Change In Strain Energy Research Articles

Effects of process parameters on electromagnetic forming of AZ31 magnesium alloy sheets at room temperature

In this work, the effects of process parameters on AZ31 magnesium alloy sheets were investigated by electromagnetic bulging experiments. The bulging height increases with increasing discharging energy, which is adjusted by tuning discharge voltage and capacitance. The limit dome height of electromagnetic forming is markedly improved as compared to quasi-static forming. In order to improve the efficiency of the energy, 0.5- and 1-mm thick Al driver sheet were used to accelerate the magnesium alloy sheets. For rupturing the AZ31 sheet, the discharging energy can be reduced from a maximum value of 4.356 kJ (no driver) to 2.304 kJ (with1-mm Al driver sheet). The numerical simulation for the electromagnetic forming of AZ31 sheet is performed by means of ANSYS FEA software. The change of velocity, strain rate, and plastic strain energy were analyzed by simulation. Compared with quasi-static forming limit results, increases in the major and minor principal strains of approximately 68 and 72 % were achieved, respectively.

Strengths and strain energies of volcanic edifices: implications for eruptions, collapse calderas, and landslides

Abstract. Natural hazards associated with volcanic edifices depend partly on how fracture resistant the edifices are, i.e. on their strengths. Observations worldwide indicate that large fluid-driven extension fractures (dikes, inclined sheets), shear fractures (landslides), and mixed-mode fractures (ring dikes and ring faults) normally propagate more easily in a basaltic edifice (shield volcano) than in a stratovolcano. For example, dike-fed eruptions occur once every few years in many basaltic edifices but once every 102-3 yr in many stratovolcanoes. Large landslides and caldera collapses also appear to be more common in a typical basaltic edifice/shield volcano than in a typical stratovolcano. In contrast to a basaltic edifice, a stratovolcano is composed of mechanically dissimilar rock layers, i.e. layers with mismatching elastic properties (primarily Young's modulus). Elastic mismatch encourages fracture deflection and arrest at contacts and increases the amount of energy needed for a large-scale edifice failure. Fracture-related hazards depend on the potential energy available to propagate the fractures which, in turn, depends on the boundary conditions during fracture propagation. Here there are two possible scenarios: one in which the outer boundary of the volcanic edifice or rift zone does not move during the fracture propagation (constant displacement); the other in which the boundary moves (constant load). In the former, the total potential energy is the strain energy stored in the volcano before fracture formation; in the latter, the total potential energy is the strain energy plus the work done by the forces moving the boundary. Constant-displacement boundary conditions favor small eruptions, landslides, and caldera collapses, whereas constant-load conditions favor comparatively large eruptions, landslides, and collapses. For a typical magma chamber (sill-like with a diameter of 8 km), the strain energy change due to magma-chamber inflation is estimated at the order of 1014 J (0.1 PJ). For comparison, the surface energy needed to form a typical feeder dike is of the same order of magnitude, or 1014 J. There are several processes besides magma-chamber inflation that may increase the strain energy in a volcano before eruption. Thus, during a typical unrest period with magma-chamber inflation, the added strain energy in the volcano is large enough for a typical feeder dike to form. An injected dike, however, only reaches the surface and becomes a feeder if it is able to propagate through the numerous layers and contacts that tend to deflect or arrest dikes. The strong elastic mismatch between layers that constitute stratovolcanoes not only encourages fracture arrest, but also the storage of more strain energy (than in a typical basaltic edifice/shield volcano) before fracture formation and failure. It is thus through producing materials of widely different mechanical properties that stratovolcanoes become strong and resilient.

