Shear Strain Energy Research Articles

The contribution of a directional preference of stiffness to the efficacy of prophylactic sacral dressings in protecting healthy and diabetic tissues from pressure injury: computational modelling studies.

The sacral region is the most common site for pressure injuries (PIs) associated with lying in bed, and such sacral PIs often commence as deep tissue injuries (DTIs) that later present as open wounds. In complex patients, diabetes is common. Because, among other factors, diabetes affects connective tissue stiffness properties, making these tissues less able to dissipate mechanical loads through physiological deformations, diabetes is an additional biomechanical risk factor for PIs and DTIs. A preventive measure with established successful clinical outcomes is the use of sacral prophylactic dressings. The objective of this study has been to expand our previous work regarding the modes of action and biomechanical efficacy of prophylactic dressings in protecting the soft tissues adjacent to the sacrum by specifically examining the role of a directional stiffness preference (anisotropy) of the dressing while further accounting for diabetic tissue conditions. Multiple three-dimensional anatomically detailed finite element (FE) model variants representing diabetic tissue conditions were used, and tissue loading state data were compared with healthy tissue simulations. We specifically compared soft tissue exposures to elevated internal shear stresses and strain energy densities (SED) near the sacrum during supine weight bearing on a standard (foam) hospital mattress without a dressing, with a prophylactic dressing lacking directional stiffness preferences and with an anisotropic dressing. Our results have clearly shown that an anisotropic dressing design reduces the peak tissue stresses and exposure to sustained tissue deformations in both healthy and diabetic cases. The present study provides additional important insights regarding the optimal structural and material design of prophylactic dressings, which in turn, informs clinicians and decision makers regarding beneficial features.

Torsional Fatigue Strength of Newly Developed Case Hardening TRIP-Aided Steel

The torsional fatigue strength of newly developed case hardening steel, i.e., transformation-induced plasticity-aided martensitic steel subjected to vacuum carburizing followed by fine particle peening, was investigated for the fabrication of downsized precision gears with high torque capacity and wear resistance. The surface-hardened layer properties—i.e., high Vickers hardness, high compressive residual stress, and a large amount of retained austenite—considerably increased the torsional fatigue limits of vacuum-carburized and fine particle peened TM and JIS-SNCM420 steels, although the notch-sensitivity to fatigue was increased. The relation between torsional and rotational bending fatigue limits for the smooth specimens was found to be between the maximum principal stress and the minimum shear strain energy criterions. On the other hand, this relation for the notched specimens was represented through the maximum principal stress criterion.

Fatigue damage prediction in multiaxial loading using a new energy-based parameter

A new approach for the definition of the critical plane and a new energy-based multiaxial fatigue parameter are proposed in this work. The normal strain energy and shear strain energy on two orthogonal material planes are used to predict fatigue damage in multiaxial fatigue loading. The influence of the Poisson effect, mean normal strain energy and the different contribution of the compressive and tensile normal strain energies are accounted for. An energy-based parameter is defined which explains the different effects of the total strain energy on different material directions. Experimental data are used to validate the capabilities of this new multiaxial fatigue parameter, including 10 materials and 33 loading paths, which cover most of the commonly used loading conditions in multiaxial fatigue tests. The results show that the proposed multiaxial fatigue parameter gives good predictions (within a life factor of two) for most of these materials and loading paths.

Modeling elasto-viscoplasticity in a consistent phase field framework

Existing continuum level phase field plasticity theories seek to solve plastic strain by minimizing the shear strain energy. However, rigorously speaking, for thermodynamic consistency it is required to minimize the total strain energy unless there is proof that hydrostatic strain energy is independent of plastic strain which is unfortunately absent. In this work, we extend the phase-field microelasticity theory of Khachaturyan et al. by minimizing the total elastic energy with constraint of incompressibility of plastic strain. We show that the flow rules derived from the Ginzburg-Landau type kinetic equation can be in line with Odqvist's law for viscoplasticity and Prandtl-Reuss theory. Free surfaces (external surfaces or internal cracks/voids) are treated in the model. Deformation caused by a misfitting spherical precipitate in an elasto-plastic matrix is studied by large-scale three-dimensional simulations in four different regimes in terms of the matrix: (a) elasto-perfectly-plastic, (b) elastoplastic with linear hardening, (c) elastoplastic with power-law hardening, and (d) elasto-perfectly-plastic with a free surface. The results are compared with analytical/numerical solutions of Lee et al. for (a-c) and analytical solution derived in this work for (d). In addition, the J integral of a fixed crack is calculated in the phase-field model and discussed in the context of fracture mechanics.

