New perspective of fracture mechanics inspired by gap test with crack-parallel compression.

The line crack models, including linear elastic fracture mechanics (LEFM), cohesive crack model (CCM), and extended finite element method (XFEM), rest on the century-old hypothesis of constancy of materials' fracture energy. However, the type of fracture test presented here, named the gap test, reveals that, in concrete and probably all quasibrittle materials, including coarse-grained ceramics, rocks, stiff foams, fiber composites, wood, and sea ice, the effective mode I fracture energy depends strongly on the crack-parallel normal stress, in-plane or out-of-plane. This stress can double the fracture energy or reduce it to zero. Why hasn't this been detected earlier? Because the crack-parallel stress in all standard fracture specimens is negligible, and is, anyway, unaccountable by line crack models. To simulate this phenomenon by finite elements (FE), the fracture process zone must have a finite width, and must be characterized by a realistic tensorial softening damage model whose vectorial constitutive law captures oriented mesoscale frictional slip, microcrack opening, and splitting with microbuckling. This is best accomplished by the FE crack band model which, when coupled with microplane model M7, fits the test results satisfactorily. The lattice discrete particle model also works. However, the scalar stress-displacement softening law of CCM and tensorial models with a single-parameter damage law are inadequate. The experiment is proposed as a standard. It represents a simple modification of the three-point-bend test in which both the bending and crack-parallel compression are statically determinate. Finally, a perspective of various far-reaching consequences and limitations of CCM, LEFM, and XFEM is discussed.

Unsaturated nanoporomechanics.

Although some important advances in the modeling of sorption and hygrothermal deformations of nanoporous materials such as hydrated cement paste, shale, coal, and some other rocks and soils have already been made, a comprehensive nanoporomechanics theory remains elusive. Here we strive to formulate it based on Gibb's free energy of the solid-fluid system and on the recently derived Nguyen-Rahimi-Bazant (NRB) isotherm, which corrects the Brunauer-Emmett-Teller (BET) isotherm for the effect of hindered adsorbed water in filled nanopores and extends through the capillary range up to saturation. The challenge is to capture all of the basic types of relevant published experimental data, including 1) a complete sorption isotherm of hydrated cement paste (including the capillary range), 2) pore size distribution, 3) autogenous shrinkage, 4) drying shrinkage and swelling, 5) water loss or humidity change due to heating, 6) thermal expansion at various humidities, and 7) water loss of specimens caused by compression. The previous models can fit only a few data types. The present model fits all of them. It is ready for computer simulations needed to minimize the deleterious moisture effects on long-time deformations, cracking damage, and fracture in concrete infrastructure and thereby to reduce indirectly the enormous carbon footprint of concrete. Adaptations to shale, coal beds, etc., are possible.

Design of quasibrittle materials and structures to optimize strength and scaling at probability tail: an apercu.

The objective in materials or structure design has been to maximize the mean strength. However, as generally agreed, engineering structures, such as bridges, aircraft or microelectromechanical systems must be designed for tail probability of failure less than 10-6 per lifetime. But this objective is not the same. Indeed, a quasibrittle material or structure with a superior mean strength can have, for the same coefficient of variation, an inferior strength at the less than 10-6 tail. This tail is unreachable by histogram testing. So, one needs a rational theory, physically based and experimentally verified indirectly, which is feasible by size effect. Focusing on the results at the writer's home institution, this inaugural article (written three years ex post facto) reviews recent results towards this goal, concerned with quasibrittle materials such as concretes, rocks, tough ceramics, fibre composites, bone and most materials on the micrometer scale. The theory is anchored at the atomic scale because only on that scale the failure probability is known-it is given by the frequency of breakage of bonds, governed by the activation energy barriers in the transition rate theory. An analytical way to scale it up to the macroscale representative volume element (RVE) has been found. Structures obeying the weakest-link model are considered but, for quasibrittle failures, the number of links, each corresponding to one RVE, must be considered as finite. The result is a strength probability distribution transiting from Weibullian to Gaussian, depending on the structure size. The Charles-Evans and Paris laws for subcritical crack growth under static and cyclic fatigue are also derived from the transition-rate theory. This yields a size-dependent Gauss-Weibull distribution of lifetime. Close agreement with numerous published test data is achieved. Discussed next are new results on materials with a well-defined microscale architecture, particularly biomimetic imbricated (or staggered) lamellar materials, exemplified by nacre, a material of astonishing mean strength compared to its constituents. This architecture is idealized as a diagonally pulled fishnet, which is shown to be amenable to an analytical solution of the strength probability distribution. The solution is verified by million Monte Carlo simulations for each of the fishnets of various shapes and sizes. In addition to the classical weakest-link and the fibre-bundle models, the fishnet is found to be the third strength probability model that is amenable to an analytical solution. The nacreous architecture is shown to provide an additional major (greater than 100%) strengthening at the 10-6 failure probability tail. Finally, it is emphasized that the most important consequence of the quasibrittleness, and also the most effective way of calibrating the 10-6 tail, is the size effect on the mean structural strength, which permeates all formulations.

