Shear Strain Energy Density Research Articles

Assessment of multiaxial fatigue behaviour of welded joints under combined bending and torsion by application of a fictitious notch radius

A major problem in the assessment of the multiaxial fatigue behaviour in welded joints is the determination of local notch stresses, since the real local radii in most cases are not known. This can be circumvented by introducing a fictitious notch radius, according to Neuber and Radaj. The calculations of local equivalent stress amplitudes for welded joints (tube–tube and flange–tube) under pure bending, pure torsion and combined in- and out-of-phase bending with torsion can then be carried out by stress-based and strain energy density-based criteria. Among the investigated methods, the most reliable results are obtained with the effective equivalent stress hypothesis, an integral interference plane oriented method, which transfers the results of complex loadings onto the safe side of the reference scatter band for pure bending. However, the best fit with the reference scatter band is realized by the application of the maximum shear and normal strain energy density parameter in the critical plane.

In Vitro Effects of Collagenase on Biomechanical Properties and Morphological Features of the Rat Molar Periodontal Ligament.

Biomechanical properties and morphological features of the rat molar periodontal ligament were examined after treatment with various concentrations of bacterial collagenase. Treatment with collagenase caused dose-dependent decreases in the maximum shear stress, maximum shear strain, tangent modulus, and failure strain energy density of the periodontal ligament. Light microscopic analysis after mechanical testing revealed that in controls, the periodontal ligament ruptured in the middle region or near the bone surface, while in the collagenase-treated specimens, it ruptured at the region adjacent to the cementum surface. Scanning electron microscopy revealed considerable degradation of the periodontal collagen fibres and fibrils by the enzyme. Treatment with collagenase markedly reduced the phase retardation values of collagens and the areas occupied by birefringent collagen fibres within the ligament. We suggest that collagenase treatment causes a decrease in the amount and density of collagen fibres and a disorganization of the fibres that reduces the strength, extensibility, stiffness, and toughness of the ligament. Our findings indicate that the periodontal collagens are load-bearing, key structural components providing structural and functional integrity to the ligament.

Numerical calculations of tectonic stress field of Chinese mainland and its neighboring regions and their applications to explanation of seismic activity

This paper made a numerical simulation to the basic tectonic stress field of Chinese mainland and its neighboring region using the visco-elasticity finite element model and the new published displacement rate result. Main contents include the simulation of maximum shear stress and its varying rate, the maximum shear strain and its varying rate, the shear strain energy density and its varying rate. In view of the high inhomogeneous distribution character of seismicity in space and time in Chinese mainland and its neighboring area, the normalized background energy value was given by means of normalized treatment to the earthquake energy release in the eastern and western parts of Chinese mainland. And the comparison of the simulation result with the actual seismicity was made. The results show that the simulation values can explain well the earthquake distribution character of Chinese mainland and its neighboring area.

Analysis of Curved Sandwich Panels with Cutouts Subjected to Combined Temperature Gradient and Mechanical Loads

The results of detailed study of the effect of the cutout on the response of curved sandwich panels are presented. The panels have honeycomb core composite face sheets. The loading consists of a temperature gradient through-the-thickness combined with pressure loading and edge shortening or edge shear. The analysis is based on a first-order shear-deformation Sanders-Budiansky type theory with the effects of large displacements, moderate rotations, transverse shear deformation and laminated anisotropic material behavior included. A mixed formulation is used with the fundamental unknowns consisting of the generalized displacements and the stress resultants of the panel. The nonlinear displacements, strain energy, principal strains, transverse shear stresses, transverse shear strain energy density, and their hierarchical sensitivity coefficients are evaluated. The hierarchical sensitivity coefficients measure the sensitivity of the nonlinear response to variations in the panel parameters, the effective properties of the face sheet layers and the core, and the micromechanical parameters. Numerical results are presented for cylindrical sandwich panels and show the effects of variations in the loading and the size of the cutout on the global and local response quantities and their sensitivity to changes in the various panel, effective layer and micromechanical parameters.

Analysis of Composite Panels Subjected to Thermo-Mechanical Loads

The results of a detailed study of the effect of cutout on the nonlinear response of curved unstiffened panels are presented. The panels are subjected to combined temperature gradient through-the-thickness combined with pressure loading and edge shortening or edge shear. The analysis is based on a first-order, shear deformation, Sanders-Budiansky-type shell theory with the effects of large displacements, moderate rotations, transverse shear deformation, and laminated anisotropic material behavior included. A mixed formulation is used with the fundamental unknowns consisting of the generalized displacements and the stress resultants of the panel. The nonlinear displacements, strain energy, principal strains, transverse shear stresses, transverse shear strain energy density, and their hierarchical sensitivity coefficients are evaluated. The hierarchical sensitivity coefficients measure the sensitivity of the nonlinear response to variations in the panel parameters, as well as in the material properties of the individual layers. Numerical results are presented for cylindrical panels and show the effects of variations in the loading and the size of the cutout on the global and local response quantities as well as their sensitivity to changes in the various panel, layer, and micromechanical parameters.