Generalization of the C0-type zigzag theory for accurate thermomechanical analysis of laminated composites

Abstract A new method based on the C0-type efficient higher-order zigzag theory (EHOZT) is proposed for the efficient and accurate thermomechanical analysis of laminated composite plates. In this method, the transverse shear strain energy is modified according to the mixed variational theorem (MVT). The transverse stress field is defined by the arbitrary m-th order zigzag model including the transverse normal strain effect to improve the accuracy, while the displacement field is obtained from the C0-type EHOZT to amplify the benefits of the numerical efficiency. The transverse displacement field is assumed to be a smooth parabolic distribution to consider the transverse normal strain effect, which has a significant role in predicting the thermal deformation. Derivative components of the transverse displacement field are eliminated from the in-plane displacement field of the C0-type EHOZT by the transverse shear stress condition. The resulting strain energy expressions are collectively referred to as the C0-type EHOZT via the MVT. The proposed theory has the computational advantage of utilizing the C0-continuity condition for finite element implementation while allowing local distributions of the transverse stress to be improved via the recovery procedure. The obtained displacements and stress distributions were compared with data available in the literature for validation.

Optimal Distribution of Damping Coefficients for Viscous Dampers in Buildings

Design guidelines for implementing viscous dampers to buildings have been broadly included in seismic design codes worldwide. Although the relationship between the damping coefficient of viscous dampers and the added damping ratio to the structure has been theoretically studied, the process of distributing the damping coefficient onto each story of a building has not been regulated by the codes. For practical applications, some distribution methods have been previously proposed. However, no comparison has been made between these proposed methods considering the controllability and design economy. In this paper, two search methods based on the genetic algorithms (GAs) are adopted to examine the optimal distribution of damping coefficients. The results are then compared with a variety of existing distribution methods. A comparison is made for the distribution methods assuming the same added damping ratio for the structure. Three two-dimensional frames are adopted in the comparison: a regular moment frame, a moment frame with a soft-story, and a setback building. The results indicated that similar seismic response reduction can be achieved by using different distribution methods if the supplemental damping ratio is the same, while the optimal story damping coefficient can be obtained by using the proposed optimization method. Moreover, the “story shear strain energy to efficient stories” (SSSEES) method, among others, offers advantages in terms of seismic reduction efficiency, economical design, and practical application simplicity.

Influence of Core Compressibility, Flexibility and Transverse Shear Effects on the Response of Sandwich Structures

This paper examines the adequacy of first order shear deformation theory (FSDT) based layered shell finite element by comparing with 2D and 3D models without imposing any constraint on the deformation behaviour of core. The effect of core compressibility and transverse flexibility in the behaviour of sandwich beams are studied. Plane and 3D models are able to capture the higher order shear stress variation across the thickness of core, whereas classical models and layered models results in constant shear stress across the thickness of the core. Results of the finite element models indicate the necessity of shear correction factor for rigid core considering shear strain energy criteria or average shear strain criteria, whereas for soft core, the shear correction factor is unity (=1).

Anisotropy and inter-condyle heterogeneity of cartilage under large-strain shear

We were the first to examine the mechanical responses of skeletally mature bovine femoral cartilage under large-strain simple shear (up to ±20%) using a multiaxial shear testing device. Since shear loading is critical in both tissue failure and chondrocyte responses, we aimed to probe (1) anisotropy with respect to the split-line direction (principal alignment of the collagen fibers near the articulating surface), (2) heterogeneity between femoral condyles, and (3) the influence of local cartilage thickness. We harvested a total of 48 cuboid cartilage specimens from four bovine knee joints. With each specimen we applied shear strains both parallel and perpendicular to the local split-line direction at a rate of 75μm/min and calculated the peak-to-peak shear stresses, shear strain–energy dissipation densities, and peak effective shear moduli. The Wilcoxon signed rank test revealed that the medial condyle was anisotropic in some mechanical measures at applied shear strains above 5%, while the lateral condyle was mechanically isotropic at all applied shear strains. The Kruskal–Wallis test revealed no significant differences in the median mechanical behavior of the lateral and medial condyles. Spearman׳s rank correlations revealed statistically significant negative monotonic correlations among thickness and most of our mechanical measures for both lateral and medial condyles at most applied strains and directions of applied shear. These results suggest that large-strain analyses account for nonlinear, anisotropic and location-dependent effects not fully realized at small strains. Our findings may inspire new experiments and models that consider anisotropy and heterogeneity of cartilage in ways previously ignored.

