Change In Strain Energy Research Articles

Mechanics and mechanisms of puncture by medical needles

Resistance to puncture is a critical property for several applications, in particular for elastomer materials used in protective clothing. To evaluate the puncture resistance of membranes, some methods have been proposed as standard tests. However, the rounded puncture probes used in these tests are very different from real pointed objects like medical needles, and may not measure the level of material resistance that correspond to them. In fact, puncture by medical needles is shown to proceed gradually as the needle cuts into the membrane. This behavior is highly different from puncture by rounded probes which occurs suddenly when the strain at the probe tip reaches the failure value. In addition, maximum force values are observed to be much smaller with medical needles. A method has been developed based on the change in strain energy with the puncture depth to evaluate the fracture energy associated to puncture. The results show that the phenomenon of puncture by medical needles involves contributions both from friction and fracture energy, in a similar way as for cutting. Prestrained samples must be used to determine the material puncture energy.

Simulation study on damage localization of a beam using evidence theory

Structural damage localization plays an important role in structural damage identification. An cumulative structural damage localization method based on evidence theory is studied in this paper. An algorithm for cumulative fusion of primary localization information is presented. In the numerical study, a fixed-end beam is inspected. Two damage cases are studied, one with single damage and the other with multiple damages. White noises are added to the beam mode shapes of the first five orders to simulate the measurement noises. First, Modal Strain Energy Change Ratio (MSECR) method is used to localize the damage elements using the noise-contaminated mode shapes. Then, the locations determined by MSECR are taken as primary information and fused cumulatively. In both the single-damage-case and the multiple-damage-case, the fused results show that damaged elements are accurately identified. Furthermore, the damage elements are distinguished much more clearly than those identified from MSECR.

Molecular mechanics and molecular dynamics study on azurin using extensible and systematic force field (ESFF)

A systematic study on the assessment of predictive power of extensible and systematic force field (ESFF) has been carried out by taking azurin as a model metalloprotein. Both molecular mechanics (MM) and molecular dynamics (MD) calculations have been performed on native azurin. In addition, the effects of metal ion substitution and mutation of axial methionine have been investigated. MM calculations with axial ligand restraints reasonably predict the structures of native and engineered azurins. It is also evident from the MD simulations that the average structures are similar to that of corresponding X-ray structures. The overall conformation of the engineered and mutated azurins is also akin to that of native protein. However, significant changes are observed in metal ion binding site upon substitution and axial mutation. It is found that the calculated change in strain energy linearly varies with the corresponding experimental redox potentials of engineered azurins.

Experimental validation of modal strain energies based damage identification method for a composite sandwich beam

A vibration-based damage identification method, based on changes in modal strain energies before and after occurrence of damage, is presented for a composite sandwich beam. Experiments were performed to obtain the natural frequencies and mode shapes for validation of the presented method. The observed changes in modal strain energies were used for the prediction of existence and location of damage in a composite sandwich beam. Subsequently, these changes were also used to predict damage extents in the two stages. In the first stage, the proposed method is used to approximate the damage extents in the face and core. These were updated to obtain more accurate values of damage extent at the second stage by using the model updating theory. Experimental and numerical results were presented to demonstrate and verify the effectiveness of this method for several single and multiple damage cases. These damage cases also include interactive damage modes. Results indicate that the proposed method is capable of identifying the location and extent of damage in the faces and core of a composite sandwich beam.

Vibration based structural damage detection in flexural members using multi-criteria approach

This paper uses dynamic computer simulation techniques to develop and apply a procedure using non-destructive methods for damage assessment in beams and plates, which are important flexural members in building and bridge structures. In addition to changes in natural frequencies, this multi-criteria procedure incorporates two methods, called the modal flexibility and the modal strain energy method, which are based on the vibration characteristics of the structure. Using the results from modal analysis, algorithms based on flexibility and strain energy changes before and after damage are obtained and used as the indices for the assessment of the status of the structural health. The objective is to evaluate the feasibility of the proposed multi-criteria method to identify and localise single and multiple damages in numerical models of flexural members having different boundary conditions. The application of the approach is demonstrated through two sets of numerical simulation studies on beam and plate structures with nine damage scenarios in each. Results show that the proposed multi-criteria method incorporating modal flexibility and modal strain energy method is effective in multiple damage assessment in beam and plate structures.