Branching of hydraulic cracks enabling permeability of gas or oil shale with closed natural fractures.

While hydraulic fracturing technology, aka fracking (or fraccing, frac), has become highly developed and astonishingly successful, a consistent formulation of the associated fracture mechanics that would not conflict with some observations is still unavailable. It is attempted here. Classical fracture mechanics, as well as current commercial software, predict vertical cracks to propagate without branching from the perforations of the horizontal well casing, which are typically spaced at 10 m or more. However, to explain the gas production rate at the wellhead, the crack spacing would have to be only about 0.1 m, which would increase the overall gas permeability of shale mass about 10,000×. This permeability increase has generally been attributed to a preexisting system of orthogonal natural cracks, whose spacing is about 0.1 m. However, their average age is about 100 million years, and a recent analysis indicated that these cracks must have been completely closed by secondary creep of shale in less than a million years. Here it is considered that the tectonic events that produced the natural cracks in shale must have also created weak layers with nanocracking or microcracking damage. It is numerically demonstrated that seepage forces and a greatly enhanced permeability along the weak layers, with a greatly increased transverse Biot coefficient, must cause the fracking to engender lateral branching and the opening of hydraulic cracks along the weak layers, even if these cracks are initially almost closed. A finite element crack band model, based on a recently developed anisotropic spherocylindrical microplane constitutive law, demonstrates these findings [Rahimi-Aghdam S, et al. (2018) arXiv:1212.11023].

A nanoscale perspective on the effects of transverse microprestress on drying creep of nanoporous solids.

The Pickett effect describes the excess non-additive strain developed during drying of a nanoporous solid material under creep. One explanation for its origins, developed using micromechanical models, is the progressive relaxation of internally developed microprestress. However, these models have not explicitly considered the effects of this microprestress on nanoscale energy barriers that govern the relative motion and displacement between nanopore walls during deformation. Here, we evaluate the nanoscale effects of transverse microprestresses on the drying creep behaviour of a nanoscale slit pore using coarse-grained molecular dynamics. We find that the underlying energy barrier depends exponentially on the transverse microprestress, which is attributed to changes in the effective viscosity and degree of nanoconfinement of molecules in the water interlayer. Specifically, as the transverse microprestress is relaxed (i.e. its magnitude decreases), the activation energy barrier is reduced, thereby leading to an acceleration of the creep behaviour and a stronger Pickett effect. Based on our simulation results, we introduce a new microprestress-dependent energy term into our existing Arrhenius model, which describes the relative displacement of pore walls as a function of the underlying activation energy barriers. Our findings further verify the existing micromechanical theories for the origin of the Pickett effect and establish a quantitative relationship between the transverse microprestress and the intensity of the Pickett effect.

Fishnet model for failure probability tail of nacre-like imbricated lamellar materials.

