The plastic strain increment of each cycle can be obtained as twice of the distance between the interception points of the stress-strain loops and the x-axis. They are plotted against the life portion in Figure 3(a), which shows that the variation of the plastic strain range was small, especially after the initial softening period. The accumulated plastic deformation was one of the quantities regarded as the **damage** initiation indicator in the Chaboche viscoplasticity model. They are plotted in Figure 3(b), which shows that for the same life portion, the accumulated plastic deformations are not the same, which may depend on the number of cycles to failure. Similar results also apply to the accumulated hystersis energy. Therefore, both of these two **damage** initiation indicators may not be suitable in this study.

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In previous works [8,18] the authors have proposed ad- vanced constitutive equations for sheet or balk metal forming accounting for thermal effect, elasto (visco) pla- sticity, mixed non linear hardening, isotropic ductile **damage** and contact with friction. These fully coupled multiphysics models has been formulating, in the frame- work of the thermodynamics of irreversible processes assuming a fully local theory in which only the first gra- dient of the displacement is required. In this work, a non local **damage** **variable** ( ) D is introduced in these con- stitutive equations replacing the classical local **damage** **variable** (D) by the non local **damage** **variable** ( ) D solution of the following partial differential equation [6]:

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In present study dynamic response of RC panel with and without opening were studied by finite element method using Abaqus application. The experimental work carried out by [8] was first validated by Abaqus to demonstrate its suitability. The results of response of reinforced concrete panel subjected to blast loading were represented in form of central deflection δ and normalized peak deflection δ/h. The thicknesses h of the slabs are 30 mm, 40 mm and 50 mm.The behaviour of concrete was simulated using concrete damaged plasticity model while plastic kinematic model used for simulation of steel. Subsequently, a parametric study on RC panel, with and without openings, are studied for the typical blast load scenarios. The response under the action of applied blast load were presented in form of displacement time history, distribution of compressive **damage** **variable** and distribution of tensile **damage** **variable**

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The **damage** **variable** was derived using reported economic **damage** estimates and hurricane model simulation results to estimate county- and parish-level **damage** estimates. Hurricane **damage** data obtained from the NCDC [19] provide **damage** estimates related to the loss of or **damage** to infrastructure, residential and commercial buildings, crops and other insurable assets. Typically, a single **damage** estimate is provided for multiple counties or parishes. To obtain estimates at a scale appropriate for this analysis, damages were attributed to counties and parishes using results from Hazus (hazards USA) model simulations. The Hazus model is a hurricane simulation model used by the US Federal Emergency Management Agency that (among other things) simulates hurricanes and storm surge inundation levels to estimate economic damages. For each storm in the dataset, county- and pa- rish-level damages were estimated according to the expected proportion of damages incurred by each jurisdic- tion as described by Hazus model results acquired from the FEMA Region IV Flood Loss Atlas [21]. So, the values that compose the **damage** **variable** are the proportion of raw observed damages reported by NCDC that is expected, according the Hazus results, to be incurred by a county or parish given the characteristics of the storm and the counties and parishes involved. Unfortunately, reliable data on damages were not available for the strongest storms either because the damages were too extensive to attribute to storm surge flooding or because storms of that intensity did not make landfall during the study period.

The cyclic indentation is calculated by FEM as follows: First, the single indentation is calculated. Next, the pressure against the hard ﬁlm at the instantaneous indentation depth s obtained in the calculation is converted to the nodal external force. Then, the calculation of the cyclic indentation is simulated using the converted nodal external forces as boundary conditions applied to the surface of the coated tool. Let us note that calculation after the interfacial debonding is not performed in the present calculation, since the evaluation of changes in the interfacial **damage** **variable** and interfacial relative displacement until the debonding is mainly focused on.

In the framework of thermodynamics, all constitutive equations of dissipative phenomena derive from a potential of dissipation. The development of **damage** mechanics in a thermodynamic framework by using the internal state **variable** theory [2] was developed by Germain [3] and later improved by Lemaitre [4], Chaboche [5], Krajcinovic [6] and many others. The **damage** evolution laws available in literature are expressed in terms of a dissipation potential and the **damage** **variable** ([5], [7] – [10]). Most of these models are empirical in nature and are obtained by a regression fit of experimental data and are applicable to metals. In this work, an analytical expression for dissipation potential is proposed by using mathematical arguments and concepts of dimensional analysis, from which a **damage** evolution model for concrete is developed.

and the fracture energy of a material with fractal cracks are investigated and their theoretical expresses in the fractal space are derived based on fracture mechanics and fractal geometry. The surface energy and the strain en- ergy in the fractal fracture zone are theoretical expressed in the fractal space. The transformation rule of **damage** variables in the fractal space and the Euclidean space is obtained which indicates that the apparent **damage** vari- able in the Euclidean space is a special case of the fractal one in the fractal space with the fractal dimension of cracks equals to 1. We introduce a plastic yield function and decompose the **damage** **variable** tensor into tensile and compressive parts to establish a plastic **damage** con- stitutive model for concrete in the Euclidean space. Gen- eralization of this model to the fractal space is done by utilizing the **damage** **variable** transformation rule.