INVERSE SQUARE ROOT MOMENT SINGULARITIES IN RECTANGULAR PLATES CONTAINING AN INTERNAL LINE SUPPORT

Two cases of a rectangular plate having moment singularities at the ends of a partial internal line support are analytically investigated. The bending of the plate by uniform loading is formulated in terms of dual-series equations. Application of the finite Hankel integral transform reduces the dual-series equations to a Fredholm integral equation of the second kind that can be solved by standard techniques. Numerical results are given for the deflections and bending moments along the line outside of an internal line support and the change in strain energy due to the presence of a partial support.

Damage Diagnosis of Frame Structures Using Modified Modal Strain Energy Change Method

This work presents a modified modal strain energy change (M-MSEC) method and its corresponding iteration process to detect damage to frame structures. Analytical results of a three-dimensional frame structure demonstrate that the quantity of damage can be identified correctly by using different modes in the M-MSEC method. A full-scale experimental study is also performed to evaluate the robustness of the M-MSEC method on damage detection as well as damage quantification. Satisfactory results are shown in relation to the modeling error, noise effect, and limited measurements.

Energy Index Method: Technique for Identification of Structural Damages

A structural damage detection method based on the change of strain energy in each element before and after the occurrence of damage is presented. The proposed method can localize and quantify both single and multiple damages. The algorithm requires only the stiffness and mass matrices of the baseline structure and a few measured mode shapes of the current structure to find the location and severity of damage. The proposed method is applied to a benchmark problem sponsored by the IASC-ASCE Task Group on Structural Health Monitoring, which was developed in order to facilitate the comparison of various damage identification methods.

Condition Assessment of Structures Under Ambient White Noise Excitation

This paper proposes a damage detection method based on the wavelet packet energy of covariance of measured acceleration responses of structures under ambient excitation. It is a model-based method comparing the measured acceleration responses before and after damage occurrence. The ambient excitation is assumed to be white noise. A damage index based on the change of modal strain energy is used for damage localization. The damage quantification is performed using the sensitivity of the wavelet packet energy of the covariance function. A cantilever five-bay truss structure is used to demonstrate the efficiency of the method with three damage scenarios. The combined two-stage approach is shown capable of locating and accurately quantifying local damages in the presence of measurement noise. A nine-bay three-dimensional truss structure is also assessed in the laboratory with the proposed method, and the whole process of damage detection with incomplete and noisy measurement, initial model error, etc., is demonstrated to be successful for identifying, with good accuracy, local damages in members.

Time-dependent stress change during failure of rocks

The energy balance of a solid subject to fracture has been explored using heat and mass transfer equations with regard to the volumetric and superficial components. In the suggested model, brittle fracture of a cracked solid considered as a heterogeneous two-phase medium is described by an equation analogous to the Griffith’s criterion for propagation of a single crack. The derived equation is used, together with estimates of relative change in specific interface area, to study the respective change of free strain energy and pressure in rocks associated with failure.

Application of the modified damage index method to timber beams

In this paper the use of two existing algorithms developed for global nondestructive evaluation to locate and evaluate localised damage in timber beams is investigated using a finite element model. These damage localisation algorithms were found, through this investigation, not to be effective in locating multiple damage scenarios and unable to evaluate the severity of damage. Hence, modifications on damage index algorithms as well as a hybrid algorithm are proposed to overcome the problems. In this study, experimental modal analysis (EMA) was used as a tool to extract mode shapes for calculating the damage index in the proposed method which utilises changes in modal strain energy between the undamaged and the damaged timber beam model. The modified damage index (MDI) method normalises the mode shape curvature and the hybrid algorithm combines the modified damage index and changes in flexibility algorithms which reflect the changes of natural frequency and mode shape. Analytical evaluations were performed to compare and verify the ability of original and modified damage localisation algorithms in locating single and multiple damage in timber beams. The modified damage index (MDI) algorithm and the hybrid damage algorithm are also used in the experimental studies to validate the effectiveness of the methods to locate and evaluate damage within timber beams by laboratory experiments.