Nacre, the iridescent material of the shells of pearl oysters and abalone, consists mostly of aragonite (a form of CaCO3), a brittle constituent of relatively low strength ([Formula: see text]10 MPa). Yet it has astonishing mean tensile strength ([Formula: see text]150 MPa) and fracture energy ([Formula: see text]350 to 1,240 J/m2). The reasons have recently become well understood: (i) the nanoscale thickness ([Formula: see text]300 nm) of nacre's building blocks, the aragonite lamellae (or platelets), and (ii) the imbricated, or staggered, arrangement of these lamellea, bound by biopolymer layers only [Formula: see text]25 nm thick, occupying [Formula: see text] of volume. These properties inspire manmade biomimetic materials. For engineering applications, however, the failure probability of [Formula: see text] is generally required. To guarantee it, the type of probability density function (pdf) of strength, including its tail, must be determined. This objective, not pursued previously, is hardly achievable by experiments alone, since [Formula: see text] tests of specimens would be needed. Here we outline a statistical model of strength that resembles a fishnet pulled diagonally, captures the tail of pdf of strength and, importantly, allows analytical safety assessments of nacreous materials. The analysis shows that, in terms of safety, the imbricated lamellar structure provides a major additional advantage-∼10% strength increase at tail failure probability [Formula: see text] and a 1 to 2 orders of magnitude tail probability decrease at fixed stress. Another advantage is that a high scatter of microstructure properties diminishes the strength difference between the mean and the probability tail, compared with the weakest link model. These advantages of nacre-like materials are here justified analytically and supported by millions of Monte Carlo simulations.

Growth model for large branched three-dimensional hydraulic crack system in gas or oil shale.

Recent analysis of gas outflow histories at wellheads shows that the hydraulic crack spacing must be of the order of 0.1 m (rather than 1 m or 10 m). Consequently, the existing models, limited to one or several cracks, are unrealistic. The reality is 10(5)-10(6) almost vertical hydraulic cracks per fracking stage. Here, we study the growth of two intersecting near-orthogonal systems of parallel hydraulic cracks spaced at 0.1 m, preferably following pre-existing rock joints. One key idea is that, to model lateral cracks branching from a primary crack wall, crack pressurization, by viscous Poiseuille-type flow, of compressible (proppant-laden) frac water must be complemented with the pressurization of a sufficient volume of micropores and microcracks by Darcy-type water diffusion into the shale, to generate tension along existing crack walls, overcoming the strength limit of the cohesive-crack or crack-band model. A second key idea is that enforcing the equilibrium of stresses in cracks, pores and water, with the generation of tension in the solid phase, requires a new three-phase medium concept, which is transitional between Biot's two-phase medium and Terzaghi's effective stress and introduces the loading of the solid by pressure gradients of diffusing pore water. A computer program, combining finite elements for deformation and fracture with volume elements for water flow, is developed to validate the new model.This article is part of the themed issue 'Energy and the subsurface'.

Transient effects of drying creep in nanoporous solids: understanding the effects of nanoscale energy barriers.

The Pickett effect is the phenomenon of creep enhancement during transient drying. It has been observed for many nanoporous solids, including concrete, wood and Kevlar. While the existing micromechanical models can partially explain this effect, they have yet to consider nanoscale dynamic effects of water in nanopores, which are believed to be of paramount importance. Here, we examine how creep deformations in a slit pore are accelerated by the motion of water due to drying forces using coarse-grained molecular dynamics simulations. We find that the drying that drives water flow in the nanopores lowers both the activation energy of pore walls sliding past one another and the apparent viscosity of confined water molecules. This lowering can be captured with an analytical Arrhenius relationship accounting for the role of water flow in overcoming the energy barriers. Notably, we use this model and simulation results to demonstrate that the drying creep strain is not linearly dependent on the applied creep stress at the nanopore level. Our findings establish the scaling relationships that explain how the creep driving force, drying force and fluid properties are related. Thus, we establish the nanoscale origins of the Pickett effect and provide strategies for minimizing the additional displacements arising from this effect.

Comminution of solids caused by kinetic energy of high shear strain rate, with implications for impact, shock, and shale fracturing.

Although there exists a vast literature on the dynamic comminution or fragmentation of rocks, concrete, metals, and ceramics, none of the known models suffices for macroscopic dynamic finite element analysis. This paper outlines the basic idea of the macroscopic model. Unlike static fracture, in which the driving force is the release of strain energy, here the essential idea is that the driving force of comminution under high-rate compression is the release of the local kinetic energy of shear strain rate. The density of this energy at strain rates >1,000/s is found to exceed the maximum possible strain energy density by orders of magnitude, making the strain energy irrelevant. It is shown that particle size is proportional to the -2/3 power of the shear strain rate and the 2/3 power of the interface fracture energy or interface shear stress, and that the comminution process is macroscopically equivalent to an apparent shear viscosity that is proportional (at constant interface stress) to the -1/3 power of this rate. A dimensionless indicator of the comminution intensity is formulated. The theory was inspired by noting that the local kinetic energy of shear strain rate plays a role analogous to the local kinetic energy of eddies in turbulent flow.

