discovered using the macro test results. In order to apply the model's applicability in finite element programs, a subroutine was ultimately constructed. The experimental data and the anticipated values from the numerical simulation are in good agreement, supporting the model's realism.

Stochastic models of multi-channel particulate transport with blockage

Particle conveying channels may be bundled together. The limited carrying capacity of the constituent channels may cause the bundle to be subject to blockages. If coupled, the blockage of one channel causes an increase in the flux entering the others, leading to a cascade of failures. Once all the channels are blocked, no additional particles may enter the system. If the blockages are of finite duration, the system reaches a steady state with an exiting flux that is reduced compared to the incoming one. We propose a stochastic model consisting of N _c channels, each with a blocking threshold of N particles. Particles enter the system's open channels according to a Poisson process, with an equally distributed input flux of intensity Λ. In an open channel the leading particle exits at a rate μ and a blocked channel unblocks at a rate [Formula: see text], where [Formula: see text]. We present and explain the methodology of an analytical description of the behavior of bundled channels. This leads to exact expressions for the steady-state output flux, for [Formula: see text], which promises to extend to arbitrary N _c and N. The results are applied to compare the efficiency of conveying a particulate stream of intensity Λ using a single, high capacity (HC) channel with multiple channels of a proportionately reduced low capacity (LC). The HC channel is more efficient at low input intensities, while the multiple LC channels have a higher throughput at high intensities. We also compare [Formula: see text] coupled channels, each of capacity N  =  2 with the corresponding number of independent channels of the same capacity. For [Formula: see text], if [Formula: see text], the coupled channels are always more efficient. Otherwise the independent channels are more efficient for sufficiently large Λ.

Mechanical Characteristics of Bovine Glisson's Capsule as a Model Tissue for Soft Collagenous Membranes

An extensive multiaxial experimental campaign on the monotonic, time- and history-dependent mechanical response of bovine Glisson's capsule (GC) is presented. Reproducible characteristics were observed such as J-shaped curves in uniaxial and biaxial configurations, large lateral contraction, cyclic tension softening, large tension relaxation, and moderate creep strain accumulation. The substantial influence of the reference state selection on the kinematic response and the tension versus stretch curves is demonstrated and discussed. The parameters of a large-strain viscoelastic constitutive model were determined based on the data of uniaxial tension relaxation experiments. The model is shown to well predict the uniaxial and biaxial viscoelastic responses in all other configurations. GC, the corresponding model, and the experimental protocols are proposed as a useful basis for future studies on the relation between microstructure and tissue functionality and on the factors influencing the mechanical response of soft collagenous membranes.

Stochastic mechanical degradation of multi-cracked fiber bundles with elastic and viscous interactions

The mechanics of fiber bundles has been largely investigated in order to understand their complex failure modes. Under a mechanical load, the fibers fail progressively while the load is redistributed among the unbroken fibers. The classical fiber bundle model captures the most important features of this rupture process. On the other hand, the homogenization techniques are able to evaluate the stiffness degradation of bulk solids with a given population of cracks. However, these approaches are inadequate to determine the effective response of a degraded bundle where breaks are induced by non-mechanical actions. Here, we propose a method to analyze the behavior of a fiber bundle, undergoing a random distribution of breaks, by considering the intrinsic response of the fibers and the visco-elastic interactions among them. We obtain analytical solutions for simple configurations, while the most general cases are studied by Monte Carlo simulations. We find that the degradation of the effective bundle stiffness can be described by two scaling regimes: a first exponential regime for a low density of breaks, followed by a power-law regime at increasingly higher break density. For both regimes, we find analytical effective expressions described by specific scaling exponents.

Time-dependent mechanical behavior of human amnion: macroscopic and microscopic characterization

Characterizing the mechanical response of the human amnion is essential to understand and to eventually prevent premature rupture of fetal membranes. In this study, a large set of macroscopic and microscopic mechanical tests have been carried out on fresh unfixed amnion to gain insight into the time-dependent material response and the underlying mechanisms. Creep and relaxation responses of amnion were characterized in macroscopic uniaxial tension, biaxial tension and inflation configurations. For the first time, these experiments were complemented by microstructural information from nonlinear laser scanning microscopy performed during in situ uniaxial relaxation tests. The amnion showed large tension reduction during relaxation and small inelastic strain accumulation in creep. The short-term relaxation response was related to a concomitant in-plane and out-of-plane contraction, and was dependent on the testing configuration. The microscopic investigation revealed a large volume reduction at the beginning, but no change of volume was measured long-term during relaxation. Tension-strain curves normalized with respect to the maximum strain were highly repeatable in all configurations and allowed the quantification of corresponding characteristic parameters. The present data indicate that dissipative behavior of human amnion is related to two mechanisms: (i) volume reduction due to water outflow (up to ∼20 s) and (ii) long-term dissipative behavior without macroscopic deformation and no systematic global reorientation of collagen fibers.

Scaling shift in multicracked fiber bundles

Bundles of fibers, wires, or filaments are ubiquitous structures in both natural and artificial materials. We investigate the bundle degradation induced by an external damaging action through a theoretical model describing an assembly of parallel fibers, progressively damaged by a random population of cracks. Fibers in our model interact by means of a lateral linear coupling, thus retaining structural integrity even after substantial damage. Monte Carlo simulations of the Young's modulus degradation for increasing crack density demonstrate a remarkable scaling shift between an exponential and a power-law regime. Analytical solutions of the model confirm this behavior, and provide a thorough understanding of the underlying physics.