A probabilistic approach for the classification of earthquakes as ‘triggered’ or ‘not triggered’

The occurrence time of earthquakes can be anticipated or delayed by external phenomena that induce strain energy changes on the faults. ‘Anticipated’ earthquakes are generally called ‘triggered’; however, it can be controversial to label a specific earthquake as such, mostly because of the stochastic nature of earthquake occurrence and of the large uncertainties usually associated to stress modelling. Here we introduce a combined statistical and physical approach to quantify the probability that a given earthquake was triggered by a given stress-inducing phenomenon. As an example, we consider an earthquake that was likely triggered by a natural event: the M = 6.2 13 Jan 1976 Kópasker earthquake on the Grímsey lineament (Tjörnes Fracture Zone, Iceland), which occurred about 3 weeks after a large dike injection in the nearby Krafla fissure swarm. By using Coulomb stress calculations and the rate-and-state earthquake nucleation theory, we calculate the likelihood of the earthquake in a scenario that contains only the tectonic background and excludes the dike and in a scenario that includes the dike but excludes the background. Applying the Bayes’ theorem, we obtain that the probability that the earthquake was indeed triggered by the dike, rather than purely due to the accumulation of tectonic strain, is about 60 to 90 %. This methodology allows us to assign quantitative probabilities to different scenarios and can help in classifying earthquakes as triggered or not triggered by natural or human-induced changes of stress in the crust.

Comparing mechano-transduction in fibroblasts deficient of focal adhesion proteins

Mechano-transduction was studied in wildtype and focal adhesion (FA) protein-deficient mouse embryonic fibroblasts (MEFs). Using a cell stretcher, we determined the effect of stretch on cell morphology, apoptosis, and phosphorylation of ERK1/2. After 20% cyclic, uniaxial stretch, FA-deficient MEFs showed morphological changes and levels of apoptosis of the order: focal adhesion kinase>p130Cas>vinculin compared to wildtype cells. ERK1/2 phosphorylation peaked in wildtype cells at around 10min, and in all FA-deficient cells at around 5min. The relative change in strain energy of FA-deficient cells compared to wildtype cells was of the order: vinculin>FAK>p130Cas. Taken together, FAK and p130Cas are more important in the stretch-mediated downstream signaling and cell survival pathway, while vinculin is more critical in maintaining cell contractility.

Damage Identification of a Beam-Like Structure Using Element Modal Strain Energies and Natural Frequencies

A two-step damage identification method based on elemental modal strain energies and natural frequencies has been presented for a beam-like structure. In the first stage, this method makes use of the change of elemental modal strain energy before and after damage to locate the potential damage regions. And in the second stage, a damage identification algorithm based on the frequency changes is developed to calculate the damage extent and further determine the actual damage locations. The performance of the proposed method is numerically demonstrated by a simply supported beam with two damage cases. Results indicate that the method can identify the damage location and quantify the damage severity accurately in a beam-like structure.

Structural Damage Localization Using D-S Evidence Theory

Damage localization is a key issue in the Structural Health Monitoring (SHM). In order to enhance the accuracy of damage localization, an approach based on D-S evidence theory is studied in this paper. First, damage results obtained from the modal strain energy change ratio (MSECR) method and the multiple damage location assurance criterion (MDLAC) method are regarded as two independent information sources, respectively. And then, the D-S evidence theory-based information fusion technique is employed to integrate these two results and make a final decision. To compare the damage identification results under different methods, a practical damage evaluation indicator is presented. Numerical study on a cantilever beam is carried out to verify the proposed method. Results indicate that the damage evaluation indicators calculated by D-S evidence theory are superior to the single method. That is to say, structural damage identification method based on D-S evidence theory performs very well in determining the damage locations.

Damage detection in truss bridges using vibration based multi-criteria approach

This paper uses dynamic computer simulation techniques to develop and apply a multi-criteria procedure using non-destructive vibration-based parameters for damage assessment in truss bridges. In addition to changes in natural frequencies, this procedure incorporates two parameters, namely the modal flexibility and the modal strain energy. Using the numerically simulated modal data obtained through finite element analysis of the healthy and damaged bridge models, algorithms based on modal flexibility and modal strain energy changes before and after damage are obtained and used as the indices for the assessment of structural health state. The application of the two proposed parameters to truss-type structures is limited in the literature. The proposed multi-criteria based damage assessment procedure is therefore developed and applied to truss bridges. The application of the approach is demonstrated through numerical simulation studies of a single-span simply supported truss bridge with eight damage scenarios corresponding to different types of deck and truss damage. Results show that the proposed multi-criteria method is effective in damage assessment in this type of bridge superstructure.