Vibration-based damage detection in beams using genetic algorithm

In this paper, an improved GA-based damage detection algorithm using a set of combined modal features is proposed. Firstly, a new GA-based damage detection algorithm is formulated for beam-type structures. A schematic of the GA-based damage detection algorithm is designed and objective functions using several modal features are selected for the algorithm. Secondly, experimental modal tests are performed on free-free beams. Modal features such as natural frequency, mode shape, and modal strain energy are experimentally measured before and after damage in the test beams. Finally, damage detection exercises are performed on the test beam to evaluate the feasibility of the proposed method. Experimental results show that the damage detection is the most accurate when frequency changes combined with modal strain-energy changes are used as the modal features for the proposed method.

Influence of electronic and steric effects on stability constants and electrochemical reversibility of divalent ion complexes with glycine and sarcosine: A glass electrode potentiometric, sampled direct current polarographic, virtual potentiometric, and molecular modelling study

Cd II complexes with glycine (gly) and sarcosine (sar) were studied by glass electrode potentiometry, direct current polarography, virtual potentiometry, and molecular modelling. The electrochemically reversible Cd II–glycine–OH labile system was best described by a model consisting of M(HL), ML, ML 2, ML 3, ML(OH) and ML 2(OH) (M = Cd II, L = gly) with the overall stability constants, as log β, determined to be 10.30 ± 0.05, 4.21 ± 0.03, 7.30 ± 0.05, 9.84 ± 0.04, 8.9 ± 0.1, and 10.75 ± 0.10, respectively. In case of the electrochemically quasi-reversible Cd II–sarcosine–OH labile system, only ML, ML 2 and ML 3 (M = Cd II, L = sar) were found and their stability constants, as log β, were determined to be 3.80 ± 0.03, 6.91 ± 0.07, and 8.9 ± 0.4, respectively. Stability constants for the ML complexes, the prime focus of this work, were thus established with an uncertainty smaller than 0.05 log units. The observed departure from electrochemical reversibility for the Cd–sarcosine–OH system was attributed mainly to the decrease in the transfer coefficient α. The MM2 force field, supplemented by additional parameters, reproduced the reported crystal structures of diaqua-bis(glycinato-O,N)nickel(II) and fac-tri(glycinato)-nickelate(II) very well. These parameters were used to predict structures of all possible isomers of (i) [Ni(H 2O) 4(gly)] + and [Ni(H 2O) 4(sar)] +; and (ii) [Ni(H 2O) 3(IDA)] and [Ni(H 2O) 3(MIDA)] (IDA = iminodiacetic acid, MIDA = N-methyl iminodiacetic acid) by molecular mechanics/simulated annealing methods. The change in strain energy, Δ U str, that accompanies the substitution of one ligand by another (ML + L′ → ML′ + L), was computed and a strain energy Δ U str = +0.28 kcal mol −1 for the reaction [Ni(H 2O) 4(gly)] + + sar → [Ni(H 2O) 4(sar)] + + gly was found. This predicts the monoglycine complex to be marginally more stable. By contrast, for the reaction [Ni(H 2O) 3IDA] + MIDA → [Ni(H 2O) 3MIDA] + IDA, Δ U str = −0.64 kcal mol −1, and the monoMIDA complex is predicted to be more stable. This correlates well with (i) stability constants for Cd–gly and Cd–sar reported here; and (ii) known stability constants of ML complex for glycine, sarcosine, IDA, and MIDA.

Thermoelastic and infrared-thermography methods for surface strains in cracked orthotropic composite materials

Two quantitative thermoelastic strain analysis (TSA) experimental methods are proposed to determine the surface strain fields in mechanically loaded orthotropic materials using the spatial distribution of temperature gradient measured from the surface. Cyclic loadings are applied to orthotropic composite specimens to achieve adiabatic conditions. The small change in surface temperatures that resulted from the change in the elastic strain energy is measured using a high sensitivity infrared (IR) camera that is synchronized with the applied loading. The first method is applied for layered orthotropic composites with a coat layer made of isotropic or in-plane transversely isotropic material. In this case, one material parameter (pre-calibrated from the surface) is required to map the strain invariant to the temperature gradients. The proposed method can be used together with Lekhnitskii’s elasticity solution to quantify the full strain field and determine mixed-mode stress intensity factors (SIFs) for crack tips in composite plates subjected to off-axis loading. The second method is formulated for orthotropic layers without a coat and it requires thermo-mechanical calibrations for two material parameters aligned with the material axes. The virtual crack closure technique (VCCT), Lekhnitskii’s and Savin’s elasticity solutions, and finite element (FE) analyses are used for demonstrations and validations of the second experimental method. The SIFs from the TSA methods are very sensitive to the uncertainty in the location of the crack tip and the unknown inelastic or damage zone size around the crack tip. The two experimental methods are effective in generating the strain fields around notched and other FRP composites.