Phase transformation of germanium by processing through high-pressure torsion: strain and temperature effects

Germanium has been processed by high-pressure torsion (HPT) under a nominal pressure of 24 GPa at room temperature and cryogenic temperature. The samples processed at room temperature were composed of a diamond-cubic Ge-I phase and a metastable tetragonal Ge-III phase. The formation of Ge-III was significantly suppressed and Ge-I and an amorphous phase, in addition to a small amount of body-centred-cubic Ge-IV, appeared in the case of cryogenic HPT processing at 100 K. The Ge-IV phase gradually disappeared at room temperature. These results indicated that shear strain and thermal energy are important for promoting the formation of Ge-III.

New enhanced first-order shear deformation theory for thermo-mechanical analysis of laminated composite and sandwich plates

Abstract This paper proposes an efficient and accurate thermal stress analysis method based on the conventional first-order shear deformation theory (FSDT). The transverse shear strain energy is modified through the mixed variational theorem. The independent transverse shear stresses are obtained from a third-order zigzag model to improve the accuracy, whereas the FSDT displacements are employed to improve the numerical efficiency. The transverse displacement field includes higher-order terms without introducing additional unknown variables by superimposing a prescribed thermal field. This allows one to consider the thermal transverse normal strain effect under the plane stress condition. The resulting strain energy expressions are collectively referred to as the enhanced first-order shear deformation theory including the transverse normal effect based on the mixed variational theorem (EFSDTM_TN). The EFSDTM_TN offers the same computational advantages as the conventional FSDT while allowing for improved local variations of stresses and displacements via a post-processing procedure. In this procedure, in-plane correction factors are introduced and determined by applying equivalent stress resultants so that the improved stresses satisfy the plate equilibrium. Finally, the obtained displacements and stress distributions are compared with the data available in the literature.

FE Analysis on Shear Deformation for Asymmetrically Hot-Rolled High-Manganese Steel Strip

Shear deformation along the longitudinal cross section of the high-manganese steel strip has been analyzed in hot asymmetrical rolling process using rigid-plastic finite element model. The friction coefficient between the rolls and the strip surfaces, the diameter of the work rolls, the speed ratio for the lower/upper rolls, the reduction rate and the initial temperature of the billet were all taken into account. Influence of these process parameters on the shear stress, the shear strain and the related shear strain energy in the center layer of the hot-rolled strip was analyzed. It is indicated that increasing the speed ratio, the reduction rate and the work roll diameter is an effective way to accumulate more shear strain energy in the strip center. A mathematical model reflecting the relationship between the shear strain energy and the process parameters has been established.

Computer modelling of bone's adaptation: the role of normal strain, shear strain and fluid flow.

Bone loss is a serious health problem. In vivo studies have found that mechanical stimulation may inhibit bone loss as elevated strain in bone induces osteogenesis, i.e. new bone formation. However, the exact relationship between mechanical environment and osteogenesis is less clear. Normal strain is considered as a prime stimulus of osteogenic activity; however, there are some instances in the literature where osteogenesis is observed in the vicinity of minimal normal strain, specifically near the neutral axis of bending in long bones. It suggests that osteogenesis may also be induced by other or secondary components of mechanical environment such as shear strain or canalicular fluid flow. As it is evident from the literature, shear strain and fluid flow can be potent stimuli of osteogenesis. This study presents a computational model to investigate the roles of these stimuli in bone adaptation. The model assumes that bone formation rate is roughly proportional to the normal, shear and fluid shear strain energy density above their osteogenic thresholds. In vivo osteogenesis due to cyclic cantilever bending of a murine tibia has been simulated. The model predicts results close to experimental findings when normal strain, and shear strain or fluid shear were combined. This study also gives a new perspective on the relation between osteogenic potential of micro-level fluid shear and that of macro-level bending shear. Attempts to establish such relations among the components of mechanical environment and corresponding osteogenesis may ultimately aid in the development of effective approaches to mitigating bone loss.