Scaling of strength and lifetime probability distributions of quasibrittle structures based on atomistic fracture mechanics.

The failure probability of engineering structures such as aircraft, bridges, dams, nuclear structures, and ships, as well as microelectronic components and medical implants, must be kept extremely low, typically <10(-6). The safety factors needed to ensure it have so far been assessed empirically. For perfectly ductile and perfectly brittle structures, the empirical approach is sufficient because the cumulative distribution function (cdf) of random material strength is known and fixed. However, such an approach is insufficient for structures consisting of quasibrittle materials, which are brittle materials with inhomogeneities that are not negligible compared with the structure size. The reason is that the strength cdf of quasibrittle structure varies from Gaussian to Weibullian as the structure size increases. In this article, a recently proposed theory for the strength cdf of quasibrittle structure is refined by deriving it from fracture mechanics of nanocracks propagating by small, activation-energy-controlled, random jumps through the atomic lattice. This refinement also provides a plausible physical justification of the power law for subcritical creep crack growth, hitherto considered empirical. The theory is further extended to predict the cdf of structural lifetime at constant load, which is shown to be size- and geometry-dependent. The size effects on structure strength and lifetime are shown to be related and the latter to be much stronger. The theory fits previously unexplained deviations of experimental strength and lifetime histograms from the Weibull distribution. Finally, a boundary layer method for numerical calculation of the cdf of structural strength and lifetime is outlined.

Strength distribution of dental restorative ceramics: finite weakest link model with zero threshold.

Ensuring a small enough failure probability is important for the design and selection of restorative dental ceramics. For this purpose, the two-parameter Weibull distribution, which is based on the weakest link model with infinitely many links, is usually adopted to model the strength distribution of dental ceramics. This distribution has been thoroughly validated for perfectly brittle materials. However, dental ceramics are generally quasibrittle because the inhomogeneity size is not negligible compared to the size of the ceramic part. For such materials, the experimental histograms of many quasibrittle materials have been shown to exhibit strong deviations from the two-parameter Weibull distribution. As a remedy, the three-parameter Weibull distribution, which has a nonzero threshold, has been proposed. However, the improvement of the fits of histograms of quasibrittle materials has been only partial. Instead of making the threshold non-zero, the correct remedy is to consider the weakest link model to have a finite number of links, each of them representing one finite-size representative volume element of material. This model has recently been justified on the basis of the probability of random jumps of atomic lattice cracks over the activation energy barriers on the free energy potential of the lattice. It is shown that, in similarity to other quasibrittle materials, this new model allows excellent fits of the experimental strength histograms of various types of dental ceramics.

Hyperelastic anisotropic microplane constitutive model for annulus fibrosus.

In a recent paper, Peng et al. (2006, "An Anisotropic Hyperelastic Constitutive Model With Fiber-Matrix Interaction for the Human Annulus Fibrosis," ASME J. Appl. Mech., 73(5), pp. 815-824) developed an anisotropic hyperelastic constitutive model for the human annulus fibrosus in which fiber-matrix interaction plays a crucial role in simulating experimental observations reported in the literature. Later, Guo et al. (2006, "A Composites-Based Hyperelastic Constitutive Model for Soft Tissue With Application to the Human Fibrosis," J. Mech. Phys. Solids, 54(9), pp. 1952-1971) used fiber reinforced continuum mechanics theory to formulate a model in which the fiber-matrix interaction was simulated using only composite effect. It was shown in these studies that the classical anisotropic hyperelastic constitutive models for soft tissue, which do not account for this shear interaction, cannot accurately simulate the test data on human annulus fibrosus. In this study, we show that the microplane model for soft tissue developed by Caner and Carol (2006, "Microplane Constitutive Model and Computational Framework for Blood Vessel Tissue," ASME J. Biomech. Eng., 128(3), pp. 419-427) can be adjusted for human annulus fibrosus and the resulting model can accurately simulate the experimental observations without explicit fiber-matrix interaction because, in microplane model, the shear interaction between the individual fibers distributed in the tissue provides the required additional rigidity to explain these experimental facts. The intensity of the shear interaction between the fibers can be adjusted by adjusting the spread in the distribution while keeping the total amount of the fiber constant. A comparison of results obtained from (i) a fiber-matrix parallel coupling model, which does not account for the fiber-matrix interaction, (ii) the same model but enriched with fiber-matrix interaction, and (iii) microplane model for soft tissue adapted to annulus fibrosus with two families of fiber distributions is presented. The conclusions are (i) that varying degrees of fiber-fiber and fiber-matrix shear interaction must be taking place in the human annulus fibrosus, (ii) that this shear interaction is essential to be able to explain the mechanical behavior of human annulus fibrosus, and (iii) that microplane model can be fortified with fiber-matrix interaction in a straightforward manner provided that there are new experimental data on distribution of fibers, which indicate a spread so small that it requires an explicit fiber-matrix interaction to be able to simulate the experimental data.