Brittle-to-ductile transition in a fiber bundle with strong heterogeneity

We analyze the failure process of a two-component system with widely different fracture strength in the framework of a fiber bundle model with localized load sharing. A fraction 0≤α≤1 of the bundle is strong and it is represented by unbreakable fibers, while fibers of the weak component have randomly distributed failure strength. Computer simulations revealed that there exists a critical composition α(c) which separates two qualitatively different behaviors: Below the critical point, the failure of the bundle is brittle, characterized by an abrupt damage growth within the breakable part of the system. Above α(c), however, the macroscopic response becomes ductile, providing stability during the entire breaking process. The transition occurs at an astonishingly low fraction of strong fibers which can have importance for applications. We show that in the ductile phase, the size distribution of breaking bursts has a power law functional form with an exponent μ=2 followed by an exponential cutoff. In the brittle phase, the power law also prevails but with a higher exponent μ=9/2. The transition between the two phases shows analogies to continuous phase transitions. Analyzing the microstructure of the damage, it was found that at the beginning of the fracture process cracks nucleate randomly, while later on growth and coalescence of cracks dominate, which give rise to power law distributed crack sizes.

Competition of strength and stress disorder in creep rupture

Based on a fiber bundle model of subcritical fracture with localized load sharing, we show that the interplay of threshold disorder and the inhomogeneous stress field gives rise to a rich dynamics with intriguing aspects. In the model, fibers fail either due to immediate breaking or to a slow damage process. When the disorder is strong, a large amount of damage occurs, which is randomly diffused over the system; however, for weak disorder, a single growing crack is formed, which proceeds in a large number of localized bursts. The microstructure of cracks is characterized by a power-law size distribution, which is analogous to percolation in the regime of diffusive damage; however, it becomes significantly steeper when a single crack dominates. Simulations showed that the size distribution of breaking bursts and of the waiting times in between have a power-law functional form with a load-dependent cutoff. The burst size exponent proved to be independent of the damage process; however, it strongly depends on the external load with a minimum value of 1.75. The waiting time distribution is sensitive to the details of the damage process with an exponent decreasing from 2.0 to 1.4 as bursts get more and more localized to an advancing crack front.

Statistical model with two order parameters for ductile and soft fiber bundles in nanoscience and biomaterials

Traditional fiber bundles models (FBMs) have been an effective tool to understand brittle heterogeneous systems. However, fiber bundles in modern nano- and bioapplications demand a new generation of FBM capturing more complex deformation processes in addition to damage. In the context of loose bundle systems and with reference to time-independent plasticity and soft biomaterials, we formulate a generalized statistical model for ductile fracture and nonlinear elastic problems capable of handling more simultaneous deformation mechanisms by means of two order parameters (as opposed to one). As the first rational FBM for coupled damage problems, it may be the cornerstone for advanced statistical models of heterogeneous systems in nanoscience and materials design, especially to explore hierarchical and bio-inspired concepts in the arena of nanobiotechnology. Applicative examples are provided for illustrative purposes at last, discussing issues in inverse analysis (i.e., nonlinear elastic polymer fiber and ductile Cu submicron bars arrays) and direct design (i.e., strength prediction).

Hierarchical simulations for the design of supertough nanofibers inspired by spider silk

Biological materials such as spider silk display hierarchical structures, from nano to macro, effectively linking nanoscale constituents to larger-scale functional material properties. Here, we develop a model that is capable of determining the strength and toughness of elastic-plastic composites from the properties, percentages, and arrangement of its constituents, and of estimating the corresponding dissipated energy during damage progression, in crack-opening control. Specifically, we adopt a fiber bundle model approach with a hierarchical multiscale self-similar procedure which enables to span various orders of magnitude in size and to explicitly take into account the hierarchical topology of natural materials. Hierarchical architectures and self-consistent energy dissipation mechanisms (including plasticity), both omitted in common fiber bundle models, are fully considered in our model. By considering one of the toughest known materials today as an example application, a synthetic fiber composed of single-walled carbon nanotubes and polyvinyl alcohol gel, we compute strength and specific energy absorption values that are consistent with those experimentally observed. Our calculations are capable of predicting these values solely based on the properties of the constituent materials and knowledge of the structural multiscale topology. Due to the crack-opening control nature of the simulations, it is also possible to derive a critical minimal percentage of plastic component needed to avoid catastrophic behavior of the material. These results suggest that the model is capable of helping in the design of new supertough materials.

Damage process of a fiber bundle with a strain gradient

We study the damage process of fiber bundles in a wedge-shape geometry which ensures a constant strain gradient. To obtain the wedge geometry we consider the three-point bending of a bar, which is modeled as two rigid blocks glued together by a thin elastic interface. The interface is discretized by parallel fibers with random failure thresholds, which become elongated when the bar is bent. Analyzing the progressive damage of the system we show that the strain gradient results in a rich spectrum of novel behavior of fiber bundles. We find that for weak disorder an interface crack is formed as a continuous region of failed fibers. Ahead of the crack a process zone develops which proved to shrink with increasing deformation, making the crack tip sharper as the crack advances. For strong disorder, failure of the system occurs as a spatially random sequence of breakings. Damage of the fiber bundle proceeds in bursts whose size distribution shows a power law behavior with a crossover from an exponent 2.5 to 2.0 as the disorder is weakened. The size of the largest burst increases as a power law of the strength of disorder with an exponent 23 and saturates for strongly disordered bundles.