Energy dissipation and failure criterion of artificial frozen soil

The failure mechanism of frozen soil is very complicated and shows closely dependence on many factors. A precise physical definition for failure state of frozen silt is not easily quantified. Energy conversion is one of the most important physical principles, and it can be inferred that the failure is the final result of an energy-driven unstable process. The explorations of intrinsic relationships among energy storage, energy release, and strength are important to understand the failure mechanism of frozen soil. In this study, the propagations of strain energy accumulation, dissipation and release are investigated. A framework is established to facilitate the analysis of failure behavior based on energy dissipation and energy release principles, and a new strength criterion is established for frozen soil. According to this criterion, frozen soil starts to fail when the ratio of elastic shear strain energy to elastic volumetric strain energy reaches a critical value. When such an approach is adopted, the problem of modeling failure initiation and propagation of frozen soil becomes greatly simplified.

The Biomechanical Responses of Mandibular Bone Installed with Fixed Partial Denture

This study aimed to evaluate the biomechanical responses in the peri-implant bony structure installed with the fixed partial dentures (FPDs). Unlike traditional configuration, the FPD considered here comprises a superstructure and is supported by three implants. The computational model of mandibular bone and the implant prosthesis were constructed based on patient-specific computerized tomography (CT) images and Computer Aided Design (CAD) tools. To better reflect the real clinical situation, the 3D real-time loading data of maximum voluntary clenching measured using piezo-electric force transducers in patient were adopted in the 3D finite element (FE) analyses (FEA). The von Mises equivalent stress, maximum shear stress, equivalent strain and strain energy density in the peri-implant bone regions are quantified. The peak stresses and strains in the peri-implant bone were observed around the neck of the implant, indicating risk of micro-motion and bone resorption. In this study, we successfully conducted a computational simulation in silico based on in vivo 3D force measurement of a specific patient. The results provided important biomechanical data for clinical treatment, potentially helping enhancing the longevity and reliability of the implant-supported FPD restoration.

Mechanical metamaterial with negative Poisson’s ratio based on circular honeycomb core

Mechanical metamaterials are artificial structures with mechanical properties defined by their structure rather than their composition. As a new type of metamaterials with unique mechanical properties and promising prospects, mechanical metamaterials have attracted great attention and become a new hot spot in the field of metamaterials. Mechanical metamaterials with negative Poisson’s ratio can exhibit novel mechanical properties such as excellent resistance capability of bending deformation and indentation. This type of materials have good prospects in many applications such as variant flexible wing skin. In this article, we adopt the design method of mechanical metamaterials to improve the structure of traditional honeycomb core and propose a new type of circular honeycomb core unit to obtain negative Poisson’s ratio. The advantage of circular honeycomb core is that this new structure is more stable than traditional concave hexagon honeycomb core. We established the corresponding mechanical model of this structure and adopted energy method to study the dependencies of structure parameters for its effective elastic modulus. The bending strain energy was taken into consideration while the tension and shear strain energy were ignored because they are very small compared with the bending strain energy. Then the expressions of effective elastic modulus in the directions of X and Y axis can be established in the condition of small deformation. In order to verify the validity of theoretical results, finite-element simulation method was employed to our study and we adopted periodic structure as the finite-element simulation model and aluminium alloy as the base material. The results of theory and the simulation have good agreements, and we found that its effective elastic modulus E x is mainly depending on its height h and thickness t while E y is mainly depending on its radius r and thickness t . And the thickness t may bring about deviation between theory and the simulation when it increases. The Poisson’s ratio of this material was also investigated through finite-element simulation method and different values of structure parameters were selected. Among these structure parameters, when h =35 mm, r ³ 21 mm and h =40 mm, r ³ 24 mm or h =45 mm, r ³ 26 mm, negative Poisson’s ratio can be obtained. The results indicate that the composite structure based on circular honeycomb core units can achieve negative Poisson’s ratio, which can be controlled by structure parameters. The excellent mechanical performance of light-weight and its negative Poisson’s ratio make circular honeycomb core a promising candidate as engineering material. And our study may pave a useful path to mechanical metamaterials with negative Poisson’s ratio.

主せん断ひずみエネルギーによる板材の成形限界の予測

主せん断ひずみエネルギーによる板材の成形限界の予測

Quantitative impact response analysis of reinforced concrete beam using the Smoothed Particle Hydrodynamics (SPH) method

The nonlinear numerical analysis of the impact response of reinforced concrete/mortar beam incorporated with the updated Lagrangian method, namely the Smoothed Particle Hydrodynamics (SPH) is carried out in this study. The analysis includes the simulation of the effects of high mass low velocity impact load falling on beam structures. Three material models to describe the localized failure of structural elements are: (1) linear pressure-sensitive yield criteria (Drucker-Prager type) in the pre-peak regime for the concrete/mortar meanwhile, the shear strain energy criterion (Von Mises) is applied for the steel reinforcement (2) nonlinear hardening law by means of modified linear Drucker-Prager envelope by employing the plane cap surface to simulate the irreversible plastic behavior of concrete/mortar (3) implementation of linear and nonlinear softening in tension and compression regions, respectively, to express the complex behavior of concrete material during short time loading condition. Validation upon existing experimental test results is conducted, from which the impact behavior of concrete beams are best described using the SPH model adopting an average velocity and erosion algorithm, where instability in terms of numerical fragmentation is reduced considerably.

