Crack propagation in the power-law nonlinear viscoelastic material

An analysis on crack creep propagation problem of power-law nonlinear viscoelastic materials is presented. The creep incompressilility assumption is used. To simulate fracture behavior of craze region, it is assumed that in the fracture process zone near the crack tip, the cohesive stress sigma(f) acts upon the crack surfaces and resists crack opening. Through a perturbation method, i. e., by superposing the Mode-I applied force onto a referential uniform stress state, which has a trivial solution and gives no effect on the solution of the original problem, the nonlinear viscoelastic problem is reduced to linear problem. For weak nonlinear materials, for which the power-law index n similar or equal to 1, the expressions of stress and crack surface displacement are derived. Then, the fracture process zone local energy criterion is proposed and based on which the formulas of cracking incubation time t

Long-range automaton models of earthquakes: Power-law accelerations, correlation evolution, and mode-switching

We introduce a conceptual model for the in-plane physics of an earthquake fault. The model employs cellular automaton techniques to simulate tectonic loading, earthquake rupture, and strain redistribution. The impact of a hypothetical crustal elastodynamic Green's function is approximated by a long-range strain redistribution law with a r(-p) dependance. We investigate the influence of the effective elastodynamic interaction range upon the dynamical behaviour of the model by conducting experiments with different values of the exponent (p). The results indicate that this model has two distinct, stable modes of behaviour. The first mode produces a characteristic earthquake distribution with moderate to large events preceeded by an interval of time in which the rate of energy release accelerates. A correlation function analysis reveals that accelerating sequences are associated with a systematic, global evolution of strain energy correlations within the system. The second stable mode produces Gutenberg-Richter statistics, with near-linear energy release and no significant global correlation evolution. A model with effectively short-range interactions preferentially displays Gutenberg-Richter behaviour. However, models with long-range interactions appear to switch between the characteristic and GR modes. As the range of elastodynamic interactions is increased, characteristic behaviour begins to dominate GR behaviour. These models demonstrate that evolution of strain energy correlations may occur within systems with a fixed elastodynamic interaction range. Supposing that similar mode-switching dynamical behaviour occurs within earthquake faults then intermediate-term forecasting of large earthquakes may be feasible for some earthquakes but not for others, in alignment with certain empirical seismological observations. Further numerical investigation of dynamical models of this type may lead to advances in earthquake forecasting research and theoretical seismology.

Nonlinear fatigue damage model based on the residual strength degradation law

In this paper, a logarithmic expression to describe the residual strength degradation process is developed in order to fatigue test results for normalized carbon steel. The definition and expression of fatigue damage due to symmetrical stress with a constant amplitude are also given. The expression of fatigue damage can also explain the nonlinear properties of fatigue damage. Furthermore, the fatigue damage of structures under random stress is analyzed, and an iterative formula to describe the fatigue damage process is deduced. Finally, an approximate method for evaluating the fatigue life of structures under repeated random stress blocking is presented through various calculation examples.

La tortura en las Siete Partidas : la pena, la prueba y la majestad. Un análisis sobre la reinstauración del tormento en la legislación castellana del siglo XIII

Resumen: Nadie, de entre los historiadores del derecho, podría animarse a negar la presencia de fuentes romanas (en especial esa compilación tardía denominada Corpus Iuris Civilis) dentro de Partidas; con particular acento en el caso del Digesto. Por esto, en términos de su materialidad, lo que se presentará aquí será un trabajo de cotejo entre títulos específicos de las obras citadas y que refieren al tópico de la tortura. Por un lado, el título 18 del libro XLVIII del Digesto junto con el título 41 del libro IX del Codex. Del otro lado, el título 30 del libro VII de Partidas. Esta comparación buscará no tanto las equivalencias textuales (que son conscientemente obviadas por los redactores a pesar de conocer a la perfección los sistemas de citado) como el sentido último de introducir estos textos en el corpus legislativo castellano. En este sentido, lo que se buscará será plantear métodos posibles para sortear el problema de la intertextualidad en un mundo sin autores.

Higher-order analysis of crack-tip fields in power-law hardening materials

In this paper, we present an exact higher-order asymptotic analysis on the near-crack-tip fields in elastic-plastic materials under plane strain, Mode I. A four- or five-term asymptotic series of the solutions is derived. It is found that when 1.6 < n less-than-or-equal-to 2.8 (here, n is the hardening exponent), the elastic effect enters the third-order stress field; but when 2.8< n less-than-or-equal-to 3.7 this effect turns to enter the fourth-order field, with the fifth-order field independent. Moreover, if n>3.7, the elasticity only affects the fields whose order is higher than 4. In this case, the fourth-order field remains independent. Our investigation also shows that as long as n is larger than 1.6, the third-order field is always not independent, whose amplitude coefficient K3 depends either on K1 or on both K1 and K2 (K1 and K2 arc the amplitude coefficients of the first- and second-order fields, respectively). Firmly, good agreement is found between our results and O'Dowd and Shih's numerical ones[8] by comparison.