[Diagnostics and therapy of hepatorenal syndrome. Recommendations of of the working group on portal hypertension of the Czech Hepatology Society and the J. E. Purkinje Czech Medical Society]. / Doporuceny postup pro diagnostiku a lécbu hepatorenálního syndromu. Doporucený postup vypracovaný skupinou pro portální hypertenzi pri Ceské hepatologické spolecnosti Ceské lékarské spolecnosti J. E. Purkyne a schválený výborem Ceské hepatologické spolecnosti Ceské lékarské spolecnosti J. E. Purkyne.

Hepatorenal syndrome is a functional renal failure in patients with advanced cirrhosis and portal hypertension or acute liver failure. It is caused by extreme vasoconstriction in renal arterial bed. Type I HRS presents as an acute renal failure, while type II HRS is chronic alteration of renal function in patients with refractory ascites. Prognosis of HRS is very poor with survival reaching several weeks in patients with HRS type I. Causal treatment is liver transplantation, other treatment options include use of splanchnic vasoconstrictors (terlipressin) together with plasmaexpansion (albumin) and TIPS. It is important to exclude nephrotoxic medication (non-steroid anti inflammatory drugs, aminoglycosides) and properly treat all infective complications in prevention of HRS.

Mechanics-based statistics of failure risk of quasibrittle structures and size effect on safety factors.

In mechanical design as well as protection from various natural hazards, one must ensure an extremely low failure probability such as 10(-6). How to achieve that goal is adequately understood only for the limiting cases of brittle or ductile structures. Here we present a theory to do that for the transitional class of quasibrittle structures, having brittle constituents and characterized by nonnegligible size of material inhomogeneities. We show that the probability distribution of strength of the representative volume element of material is governed by the Maxwell-Boltzmann distribution of atomic energies and the stress dependence of activation energy barriers; that it is statistically modeled by a hierarchy of series and parallel couplings; and that it consists of a broad Gaussian core having a grafted far-left power-law tail with zero threshold and amplitude depending on temperature and load duration. With increasing structure size, the Gaussian core shrinks and Weibull tail expands according to the weakest-link model for a finite chain of representative volume elements. The model captures experimentally observed deviations of the strength distribution from Weibull distribution and of the mean strength scaling law from a power law. These deviations can be exploited for verification and calibration. The proposed theory will increase the safety of concrete structures, composite parts of aircraft or ships, microelectronic components, microelectromechanical systems, prosthetic devices, etc. It also will improve protection against hazards such as landslides, avalanches, ice breaks, and rock or soil failures.

[The diagnostics and therapy of hepatic encephalopathy. Recommendations of of the working group on portal hypertension in the Czech Hepatology Society and the J. E. Purkinje Czech Medical Society]. / Diagnostika a lécba jaterní encefalopatie. Doporucený postup vypracovaný skupinou pro portální hypertenzi pri Ceské hepatologické spolecnosti Ceské lékarské spolecnosti J. E. Purkyne a schválený výborem Ceské hepatologické spolecnosti Ceské lékarské spolecnosti J. E. Purkyne.