Influence of die-shift-distance of overhang dies on residual thermal shear stress in 5-chip SiP after EMC curing

This paper investigates the effects of the die-shift-distance (DSD) of overhang dies on residual thermal shear stress and warpage in a 5-chip stacked-die system-in-packaging (SDSiP) implementation. The proposed 5-chip SDSiP includes a single microprocessor (chip 1) and four pieces of dynamic random access memory (chips 2 to 5) with chip 4 stacked atop chip 2 and chip 5 stacked atop chip 3. Computer software based on finite element method (ANSYS) in conjunction with the measured material properties made it possible to obtain the shear stress, shear strain, warpage, and shear strain energy density (U0) within the chips in the 5-chip SDSiP. We also conducted experiments to obtain the interfacial shear stress as well as U0 between the EMC and die, which was compared with the numerical U0. When the DSD exceeded 0.4mm, the position of maximum shear stress at EMC/die interface in the 5-chip SDSiP changed from chip 4 to chip 1 due to a decrease in the rigidity of the stacked dies. Maximum warpage in the 5-chip SDSiP appeared in the top-left corner with movement in a downward direction. This effect can be attributed to mismatch in the CTE among the various materials in the 5-chip SDSiP.

Estimation of thermal noise for spindle optical reference cavities

Thermal noise in optical reference cavities sets a severe limit to the frequency stability of ultra-stable lasers of the order of a few parts of 10−16 at 1s. Various reference cavity designs have been developed to attempt to attain ultimate performance. Numata derived three equations based on strain energy and the fluctuation–dissipation-theorem (FDT) to estimate the noise contributions of the spacer, substrates and coatings, and these equations work well for cylindrical cavities. However, only axial strain energy has been calculated previously. Extending from that, we derive the thermal noise for a spindle spacer, including the contribution of shearing strain energy, based on FDT, and focusing on the spacer geometry and materials. We compare our new approach with finite element analysis (FEA) of the strain energy in spindle cavities, and conclude that the new analytic estimate for the spindle spacer contributions fits better with FEA.

Analysis and homogenization of functionally graded viscoelastic porous structures with a higher order plate theory and statistical based model of cellular distribution

Functionally graded materials (FGMs) have the advantage of continuous microstructure over conventional composite materials. This continuity eliminates many undesired problems like delamination and abrupt change of material properties as in conventional composites. It is also favoured for numerical analysis when homogenizing the properties with a continuous function. Most of the focus has been on particulate-based functionally graded composites and metallic–ceramic FGMs which performed very well in thermal-barrier system and many other applications. Little attention has been on functionally graded porous structures. In this work, we study experimental and numerical procedures of this class of material using a constrained foaming process and homogenization based finite element analysis with plate theory. Plate-like structures of polylactic acid (PLA) are fabricated with a constrained foaming process. The fabricated structures have a gradual porosity with variable cellular size throughout the thickness but homogeneous on-average at parallel planar sections. SEM characterization of the microstructure is statistically analysed with Burr distribution and used as an input to a new homogenization model that accounts for cellular distribution. A higher order plate theory is developed for the analysis that satisfies the free traction condition a priori to the consistency of transverse shear strain energy which had been rarely considered by similar theories in the area. Implementing the theory in finite element procedure necessitates the curvature continuity across elements. This was resolved by implementing the penalty enforcement technique and the use of conforming/nonconforming finite elements with derivative based nodal degrees of freedom. The conforming element showed a better convergence and thus selected for further analysis. The linear viscoelastic behaviour of PLA is assumed to obey Boltzmann superposition principle with hereditary integrals. The stress relaxation functions are determined experimentally for property characterization and from the homogenization model. The proposed plate theory and homogenization model agree very well with the work done by other researchers and experimental data. The numerical tool proved its validity for conducting accurate computer experiments with the minimal input about material properties and microstructure.