Higher-order analysis of crack tip fields in elastic power-law hardening materials

A HIGHER-ORDER asymptotic analysis of a stationary crack in an elastic power-law hardening material has been carried out for plane strain, Mode 1. The extent to which elasticity affects the near-tip fields is determined by the strain hardening exponent n. Five terms in the asymptotic series for the stresses have been derived for n = 3. However, only three amplitudes can be independently prescribed. These are K1, K2 and K5 corresponding to amplitudes of the first-, second- and fifth-order terms. Four terms in the asymptotic series have been obtained for n = 5, 7 and 10; in these cases, the independent amplitudes are K1, K2 and K4. It is found that appropriate choices of K2 and K4 can reproduce near-tip fields representative of a broad range of crack tip constraints in moderate and low hardening materials. Indeed, fields characterized by distinctly different stress triaxiality levels (established by finite element analysis) have been matched by the asymptotic series. The zone of dominance of the asymptotic series extends over distances of about 10 crack openings ahead of the crack tip encompassing length scales that are microstructurally significant. Furthermore, the higher-order terms collectively describe a spatially uniform hydrostatic stress field (of adjustable magnitude) ahead of the crack. Our results lend support to a suggestion that J and a measure of near-tip stress triaxiality can describe the full range of near-tip states.

Singular behaviour near the tip of a sharp V-notch in a power law hardening material

This paper presents an asymptotic analysis of the near-tip stress and strain fields of a sharp V-notch in a power law hardening material. First, the asymptotic solutions of the HRR type are obtained for the plane stress problem under symmetric loading. It is found that the angular distribution function of the radial stress sigma(r) presents rapid variation with the polar angle if the notch angle beta is smaller than a critical notch angle; otherwise, there is no such phenomena. Secondly, the asymptotic solutions are developed for antisymmetric loading in the cases of plane strain and plane stress. The accurate calculation results and the detailed comparisons are given as well. All results show that the singular exponent s is changeable for various combinations of loading condition and plane problem.

A unified law of motion of lithospheric plates and the driving mechanism

From observed data on lithospheric plates, a unified empirical law for plate motion,valid for continental as well as oceanic plates, is obtained in the following form: The speedof plate motion U depends linearly on a geometric parameter T_d, ratio of the sum of effectiveridge length and trench arc length to the sum of area of continental part of plate and total areaof cold sinking slab. Based on this unified law, a simple mechanical analysis shows that, themain driving forces for lithospheric plates come from push along the mid-ocean ridge andpull by the cold sinking slab, while the main drag forces consist of the viscous traction beneaththe continental part of plate and over both faces of the sinking slab. Moreover, the specific-push along ridge and pull by slab are found to be of equal magnitude.

Science-based restoration monitoring of coastal habitats, Volume One: A framework for monitoring plans under the Estuaries and Clean Waters Act of 2000 (Public Law 160-457)

Executive Summary: The Estuary Restoration Act of 2000 (ERA), Title I of the Estuaries and Clean Waters Act of 2000, was created to promote the restoration of habitats along the coast of the United States (including the US protectorates and the Great Lakes). The NOAA National Centers for Coastal Ocean Science was charged with the development of a guidance manual for monitoring plans under this Act. This guidance manual, titled Science-Based Restoration Monitoring of Coastal Habitats, is written in two volumes. It provides technical assistance, outlines necessary steps, and provides useful tools for the development and implementation of sound scientific monitoring of coastal restoration efforts. In addition, this manual offers a means to detect early warnings that the restoration is on track or not, to gauge how well a restoration site is functioning, to coordinate projects and efforts for consistent and successful restoration, and to evaluate the ecological health of specific coastal habitats both before and after project completion (Galatowitsch et al. 1998). The following habitats have been selected for discussion in this manual: water column, rock bottom, coral reefs, oyster reefs, soft bottom, kelp and other macroalgae, rocky shoreline, soft shoreline, submerged aquatic vegetation, marshes, mangrove swamps, deepwater swamps, and riverine forests. The classification of habitats used in this document is generally based on that of Cowardin et al. (1979) in their Classification of Wetlands and Deepwater Habitats of the United States, as called for in the ERA Estuary Habitat Restoration Strategy. This manual is not intended to be a restoration monitoring “cookbook” that provides templates of monitoring plans for specific habitats. The interdependence of a large number of site-specific factors causes habitat types to vary in physical and biological structure within and between regions and geographic locations (Kusler and Kentula 1990). Monitoring approaches used should be tailored to these differences. However, even with the diversity of habitats that may need to be restored and the extreme geographic range across which these habitats occur, there are consistent principles and approaches that form a common basis for effective monitoring. Volume One, titled A Framework for Monitoring Plans under the Estuaries and Clean Waters Act of 2000, begins with definitions and background information. Topics such as restoration, restoration monitoring, estuaries, and the role of socioeconomics in restoration are discussed. In addition, the habitats selected for discussion in this manual are briefly described. (PDF contains 116 pages)

An observer-based vaccination control law for an SEIR epidemic model based on feedback linearization techniques for nonlinear systems

This paper presents a vaccination strategy for fighting against the propagation of epidemic diseases. The disease propagation is described by an SEIR (susceptible plus infected plus infectious plus removed populations) epidemic model. The model takes into account the total population amounts as a refrain for the illness transmission since its increase makes the contacts among susceptible and infected more difficult. The vaccination strategy is based on a continuous-time nonlinear control law synthesised via an exact feedback input-output linearization approach. An observer is incorporated into the control scheme to provide online estimates for the susceptible and infected populations in the case when their values are not available from online measurement but they are necessary to implement the control law. The vaccination control is generated based on the information provided by the observer. The control objective is to asymptotically eradicate the infection from the population so that the removed-by-immunity population asymptotically tracks the whole one without precise knowledge of the partial populations. The model positivity, the eradication of the infection under feedback vaccination laws and the stability properties as well as the asymptotic convergence of the estimation errors to zero as time tends to infinity are investigated.

Adaptive variable structure control law for a variable speed wind turbine

Presentado en el 13th WSEAS International Conference on Automatic Control, Modelling and Simulation, ACMOS'11