Scaling shift in multicracked fiber bundles

Thermal effects on fracture and the brittle-to-ductile transition

The fracture behavior of brittle and ductile materials can be strongly influenced by thermal fluctuations, especially in micro- and nanodevices as well as in rubberlike and biological materials. However, temperature effects, in particular on the brittle-to-ductile transition, still require a deeper theoretical investigation. As a step in this direction we propose a theory, based on equilibrium statistical mechanics, able to describe the temperature-dependent brittle fracture and brittle-to-ductile transition in prototypical discrete systems consisting in a lattice with breakable elements. Concerning the brittle behavior, we obtain closed form expressions for the temperature-dependent fracture stress and strain, representing a generalized Griffith criterion, ultimately describing the fracture as a genuine phase transition. With regard to the brittle-to-ductile transition, we obtain a complex critical scenario characterized by a threshold temperature between the two fracture regimes (brittle and ductile), an upper and a lower yield strength, and a critical temperature corresponding to the complete breakdown. To show the effectiveness of the proposed models in describing thermal fracture behaviors at small scales, we successfully compare our theoretical results with molecular dynamics simulations of Si and GaN nanowires.

On the utility of hierarchical self-healing fiber bundle materials under different environments

Bio-materials use a hierarchical structure to optimize their self-healing mechanical behavior. However, the utility may be restricted by different environments. In this paper, based on the previous work in Ji and Li (J Mater Sci 53:14858-14870, 2018) on the constitutive relation of hierarchical self-healing fiber bundle materials (FBMs), the stability is investigated for the mechanical-environmental interaction system established in Ji and Li (Int J Fract 212:105-112, 2018). With the principle of total potential, the stability criterion is proposed. The critical environment stiffness is derived and the system is therefore classified into the absolutely stable one and the conditionally stable one. For the conditionally stable system, the applied strain of FBMs reduces to be [0,[Formula: see text]], where [Formula: see text] is the cutoff strain. Finally, the toughness of hierarchical self-healing FBMs is studied for different interaction systems. The results show that in the absolutely stable system there exists a critical healing rate across which the toughness benefits from a hierarchical structure. In the conditionally stable system, the toughness is significantly affected by the environment stiffness, i.e., the toughness of a FBM increases with a rising hierarchical level, whereas it decreases with a rising healing rate. Moreover, the critical healing rate for toughness becomes greater compared to that in an absolutely stable system.

Rate-dependent force-extension models for single-molecule force spectroscopy experiments

Single-molecule force spectroscopy techniques allow for the measurement of several static and dynamic features of macromolecules of biological origin. In particular, atomic force microscopy, used with a variable pulling rate, provides valuable information on the folding/unfolding dynamics of proteins. We propose here two different models able to describe the out-of-equilibrium statistical mechanics of a chain composed of bistable units. These latter represent the protein domains, which can be either folded or unfolded. Both models are based on the Langevin approach and their implementation allows for investigating the effect of the pulling rate and of the device intrinsic elasticity on the chain unfolding response. The theoretical results (both analytical and numerical) have been compared with experimental data concerning the unfolding of the titin and filamin proteins, eventually obtaining a good agreement over a large range of the pulling rates.

Full Statistics of Conjugated Thermodynamic Ensembles in Chains of Bistable Units

The statistical mechanics and the thermodynamics of small systems are characterized by the non-equivalence of the statistical ensembles. When concerning a polymer chain or an arbitrary chain of independent units, this concept leads to different force-extension responses for the isotensional (Gibbs) and the isometric (Helmholtz) thermodynamic ensembles for a limited number of units (far from the thermodynamic limit). While the average force-extension response has been largely investigated in both Gibbs and Helmholtz ensembles, the full statistical characterization of this thermo-mechanical behavior has not been approached by evaluating the corresponding probability densities. Therefore, we elaborate in this paper a technique for obtaining the probability density of the extension when force is applied (Gibbs ensemble) and the probability density of the force when the extension is prescribed (Helmholtz ensemble). This methodology, here developed at thermodynamic equilibrium, is applied to a specific chain composed of units characterized by a bistable potential energy, which is able to mimic the folding and unfolding of several macromolecules of biological origin.

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. 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.

Spin variable approach for the statistical mechanics of folding and unfolding chains

The force-extension response of chains composed of bistable (or multistable) units strongly depends on the applied boundary conditions. As a matter of fact, isotensional conditions (soft devices) lead to a plateau-like response, whereas isometric conditions (hard devices) lead to a sawtooth-like pattern. We develop an equilibrium statistical mechanics methodology, based on the introduction of a set of discrete or spin variables, which is able to describe the thermal and mechanical properties of a folding and unfolding chain under arbitrary external conditions. In particular, we will work within the Gibbs and Helmholtz ensembles, which correspond to soft and hard devices, respectively. We introduce a one-dimensional system composed of multistable units and a bistable freely jointed chain. For both systems we obtain explicit expressions for the force-extension relation and we study the spinoidal behavior induced by the isometric conditions.

Stability of radiation-damaged DNA after multiple strand breaks

Radiation induced double-strand breaks in DNA are more stable against thermal and mechanical stress than usually thought.

Real-time mechanical characterization of DNA degradation under therapeutic X-rays and its theoretical modeling

The killing of tumor cells by ionizing radiation beams in cancer radiotherapy is currently based on a rather empirical understanding of the basic mechanisms and effectiveness of DNA damage by radiation. By contrast, the mechanical behaviour of DNA encompassing sequence sensitivity and elastic transitions to plastic responses is much better understood. A novel approach is proposed here based on a micromechanical Silicon Nanotweezers device. This instrument allows the detailed biomechanical characterization of a DNA bundle exposed to an ionizing radiation beam delivered here by a therapeutic linear particle accelerator (LINAC). The micromechanical device endures the harsh environment of radiation beams and still retains molecular-level detection accuracy. In this study, the first real-time observation of DNA damage by ionizing radiation is demonstrated. The DNA bundle degradation is detected by the micromechanical device as a reduction of the bundle stiffness, and a theoretical model provides an interpretation of the results. These first real-time observations pave the way for both fundamental and clinical studies of DNA degradation mechanisms under ionizing radiation for improved tumor treatment.

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.