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at this time of the year. Indeed, as the Food and Agriculture Organization reports, deciduous fruit trees, which are the most common plants cultivated in the northern region, are more sensitive in spring and autumn (Snyder and de Melo-Abreu, 2005). Likewise, Rodrigo (2000) reports that in temperate climates, losses due to frosts during bloom are more important than those due to low winter temperatures. For the southern re- gion, though, results are not statistically significant with re- spect to the effect of spring versus the effect of autumn, thus spring is not by definition expected to be associated with higher costs. According to Rodrigo (2000), freezing injuries to fruit trees can be associated with low temperatures prior to dormancy in the autumn, in midwinter during dormancy, or during and after budbreak in the spring. According to the re- gression results, in the period 1999–2009, spring and autumn in the southern region exhibited approximately the same rate of financial losses and similar rates of daily losses due to crop **damage** during frost events (EUR 41 and 45 million for spring and autumn frost events, respectively), which partly explains the regression analysis outcomes.

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For all 127 cases, we collected data for wind speed at landfall, total economic loss (TD), GDP exposed in the storm swath, storm duration, the length of existing seawalls and the wetland area traversed by storms to include in the regression analysis. The ordinary least square (OLS) estimate of the regression is summarized in Table 3 and is listed in Eq. (6). The model yielded a R 2 of 0.592. The associated sign of wetlands is negative and remains signi ﬁ cant when other confounding variables were added progressively. The fact that the coe ﬃ cient of wetlands re- mained negative and signiﬁcant implies that coastal wetlands did play a protective role. The coe ﬃ cient for wetlands of − 0.1966 indicates that the total economic **damage** decreases rapidly with increasing wetlands area. Aside from the wetlands, the other signiﬁcant determinants of economic **damage** by storm include wind speed at landfall, storm duration and the presence of seawalls. As expected, both wind speed and storm duration signiﬁcantly aﬀected the relative economic **damage** caused by storm. The relative economic **damage** increases as the 3.059 power of the wind speed at landfall during storm and the 1.0014 power of the storm duration. To control for the eﬀect of protective structures along the China’s coast, we included a **variable** capturing the presence of seawalls in the regression model. The negative sign of the seawalls suggests that the longer the seawalls in the storm swath the lower the storm **damage**. The coeﬃcient is negative and signiﬁcant implying that in areas where seawalls were present, coastal community su ﬀ ered less economic **damage**. On average, the expected reduction in the log count of relative economic **damage** (TD/GDP) with a kilometre increase in seawall cover is 0.0035.

merous macroscopic models is mainly imposed by the com- plexity and the variety of the observed behaviors (Pigeon, 1969; Chaboche, 1993; Rabier, 1989; Marigo, 1985). Most approaches favor the simplicity of the formulation by using a single scalar **damage** parameter to describe density of de- fects. More realistic **damage** model requires a tensorial for- mulation for a system of defects strongly influenced by the local field of stress. Some models take into account the uni- lateral effect (Badel et al., 2007; Halm and Dragon, 1998; Desmorat et al., 2007; Challamel et al., 2005; Alliche and Dumontet, 2011) and the dissymmetry between tension and compression.