Two-Stage Multi-damage Detection Method Based on Energy Balance Equation

In order to solve structural multi-damage identification problem, a two-stage damage detection method based on energy balance equation and evidence fusion is presented. First, a Frequency Change Identification (FCI) method and Modal Strain Energy Dissipation Ratio (MSEDR) method are utilized to preliminarily identify structural damage locations, and then a Fusion Damage Localization (FDL) method based on evidence theory is proposed to precisely detect damage locations. The FDL method mainly utilizes evidence theory to combine both the FCI localization information and the MSEDR localization information. Thus, more precise damage localization information can be acquired. After the damaged locations are determined, an Energy Balance Equation (EBE) index is presented to identify structural damage extent. Considering that strain energy dissipation should be equal to the change of modal strain energy, a quartic EBE equation is deduced, and structural damage extent can be obtained through the solution of the equation. An average quantification index is also proposed to improve identification precision. The simulation results demonstrate that the FDL method can perfectly detect structural damage locations, and the EBE index and average index can identify structural damage extent.

Effect of Material Ultimate Plasticity Strain on Collapse Resistant Capacity of 3D Steel Frame Structure during Earthquake

The collapse of structures caused by earthquakes causes catastrophic loss of life. Such collapse is typically caused by the inability of the structural system to redistribute its loads following the failure of one or more structural members to carry gravity loads. To study its mechanism in detail, numerical simulation is a significant method to reproduce the whole process of collapse in structural level. However, the traditional method was based on macro factors for collapse analysis and energy change in collapse process was less analyzed before, in fact, the kinds of energy components change with earthquake acceleration inputted and therefore it is necessary to analyze structural whole collapse process in terms of energy method. A three-dimensional computer simulation of the collapse of a real steel frame structure has been conducted using the LS-DYNA computer program in this paper. The responses and kinds of energy components of the structure under seismic loads are analyzed at different ultimate plasticity strain values and the strain energy change rate method for evaluating structure collapse is proposed in this paper. At last, the three main collapse patterns of structures are proposed.

A compression line for soils with evolving particle and pore size distributions due to particle crushing

In this study it is supposed that energy is dissipated in two ways when particle crushing occurs. The first is the release of strain energy stored in the crushed particle and is analogous to the creation of surface. The second is due to the load redistribution and change of stored strain energy of the surrounding soil. Terms for these two mechanisms are included in a Cam-clay type energy equation. By defining particle and pore size distributions during the crushing process using fractals, and by equating particle and pore surface areas, a closed-form expression is obtained for a limiting compression line in the double logarithmic voids ratio–stress plane. The limiting compression line and the evolving particle size distribution are matched well by the theory for two silica sands loaded in oedometric compression to high stresses. Evidently, energy dissipation due to load redistribution is significantly larger than energy dissipation due to the creation of surface.

Quasi-static simulation of constrained layered damped laminated curvature shells subjected to low-velocity impact

With experiments, this study discussed the characteristics of composite curvature shells with constrained layered damping (CLD) subjected to low-velocity impact as well as compared the reactions of the curvature shells with/without CLD. In addition to the experiments, this study proposed the quasi-static simulation, which could rapidly obtain the results with different impact velocities and drift masses with the force–displacement curve of static crushing test, to receive the results subjected to low-velocity impact under various impact conditions. The shell specimens were laminated with two stacking sequences collocating two different drift masses and impact velocities. The experiment of low-velocity impact applied Dynatup-GRC8250 and IDA system to measure the impact force at various time-points in the process of impact and, with the conservation of energy, changes of velocity and strain energy in the impact process could be calculated with the initial velocity of the impact. Finally, the quasi-static simulations were compared with the experiments to verify the accuracy of simulations, and results were found satisfactory.

Anisotropic lattice strain relaxation of MgO/SrTiO 3(001) in a textured island growth mode

The out-of-plane and in-plane lattice parameters were measured by in-situ reflection high-energy electron diffraction (RHEED) at the initial growth stage of MgO thin films on SrTiO 3(001) substrates in the growth mode of islands. The in-plane lattice was found to relax immediately after initiating the film deposition, and the majority of the in-plane strain was relieved at the film thickness of 2 nm. Beyond the thickness, the in-plane lattice almost was kept unchanged, and the out-of-plane lattice continued to relax gradually. The anisotropic strain can be attributed to the change of strain energy due to film texture during the ripening process. The relationship between strain and texture, grain size was discussed from the viewpoint of energy competition.