Curved Sandwich Panels Subjected to Temperature Gradient and Mechanical Loads

The results of a detailed study of the nonlinear response of curved sandwich panels with composite face sheets, subjected to a temperature gradient through the thickness combined with mechanical loadings, are presented. The analysis is based on a first-order shear-deformation Sanders-Budiansky-type theory, including the effects of large displacements, moderate rotations, transverse shear deformation, and laminated anisotropic material behavior. A mixed formulation is used with the fundamental unknowns consisting of the generalized displacements and the stress resultants of the panel. The nonlinear displacements, strain energy, principal strains, transverse shear stresses, transverse shear strain energy density, and their hierarchical sensitivity coefficients are evaluated. The hierarchical sensitivity coefficients measure the sensitivity of the nonlinear response to variations in the panel parameters, the effective properties of the face sheet layers and the core, and the micromechanical parameters. Numerical results are presented for cylindrical panels subjected to combined pressure loading, edge shortening or extension, edge shear, and a temperature gradient through the thickness. The results show the effects of variations in the loading and the panel aspect ratio, on the nonlinear response, and its sensitivity to changes in the various panel, effective layer, and micromechanical parameters.

Thermomechanical buckling and postbuckling responses of composite panels with skewed stiffeners

The results of a detailed study of the buckling and postbuckling responses of composite panels with skewed stiffeners are presented. The panels are subjected to applied edge displacements and temperature changes. A first-order shear-deformation geometrically nonlinear shallow-shell theory that includes the effects of laminated anisotropic material behavior is used to model each section of the stiffeners and the skin. A mixed formulation is used in the analysis with the fundamental unknowns consisting of the generalized displacements and the stress resultants of the panel. The nonlinear displacements, strain energy, transverse shear stresses, transverse shear strain energy density, and their hierarchical sensitivity coefficients are evaluated. The hierarchical sensitivity coefficients measure the sensitivity of the buckling and postbuckling responses to variations in three sets of interrelated parameters; namely, the panel stiffnesses; the effective material properties of the individual layers; and the constituent material parameters (fibers, matrix, interface and interphase). Numerical results are presented for rectangular panels with open section I-stiffeners, subjected to edge shortening and uniform temperature change. The results show the effects of variations in the material properties of the skin and the stiffener on the buckling and postbuckling responses of the panel, as well as on the sensitivity coefficients.

Evidence of structural and material adaptation to specific strain features in cortical bone

Background Functionally induced strains provide epigenetic signaling for bone modeling and remodeling activities. Strain gauge documentation of the equine third metacarpal reveals a neutral axis passing through the craniolateral cortex, resulting in a narrow band of cortex loaded predominantly in tension, with the remainder of the cortex experiencing a wide range of compression strain magnitudes that are maximal in the caudomedial cortex. This predictable strain pattern provides a model for examining the hypothesis that strain mode, magnitude, and strain energy density are potential correlates of compact bone structural and material organization. Methods Structural and material variables were quantified in nine equine (standard breeds) third metacarpals for comparison with the in vivo strain milieu that was evaluated in thoroughbred horses. The variables quantified included secondary osteon population density (OPD), fractional area of secondary bone (FASB), fractional area of porous spaces, collagen fiber orientation, mineral content (% ash), and cortical thickness. Each bone was sectioned transversely at 50% of length, with subsequent quantification of eight radial sectors and three intracortical regions (periosteal, middle, endosteal). Linear regression analysis compared these variables to magnitudes of corresponding regional in vivo longitudinal strain, shear strain, and strain energy density values reported in the literature. Results The craniolateral (“tension”) cortex of this bone is distinguished by its 30% lower FASB and with the lateral cortex exhibits 20% darker gray level (more longitudinal collagen) compared with the average of all other locations. Conversely, the remaining (“compression”) cortices as a group have a high OPD, are more extensively remodeled, and contain more oblique-to-transverse collagen. The caudal cortices (caudomedial, caudal, caudolateral) are significantly thinner (P < 0.01) and have 4% lower mineral content (P < 0.05) than all other locations. Moderately strong correlations exist between collagen fiber orientation and normal strain (r = 0.752) and shear strain (r = 0.555). When normal and shear strains were transformed to their respective absolute values, thus eliminating the effects of strain mode (tension vs. compression), these correlation coefficients decreased markedly. Conclusions Collagen fiber orientation is related to strain mode and may function to accentuate rather than attenuate bending. These differences may represent adaptations that function synergistically with bone geometry to promote a beneficial strain distribution and loading predictability during functional loading. © 1996 Wiley-Liss, Inc.