Unfortunately for most dynamic systems the evolution relation (3) is not available. The Fourier analysis of the motion of many nonlinear systems will lead to a continuous spectrum, which is associated with an infinite number of modes. Nonlinear dynamics suggests a more general approach to study the dynamics of a system in its phase space, vis. by studying its attractor, which can be characterized by its invariants- the Lyapunov spec- trum, the entropy and different dimensions. It can be argued and there is much evidence that these characteris- tics change with the introduction of **damage** (Hunter al 2000, Todd et al 2001, Trendafilova 2002, Trendafilova 2003, Moniz et al 2005). The Lyapunov spectrum of a dynamic system characterises the average rate of con- traction or expansion in each of the principal geometric directions of the state space. For a linear vibrating sys- tem the Lyapunov exponents are determined by the real parts of the eigen values of the state space matrix of the system. Since it is clear that many **damage** scenarios affect the eigen state of a structure (Brincker et al,1994, Hunter et al,2000) then it can be argued that **damage** will affect the Lyapunov spectrum of a vibrating structure and hence – the geometry of its state space. Some of our and other authors’ research has shown, and it has been experimentally confirmed, that the Lyapunov exponents and the geometry of the attractor of a vibrat- ing system not only change under the introduction of **damage**, but they are rather sensitive to different kinds of **damage** (Todd et al,2001, Nichols et al 2003, Trendafilova 2002, Trendafilova 2003, Craig et al 2000). Unfor- tunately these invariants are on a lot of occasions are rather difficult to estimate precisely enough from data. There are methods for their estimation but they offer somewhat approximate results which on some occasions might be quite erroneous and might somewhat differ from the real invariants. This can be considered as a dis- advantage when using these invariants for **damage**/fault isolation purposes.

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at the inner surface of the main wall Fig. 20(a). This scenario was also well captured in the numerical model Fig. 20(b). At this stage in the experiment, the wall was unloaded and no further **damage** in the wall was reported in [31], similarly at the same loading stage the numerical model showed no complete cracks in the actual masonry units themselves, or crushing of masonry of under com- pression Fig. 21, and the numerical model continued to sustain fur- ther pressure. However, the numerical model shows multiple distributed diagonal cracks rather than individual diagonal cracks as occurred in the experiment. This difference may be due to the inaccuracies in the adopted material properties. As previously dis- cussed, some of the material parameters used in the numerical model have been estimated based on relevant parameters available in the literature, this situation is due to the absence of all required parameters in the experiment. Another potential source of differ- ence is the fact that the properties of the unit-mortar interfaces were defined to be the same in the entire wall, this assumption results in the equal contribution of the unit-mortar joints to dis- tribute the flexural stresses in the regions of the concentrated stresses. Realistically, the strength of the unit-mortar joints is unli- kely to be entirely uniform within a masonry assemblage due to various effects such as workmanship, quality of mortar, etc. Corre- spondingly, the cracks usually form individually along the rela- tively weaker joints.

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Abstract: To determine specific characteristics necessary for the computation of the C factor in RUSLe for time- **variable** crops, measurements were carried out in fields with selected agricultural crops grown by conventional practices. Sloping plots on an experimental area in Třebsín locality and farm fields were used to measure surface runoff and soil loss by erosion in conditions of natural and simulated rainfall. Basic characteristics to compute the C factor were determined in the particular growth phases of selected crops – sunflower, flax, poppy and rape. effective root mass, canopy cover and fall height of rain drops were measured.

The two main points of the method are detailed in the following sections. The counting **variable** that is used has to be good representative of the all components of the stress tensor and also of their real evolution versus time. The fatigue life is assessed at the point of the mechanical component where the stress states history is known by considering all the possible material planes through that point. As the crack initiation is developing on one particular plane of the material, all the possible orientations of the considered plane are examined and the **damage** is assessed through the stresses that the loading induces on that plane. This concept is the origin of the plane per plane **damage** and fatigue life valuation. Two linear and non linear **damage** law and cumulation rules have been adapted to multiaxial stress states to allow fatigue lives assessments. The method is general, i.e. suitable for any kind of loading history. The different steps of the procedure are described on the following flow chart (figure 1).

with UHL resulting from intracranial tumors based on MRI scanning and auditory assessment (pure tone audi- ometry, described below). Six of the patients were confirmed pathologically as having meningioma and were excluded from the experiment. Therefore, we reported results of the other 42 UHL patients with the same eti- ology. Twenty-one patients had hearing **damage** in the left ear, and 21 patients had hearing **damage** in the right ear. Twenty-four normal control (NC) participants were recruited from the local community in Beijing, with age, gender and education matched to the patients. All the controls also underwent the same MRI and auditory tests. These assessments were necessary for the patients during their clinical management, with no additional cost for them, and the control group received all the tests for free. The study was conducted on the UHL patients with AN preoperatively, and all the UHL participants had undergone the craniotomy to remove the neuromas after the MRI and auditory exam according to the clinical arrangement. All participants were right-handed and reported no previous or current psychiatric disorders (see Table 1 for participant demographics and auditory character- istics). Participants were informed of the requirements and provided written consent prior to participation. The Institutional Review Board of Beijing Tiantan Hospital of Capital Medical University approved this study, and the study procedures were carried out in accordance with the approved programs.