Microstructure evolution of a [011] orientation single crystal nickel-base superalloy during tensile creep

Microstructure of [011] oriented single crystal nickel-base superalloy consists of the cubical γ′ phase embedded coherently in the γ matrix, and arranged regularly along 〈100〉 orientations. After tensile creep, the cubical γ′ phase in the alloy is transformed into the strip-like rafted structure along [001] direction under the ordering transformation free-energy and strain energy change. And the directional growing of γ′ phase is attributed to the atoms Al and Ta into (001) plane to form the stable stacking mode.

Structural Damage Detection Based on Strain Energy and Evidence Theory

In order to solve the damage detection problem, a damage detection method based on strain energy and evidence theory is presented in this paper. First, an evidence theory method is proposed to identify structural damage locations. Then, structural modal strain energy is utilized to quantify structural damage extents. In general, structural strain energy dissipation should be equal to the change of modal strain energy, according to this theory, a new energy equation is deduced, and structural damage extent can be obtained through the solution of the equation. The simulation results show that the method can perfectly identify damage locations and extents. Therefore, the proposed method is effective for the structural damage identification.

DAMAGE DETECTION IN A COMPOSITE BEAM WITH A DOUBLE EDGE CRACK USING FINITE ELEMENT ANALYSIS

Cracks in vibrating component can initiate catastrophic failures. The presences of cracks change the physical characteristics of a structure which in turn alter its dynamic response characteristics. Therefore there is need to understand dynamics of cracked structures. Crack depth and location are the main parameters for the vibration analysis. So it becomes very important to monitor the changes in the response parameters of the structure to access structural integrity, performance and safety. A number of analytical, numerical and experimental techniques are available for the study of damage identification in beams. The objective of this paper is to develop a damage detection method in a composite cantilever beam with a double edge crack has been studied using finite element method. The vibration-based damage detection methods are based on the fact that changes of physical properties (stiffness, mass and damping) due to damage will manifest themselves as changes in the structural modal parameters (natural frequencies, mode shapes and modal damping). The task is then to monitor the selected indicators derived from modal parameters to distinguish between undamaged and damaged states. In the present study, vibration analysis is carried out on a cantilever beam with two open transverse cracks, to study the response characteristics and damage identification is based on the damage index method. Suitable boundary conditions are used to find out natural frequency and mode shapes. The results obtained numerically are validated with the results obtained from the simulation. The simulations have done with the help of ANSYS software. The importance of using damage patterns from the damage index method, (which is based on changes in modal strain energies) is that only measured mode shapes are required in the damage identification. The results shows, the damage index based method is capable of identification of damage and severity of damage in a structure.

A strain-controlled hot-mix asphalt fatigue model considering low and high cycles

The fatigue life of hot-mix asphalt (HMA) is widely accepted as the number of loading cycles required to reach 50% of its initial flexural stiffness (N f-50%). However, it is difficult to recognise the threshold between the elastic, where no damage occurs, and plastic ranges, where cracks begin to initiate. Phenomenological fatigue behaviours under cyclic loading are classified into three stages: primary (high dissipated strain-energy change without cracking), secondary (constant dissipated strain-energy change between two consecutive hysteresis loading loops) and tertiary (rapid change in dissipated strain energy after crack initiation). However, the threshold between the secondary and tertiary stages cannot be considered fatigue failure using the N f-50% criterion. This study clarifies the dissipated energy changes during loading and proposes four parameters to define fatigue behaviour of 13-mm dense-graded HMA using bending beam at various strain amplitudes. In addition, a fatigue life threshold, at the transition from stable behaviour to the fatigue failure, is also proposed.

Application of the damage index method for plate-like structures to timber bridges

The paper presents a research recently completed by the authors utilizing a method of damage evaluation for identifying damage in timber bridges, numerically and experimentally. The method utilizes changes in modal strain energy between the undamaged and damaged states of plate-like structures. A finite element model of a laboratory timber bridge was developed to investigate the capabilities and limitations of the method to detect damage. A simple four-girder bridge was fabricated and tested in a laboratory to verify the method. The numerical studies showed that the method can correctly identify single and multiple damage locations within the bridge. The experimental studies also showed promising results for detecting severe damage, but less effective for light and medium damage. Copyright © 2009 John Wiley & Sons, Ltd.