Damage localisation and severity evaluation of a beam-like timber structure based on modal strain energy and flexibility approaches

Timber bridges are often exposed to harsh environmental conditions, which, over time, can lead to deterioration resulting from decay, insect attack, weathering, and mechanical damage. In turn, this deterioration may lead to a loss of structural integrity that is detrimental to the structure and its users. Non-destructive evaluation (NDE) techniques provide effective means for assessment of current structural integrity status of given structures. As a global NDE technique, vibration-based damage identification techniques have received increasing attention for structural damage evaluation. Among them, there is a popular and promising damage identification method called the damage index method based on calculating the change of modal strain energy before and after damage. Despite its popularity, however, a systematic investigation on its capability and limitations in locating and quantifying damage is yet to be reported, especially for structures suffering multiple damage. In this paper, after reviewing the current NDE methods, the focus was set on the vibration-based NDE methods, in particular the damage index method. The investigation was based on finite element analysis (FEA) results of a timber beam by which the capability and limitation of the damage index was fully explored. As a result of the investigation, a new hybrid algorithm combining modified damage index (MDI) and change in flexibility algorithms is proposed for damage localisation and severity evaluation. The numerical results indicate that the proposed hybrid algorithms based on MDI method and flexibility have clear advantages in detecting damage locations and evaluating damage severities, especially for multiple damage cases.

Atomistic-continuum and ab initio estimation of the elastic moduli of single-walled carbon nanotubes

This paper deals with the calculation of elastic moduli and stress–strain curves for single-walled carbon nanotubes (SWNTs) using a computationally efficient, atomistically enriched continuum analysis. This approach is adopted to estimate shear and Young’s moduli and obtain stress–strain curves for carbon nanotubes (CNTs) subject to coupled extension and twist deformations. This accounts for the effects of natural extension-twist coupling [K. Chandraseker, S. Mukherjee, ASME J. Appl. Mech. 73 (2) (2006) 315–326; K. Chandraseker, S. Mukherjee, Y.X. Mukherjee, Int. J. Solids Struct. 43 (2006) 7128–7144] on SWNT constitutive properties. The constitutive properties are evaluated by assuming a cylindrical reference configuration [Chandraseker and Mukherjee, 2006; Chandraseker et al., 2006] rather than a planar graphene sheet [P. Zhang, Y. Huang, P.H. Geubelle, P.A. Klein, K.C. Hwang, Int. J. Solids Struct. 39 (2002) 3893–3906; M. Arroyo, T. Belytschko, Phys. Rev. B 69 (2004) 115415] thereby allowing for the anisotropy and change in strain energy that results from the finite deformation required to roll up a graphene sheet into a nanotube [M. Arroyo, T. Belytschko, Phys. Rev. B 69 (2004) 115415]. The Tersoff–Brenner multi-body empirical interatomic potential for carbon [J. Tersoff, Phys. Rev. B 37 (1988) 6991–7000; D.W. Brenner, Phys. Rev. B 42 (1990) 9458–9471] is used to model the C–C bond energies in this work. This enables exact analytic evaluation of the derivatives of the strain energy density rather than a numerical approach. Consistent values obtained corresponding to these material properties indicate that they do not depend strongly on the chirality of the nanotube [R. Saito, G. Dresselhaus, M.S. Dresselhaus, Physical Properties of Carbon Nanotubes, Imperial College Press, London, 1998 [7]]. The relative magnitudes of the Young’s and shear moduli obtained from this approach fall within the well known range in classical elasticity theory in most cases, and the computed values for the moduli agree well with existing experimental results and atomistic studies that employ the same interatomic potential. Further, in the present work, the moduli are also evaluated using a more accurate, albeit computationally expensive, ab initio density-functional-theoretic (DFT) approach (see for e.g., [D. Sáncez-Portal, E. Artacho, J.M. Soler, A. Rubio, P. Ordejón, Phys. Rev. B 59 (1999) 12678; K.N. Kudin, G.E. Scuseria, B.I. Yakobson, Phys. Rev. B 64 (2001) 235406]). A comparison between these values and the ones from the atomistic-continuum analysis brings to notice some of the advantages and limitations of both these approaches.