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The objection that this response might give rise to a fresh difficulty merely assumes, however, that the test for whether an inherent defect is substantial, and the test for whether the work required to remove the defect requires repair or renewal, are the same test. But there is no reason to make such an assumption. One can conceivably have a defect of a substantial kind, which nevertheless does not require renewal of the whole building. Clearly, there is a difference between a building that is not fitted with expansion joints – and the consequences that ensue from that omission – and a building which has defective putties fitted around its window frames. Certainly the difference is one of degree, but there is nevertheless a significant difference between these cases. Arguably, in Ravenseft, a building with the necessary expansion joints and cladding was a building different in kind from one without the same, even though the work required was not held to amount to renewal, because the consequences of the defect were substantial. It is this consideration of a defect of a substantial kind that lies behind the decision of Sir Brett Cloutman VC in Collins v Flynn. There, and in the two important cases concerning inherent defects that Sir Brett Cloutman reviewed – Wright v Lawson and Pembery v Lamdin – the work required did not amount to the renewal of the whole of the building, but only of a subsidiary part. Nevertheless, because the inherent defect was of a substantial kind, Sir Brett Cloutman, following those decisions, held that it was outside the repair covenant. This shows that whether or not an inherent defect is of a substantial kind is decided according to a different test from whether or not the work required to remedy **damage** amounts to renewal of substantially the whole of the building. The two tests need not, and in fact do not, coincide. Yet, as we have seen, the test for whether the defect is of a substantial kind has, by some judges, most notably

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This dissertation presents a framework for evaluating seismic fragilities of reinforced concrete structures like shear walls in nuclear power plants. A hybrid approach is proposed that is based on using large scale experimentally validated finite element models to evaluate the fragility considering the uncertainties and randomness in the material properties as well as seismic loads. A methodology is proposed to identify and characterize the parameters of concrete constitutive model such as **damage**-plasticity model. A Bayesian technique is proposed to update the existing fragility curves using the data obtained from nonlinear time history analyses. Fragility curves are developed for different performance criteria that corresponds to multiple **damage** limit states based on different engineering design parameters like maximum shear force, maximum shear deformation, maximum inter story drift ratio and maximum shear strains. This dissertation is organized primarily into three manuscripts that focus on describing the following aspects of the proposed framework:

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The **damage** of a composite structure was ana- lysed as a part of the conducted research. Experi- mental testing of the process of axial compression of a structure was conducted in room temperature with the traverse moving at a constant speed equal 2 mm/s. The tests were ran using special heads with flat working surfaces, using additional panel bases, which ensured simple support to the end cross-sections of the column. The experimen- tal tests were conducted for the full range of load, until the **damage** of the composite material. The boundary conditions for the real structure are pre- sented further in the study in Figure 2a.

Telomere length was measured at 10 days, 30 days and 1 year after the experiment. Telomere length was measured on DNA extracted from red blood cells (stored for 3 months at – 20°C until analysis) using DNeasy Blood and Tissue kit (Qiagen). Blood is an appropriate tissue to measure telomere length in this case as erythrocytes are nucleated in birds. Moreover, sampling is not invasive, and blood telomere length is correlated with telomere length in other tissues (Reichert et al., 2013). Telomere length was assessed by the quantitative real-time amplification (qPCR) procedure (Cawthon, 2002) previously used in zebra finches (Criscuolo et al., 2009). Relative telomere length is expressed as the ratio (T/S) of telomere repeat copy number (T) to a control single gene copy number (S). We used glyceraldehyde 3-phosphate dehydrogenase (GAPDH) as a non-**variable** control gene (Smith et al., 2011). Forward and reverse primers for the GAPDH gene were 5′-AACCAGCCAAGTACGATGACAT-3′ and 5′- CCATCAGCAGCAGCCTTCA-3′, respectively. Telomere primers were: Tel1b (5′-CGGTTTGTTTGGGTTTGGGTTTGGGTTTGGGTTTGGGTT- 3′) and Tel2b (5′-GGCTTGCCTTACCCTTACCCTTACCCTTACCC - TTACCCT-3′). qPCR for both telomeres and GAPDH was performed using 5 ng of DNA with sets of primers Tel1b/Tel2b (or GAPDH-F/GAPDH-R), each used at a concentration of 200 nmol l −1 /200 nmol l −1 , in a final volume

This work provided a new approach and technique to NDT. Such approach evaluates structures more accu- rately as it links the main principles of PSNR and WT into a single algorithm that is applied to uncover level and extent of **damage**. Such way of testing can be also used to evaluate material strength and ability to withstand impacts.

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