UNLABELLED: Hepatic encephalopathy (HE) is a set of reversible neuropsychic features which occur in connection with hepatic cirrhosis or acute hepatic failure. We distinguish manifest HE (with clinical symptoms) and minimal FE (normal clinical finding, abnormal psychometric or neurophysiologic exam). The diagnosis is clinical or laboratory one. From the auxiliary examinations in common practice the number connection test is sufficient. THERAPY: Presence of hepatic encephalopathy should lead to the consideration of the possibility to solve basic disease by hepatic transplantation. Conservative therapy lies in 1. Basic disease elimination, 2. Measures lowering the ammonia level in blood--optimalization of protein intake, administration of indigestible disaccharides (lactulose, lactitol) and fill sterilisation by antibiotics (Rifaxin, Metronidazol), ornitine-aspartate administration, 3. Influencing the changes in amino acid metabolism (administration of branched chain amino acids--BCAA). Prognosis depends on the advancement of the disease, after hepatic transplantation the clinical symptoms of HE are mostly fully reversible.

[Diagnostics and treatment of hepatocellular carcinoma. Recommendations of the Portal Hypertension Working Group of the Czech Hepatology Society and the J.E. Purkinje Czech Medical Society ]. / Diagnostika a lécba hepatocelulárního karcinomu.

Hepatocellular carcionma (HCC) is almost exclusively associated with liver cirrhosis as a significant HCC risk marker in advanced countries. Applicable therapy depends on early diagnosis, and risk patients should be screened for the presence of HCC on a regular basis. Liver ultrasound and determination of alpha-fetoprotein serum levels (AFP) are the screening methods used. Spiral CT is the most often used method for HCC staging. Non-invasive methods may under certain circumstances replace aimed biopsy. There are 3 basic curative therapies for the early stage of HCC: liver transplantation, surgical resection and different methods of local destruction of tumour (i.e., ethanolisation, thermoablation, etc.). Patients at medium stage of HCC may profit from chemoembolisation. Current available systemic chemotherapy is ineffective. Patients with advanced HCC are treated symptomatically. Patient survival prognosis after the application of one of the above treatment methods may be similar with that for HCC free cirrhosis patients, however, prognosis for advanced HCC patients is bad, with survival period from one to nine months.

Scaling theory for quasibrittle structural failure.

This inaugural article has a twofold purpose: (i) to present a simpler and more general justification of the fundamental scaling laws of quasibrittle fracture, bridging the asymptotic behaviors of plasticity, linear elastic fracture mechanics, and Weibull statistical theory of brittle failure, and (ii) to give a broad but succinct overview of various applications and ramifications covering many fields, many kinds of quasibrittle materials, and many scales (from 10(-8) to 10(6) m). The justification rests on developing a method to combine dimensional analysis of cohesive fracture with second-order accurate asymptotic matching. This method exploits the recently established general asymptotic properties of the cohesive crack model and nonlocal Weibull statistical model. The key idea is to select the dimensionless variables in such a way that, in each asymptotic case, all of them vanish except one. The minimal nature of the hypotheses made explains the surprisingly broad applicability of the scaling laws.

[A vasoactive-intestinal-polypeptide producing tumor (VIPoma) as an uncommon cause of life-threatening hypokalemia]. / Nádor z bunek produkujících vazoaktivní intestinální polypeptid (VIPom) jako vzácná prícina zivot ohrozující hypokalémie.

The authors present a case of a 40-year-old female patient examined repeatedly in the course of 11 years and hospitalized on account of pain in the hypogastrium, subfebrile temperatures, watery diarrhoea, hypokaliaemic alkalosis, weakness, fatigue and loss of body weight. As to laboratory examinations hypokaliaemia, hyponatraemia, metabolic alkalosis, irregularly elevated CRP values and minor leucocytosis predominated. A weight loss of cca 8 kg along with a severe mineral deficiency and clinical symptomatology called for parenteral nutrition with a mean daily substitution of 240 mmol K and 200 mmol Na. Due to the clinical condition and non-specific results of graphic and histological examinations the possibility of a VIPoma was considered. This diagnosis was confirmed by laboratory examinations and clinically--after the onset of corticoid treatment marked improvement of the general condition occurred. Finally the authors discuss diagnostic and in particular therapeutic possibilities in this disease.