A circular inhomogeneity with interface slip and diffusion under in-plane deformation

We consider the in-plane deformation of a circular elastic inhomogeneity embedded in an infinite elastic matrix subjected to remote uniform stresses or uniform heat flow. The inhomogeneity and matrix have different material properties. The rate-dependent slip and mass transport by stress-driven diffusion concurrently occur on the inhomogeneity/matrix interface. For the remote uniform stress case, it is observed that the internal stresses within the inhomogeneity are quadratic functions of the coordinates x and y, and decay with two relaxation times. Interestingly the average mean stress within the circular inhomogeneity is in fact time-independent. As time approaches infinity, the internal stress field within the inhomogeneity becomes uniform and hydrostatic. In addition the change of strain energy due to the introduction of the circular elastic inhomogeneity is derived, containing various existing results as special cases. Furthermore, a simple condition leading to an internal uniform stress state within the inhomogeneity is found. This condition, which is independent of the elastic properties of the inhomogeneity and matrix, gives a simple relationship between the interface drag and diffusion parameters. For the remote heat flow case, the internal thermal stresses are linear functions of the coordinates x and y and decay only with a single relaxation time. Numerical results are presented to demonstrate the obtained solution and the corresponding physics.

Age Dependent Mechanical Properties of the Infant Porcine Parietal Bone and a Correlation to the Human

An infant less than 18 months of age with a skull fracture has a one in three chance of abuse. Injury biomechanics are often used in the investigation of these cases. In addition to case-based investigations, computer modeling, and test dummies, animal model studies can aid in these investigations. This study documents age effects on the mechanical properties of parietal bone and coronal suture in porcine infants and correlates the bending properties of the bone to existing human infant data. Three beam specimens were cut from porcine specimens aged 3 days, 7 days, 10 days, 14 days, 18 days, and 21 days: one across the coronal suture and two from the parietal bone, one parallel to and one perpendicular to the coronal suture. An actuator-mounted probe applied four-point bending in displacement control at 25 mm/s until failure. Bending stiffness of bone specimens increased with age; bone-suture-bone specimens showed no change up to 14 days but increased from 14 days to 18 days. All three specimen types showed decreases in ultimate stress with age. Ultimate strain for the bone-suture-bone specimens was significantly higher than that for the bone specimens up to 14 days with no differences thereafter. There was no change in the bending modulus with age for any specimen type. Bone-suture-bone bending modulus was lower than that of the bone specimens up to 14 days with no differences thereafter. There was no change in strain energy to failure with age for the bone specimens; bone-suture-bone specimens showed no change up to 14 days but decreased from 14 days to 18 days. There was an increase in specimen porosity with age. Correlation analysis revealed a weak (-0.39) but significant and negative correlation between ultimate stress and porosity. While the mechanical properties of parietal bone and coronal suture did not change significantly with age, bone specimens showed an increase in bending stiffness with age. Bone-suture-bone specimens showed an increase in bending stiffness only between 14 days and 18 days of age. Correlation analyses using existing and new data to compute the bending rigidity of infant parietal bone specimens suggested that days of pig age may correlate with months of human age during the most common time frame of childhood abuse cases.

Damage detection in jacket type offshore platforms using modal strain energy

Structural damage detection, damage localization and severity estimation of jacket platforms, based on calculating modal strain energy is presented in this paper. In the structure, damage often causes a loss of stiffness in some elements, so modal parameters; mode shapes and natural frequencies, in the damaged structure are different from the undamaged state. Geometrical location of damage is detected by computing modal strain energy change ratio (MSECR) for each structural element, which elements with higher MSECR are suspected to be damaged. For each suspected damaged element, by computing cross-modal strain energy (CMSE), damage severity as the stiffness reduction factor -that represented the ratios between the element stiffness changes to the undamaged element stiffness- is estimated. Numerical studies are demonstrated for a three dimensional, single bay, four stories frame of the existing jacket platform, based on the synthetic data that generated from finite element model. It is observed that this method can be used for damage detection of this kind of structures.