Damage Localization and Finite-Element Model Updating Using Multiresponse NDT Data

New techniques for both finite-element model updating and damage localization are presented using multiresponse nondestructive test (NDT) data. A new protocol for combining multiple parameter estimation algorithms for model updating is presented along with an illustrative example. This approach allows for the simultaneous use of both static and modal NDT data to perform model updating at the element level. A new damage index based on multiresponse NDT data is presented for damage localization of structures. This index is based on static and modal strain energy changes in a structure as a result of damage. This method depicts changes in physical properties of each structural element compared to its initial state using NDT data. Deficient or potentially damaged structural elements are then selected as the unknown parameters to be updated by parameter estimation. Error function normalization, error function stacking, and multiresponse parameter estimation methods are proposed for using multiple data types for simultaneous stiffness and mass parameter estimation. Also, multiple sets of measurements with various sizes and missing data points can be utilized. This paper uses a laboratory grid model of a bridge deck built at the University of Cincinnati Infrastructure Institute and the corresponding NDT data for validation of the above damage localization and model updating methods. Multiresponse parameter estimation has been utilized to update the stiffness of bearing pads, and both the stiffness and mass of the connections, using static and dynamic NDT data. The static and modal responses of the updated grid model presented a closer match with the NDT data than the responses from the initial model.

Near-Source Released Energy in Relation to Fracture Energy on Earthquake Faults

The near-source energy released on a fault is estimated through the strain energy change and the fracture energy from the results of kinematic waveform inversion and dynamic modeling for two different types of earthquakes: a shallow crustal earthquake, the 2000 Tottori, Japan ( M w 6.6) earthquake, and an in-slab event, the 1999 Oaxaca, Mexico ( M w 7.5) earthquake. The procedure incorporates the spatial distribution of slip, critical slip-weakening distance, stress drop, and strength excess. The results show that the near-source energy density estimated over major asperities on the fault is nearly the same for the two earthquakes, while the fracture energy on the in-slab fault is appreciably larger than that for the crustal fault, suggesting higher strength in the in-slab fault zone. The near-source released energy on major asperities is significantly larger than the fracture energy in the two earthquakes.

Framework for optimal design of porous scaffold microstructure by computational simulation of bone regeneration

In bone tissue engineering using a biodegradable scaffold, geometry of the porous scaffold microstructure is a key factor for controlling mechanical function of the bone–scaffold system in the regeneration process as well as after the regeneration. In this study, we propose a framework for the optimal design of the porous scaffold microstructure by three-dimensional computational simulation of bone tissue regeneration that consists of scaffold degradation and new bone formation. The rate of scaffold degradation due to hydrolysis, that leads to decrease in mechanical properties, was simply assumed to relate to the water content diffused from the surface to the bulk material. For the new bone formation on both bone and scaffold surfaces, the rate equation of trabecular surface remodeling driven by mechanical stimulation was applied. Solving these two phenomena in the same time frame, the bone regeneration process in the bone–scaffold system was predicted by computational simulation using a voxel finite element method. The change in the mechanical function of the bone–scaffold system during the regeneration process was quantitatively evaluated by measuring the change in total strain energy, and this was used for the evaluation function to optimize the scaffold microstructure that provides the desired mechanical function during and after the bone regeneration process. A case study conducted for the scaffold with a simple microstructure demonstrated that the proposed simulation method could be applied to the design of a porous scaffold microstructure. In addition, the regeneration process was found to be very complex even though the simple rate equations for scaffold regeneration and new bone formation were used because of the coupling effects of these phenomena.

Raman study and theoretical calculations of strain in GaN quantum dot multilayers

Changes in strain and phonon mode energy in stacks of self-assembled GaN quantum dots embedded in AlN have been studied by means of Raman spectroscopy as a function of the number of periods. The ${E}_{2H}$ phonon modes related to the quantum dots and AlN spacers are clearly resolved, and their energies allow monitoring the state of strain of the dots and AlN spacers simultaneously. The evolution of the measured phonon frequencies and the associated strains are discussed in comparison with theoretical calculations of the inhomogeneous strain distribution in a system of coherent misfitting inclusions.