Fracturing Rate Effect and Creep in Microplane Model for Dynamics

The formulation of microplane model M4 in Parts I and II is extended to rate dependence. Two types of rate effect in the nonlinear triaxial behavior of concrete are distinguished: (1) Rate dependence of fracturing (microcrack growth) associated with the activation energy of bond ruptures, and (2) creep (or viscoelasticity). Short-time linear creep (viscoelasticity) is approximated by a nonaging Maxwell spring-dashpot model calibrated so that its response at constant stress would be tangent to the compliance function of model B3 for a time delay characteristic of the problem at hand. An effective explicit algorithm for step-by-step finite-element analysis is formulated. The main reason that the rate dependence of fracturing must be taken into account is to simulate the sudden reversal of postpeak strain softening into hardening revealed by recent tests. The main reason that short-time creep (viscoelasticity) must be taken into account is to simulate the rate dependence of the initial and unloading stiffness. Good approximations of the rate effects observed in material testing are achieved. The model is suitable for finite-element analysis of impact, blast, earthquake, and short-time loads up to several hours duration.     

Fracture behaviour of alumina and zirconia thin layered laminate

Laminates with strong bonds between thin layers were examined in this work to explore the influence of developed internal stresses on the fracture behaviour. A set of laminates having different level of internal stresses were prepared. Alumina and zirconia were the model materials for evenly alternating layers. The electrophoretic deposition technique was used for manufacturing of the laminates. The basic mechanical properties as elastic modulus and flexural strength were determined for all prepared materials. The crack propagation changes due to effect of internal stresses, elastic mismatch and surface effects were investigated using modified single edge notched beam technique. An extensive fractographical analysis of fracture surfaces was undertaken using laser confocal microscopy. The changes of the crack direction when crack propagates through alternating layers under different angels were described. Further, the effect of the internal stresses level within individual layers was reported.     

Decomposition of Nitrous Oxide over Fe-Ferrierites. Effect of High-Temperature Pretreatment on the Formation of Deposited Oxygen

The dehydration of Fe-ferrierites doubled the decomposition of N₂O at 200 ° C and corresponding deposition of oxygen. The rehydration resulted in a reversible process. Samples with iron located predominantly in cationic positions (Fe/Al 0.05–0.25) exhibited the O _dep /Fe ratio of ca. 0.5 and 1 after pretreatment at 450 and 700 °C, respectively.     

Microplane Model M5f for Multiaxial Behavior and Fracture of Fiber-Reinforced Concrete

Despite impressive advances, the existing constitutive and fracture models for fiber-reinforced concrete (FRC) are essentially limited to uniaxial loading. The microplane modeling approach, which has already been successful for concrete, rock, clay, sand, and foam, is shown capable of describing the nonlinear hardening–softening behavior and fracturing of FRC under not only uniaxial but also general multiaxial loading. The present work generalizes model M5 for concrete without fibers, the distinguishing feature of which is a series coupling of kinematically and statically constrained microplane systems. This feature allows simulating the evolution of dense narrow cracks of many orientations into wide cracks of one distinct orientation. The crack opening on a statically constrained microplane is used to determine the resistance of fibers normal to the microplane. An effective iterative algorithm suitable for each loading step of finite element analysis is developed, and a simple sequential procedure for identifying the model parameters from test data is formulated. The model allows a close match of published test data on uniaxial and multiaxial stress–strain curves, and on multiaxial failure envelopes.     

Confinement-shear lattice CSL model for fracture propagation in concrete

A previously developed lattice model is improved and then applied to simulations of mixed-mode crack propagation in concrete. The concrete meso-structure is simulated by a three-dimensional lattice system connecting nodes which represent the centers of aggregate particles. These nodes are generated randomly according to the given grain size distribution. Only coarse aggregates are taken into account. Three-dimensional Delaunay triangulation is used to determine the lattice connections. The effective cross-section areas of connecting struts are defined by performing a three-dimensional domain tessellation partly similar to Voronoi tessellation. The deformations of each link connecting two adjacent aggregate pieces are defined in the classical manner of Zubelewicz and Ba?ant in which rigid body kinematics is assumed to characterize the displacement and rotation vectors at the lattice nodes. Each strut connecting adjacent particles can transmit both axial and shear forces. The adopted constitutive law simulates fracture, friction and cohesion at the meso-level. The behavior in tension and shear is made dependent on the transversal confining strain, which is computed assuming a linear displacement field within each tetrahedron of Delaunay triangulation, and neglecting the effect of the particle rotations. A mid-point explicit scheme is used to integrate the governing equations of the problems. General procedures to handle the boundary conditions and to couple the lattice mesh to the usual elastic finite element mesh are also formulated. Numerical simulations of mixed-mode fracture test data are used to demonstrate that the model is capable of accurately predicting complex crack paths and the corresponding load-deflection responses observed in experiments.     

Fast algorithm for nonparametric arbitrage-free SPD estimation

State price density (SPD) contains important information concerning market expectations. An estimator of the SPD based on observed European option prices, taking into account the time of the trade, has been previously considered. Financial markets produce huge amounts of data and, due to time constraints, it is not always possible to calculate the estimator using all available data. Using a model for the covariance structure of the observed option prices, the algorithm identifies observations with little importance to the estimator. Dropping these observations increases the speed of computation and allows frequenter updating of the estimator. The algorithms efficiently use indices that combine information contained in the data. Fast algorithms are proposed and their properties are investigated using both simulated and real data sets.     

Consequences of diffusion theory for shrinkage of concrete

The paper reviews the known consequences of diffusion theory for the mathematical modelling of shrinkage, including the size dependence of drying half-time, and the initial and final asymptotic shapes of the time curves of total moisture loss, to which shrinkage is proportional. The mathematical arguments are extended and presented with greater rigour and generality than before, taking the non-linearity of the diffusion equation as well as ageing into account.     

Micropore structure analysis of coal from adsorption isotherms of methanol

Results are presented of a study of the distribution of pore volume and surface in micropores of coal from adsorption equilibria of methanol vapours at temperatures ranging between 293 and 343 K according to a new method. Typical parameters of the micropore structure of twenty samples of coals of carbon contents between 64 and 91% are calculated for a model of cylindrical pores. The micropore surface areas are compared with the results obtained by using the DKR and BET equations, and with already published data from small-angle X-ray scattering. The agreement between results is satisfactory. This evidence suggests that the use of the new method of evaluating the basic parameters of the microstructure can be recommended.