Evidence of structural and material adaptation to specific strain features in cortical bone.

Functionally induced strains provide epigenetic signaling for bone modeling and remodeling activities. Strain gauge documentation of the equine third metacarpal reveals a neutral axis passing through the craniolateral cortex, resulting in a narrow band of cortex loaded predominantly in tension, with the remainder of the cortex experiencing a wide range of compression strain magnitudes that are maximal in the caudomedial cortex. This predictable strain pattern provides a model for examining the hypothesis that strain mode, magnitude, and strain energy density are potential correlates of compact bone structural and material organization. Structural and material variables were quantified in nine equine (standard breeds) third metacarpals for comparison with the in vivo strain milieu that was evaluated in thoroughbred horses. The variables quantified included secondary osteon population density (OPD), fractional area of secondary bone (FASB), fractional area of porous spaces, collagen fiber orientation, mineral content (% ash), and cortical thickness. Each bone was sectioned transversely at 50% of length, with subsequent quantification of eight radial sectors and three intracortical regions (periosteal, middle, endosteal). Linear regression analysis compared these variables to magnitudes of corresponding regional in vivo longitudinal strain, shear strain, and strain energy density values reported in the literature. The craniolateral ("tension") cortex of this bone is distinguished by its 30% lower FASB and with the lateral cortex exhibits 20% darker gray level (more longitudinal collagen) compared with the average of all other locations. Conversely, the remaining ("compression") cortices as a group have a high OPD, are more extensively remodeled, and contain more oblique-to-transverse collagen. The caudal cortices (caudomedial, caudal, caudolateral) are significantly thinner (P < 0.01) and have 4% lower mineral content (P < 0.05) than all other locations. Moderately strong correlations exist between collagen fiber orientation and normal strain (r = 0.752) and shear strain (r = 0.555). When normal and shear strains were transformed to their respective absolute values, thus eliminating the effects of strain mode (tension vs. compression), these correlation coefficients decreased markedly. Collagen fiber orientation is related to strain mode and may function to accentuate rather than attenuate bending. These differences may represent adaptations that function synergistically with bone geometry to promote a beneficial strain distribution and loading predictability during functional loading.

Nonlinear and postbuckling analyses of curved composite panels subjected to combined temperature change and edge shear

The results of a detailed study of the nonlinear and postbuckling responses of curved unstiffened composite panels with central circular cutouts are presented. The panels are subjected to uniform temperature change and an applied in-plane edge shear loading. The analysis is based on a first-order shear-deformation Sanders-Budiansky type theory with the effects of large displacements, moderate rotations, transverse shear deformation and laminated anisotropic material behavior included. A mixed formulation is used with the fundamental unknowns consisting of the generalized displacements and the stress resultants of the panel. The nonlinear displacements, strain energy, transverse shear stresses, transverse shear strain energy density, and their hierarchical sensitivity coefficients are evaluated. Numerical results are presented for cylindrical panels with central circular cutouts and are subjected to uniform temperature change and an applied in-plane edge shear loading. The results show the effects of variations in the panel curvature, hole diameter, laminate stacking sequence and fiber orientation, on the nonlinear and postbuckling panel responses, and their sensitivity to changes in the various panel, layer and micromechanical parameters.

Nonlinear and postbuckling responses of curved composite panels with cutouts

The results of a detailed study of the nonlinear and postbuckling responses of curved unstiffened composite panels with central circular cutouts are presented. The panels are subjected to applied edge displacements and temperature changes. The analysis is based on a first-order shear-deformation Sanders-Budiansky type theory with the effects of large displacements, moderate rotations, transverse shear deformation and laminated anisotropic material behavior included. A mixed formulation is used with the fundamental unknowns consisting of the generalized displacements and the stress resultants of the panel. The nonlinear displacements, strain energy, transverse shear stresses, transverse shear strain energy density, and their hierarchical sensitivity coefficients are evaluated. The hierarchical sensitivity coefficients measure the sensitivity of the nonlinear response to variations in three sets of interrelated parameters; namely, the panel stiffnesses, the material properties of the individual layers, and the material properties of the constituents (fibers, matrix, interface and interphase). Numerical results are presented for cylindrical panels with central circular cutouts subjected to edge shortening and uniform temperature change, showing the effects of variations in the panel curvature, hole diameter, laminate stacking sequence and fiber orientation, on the nonlinear and postbuckling panel responses, and their sensitivity to changes in the various panel, layer and micromechanical parameters.

TEM observation of intergrowth structures in the HgBa 2Ca 2Cu 3O y ceramic superconductor

Intergrowth structures, which occur in the HgBa 2Ca 2Cu 3O y ceramic superconductor, were observed by means of transmission electron microscopy (TEM). There are at least two types of intergrowth structure: Hg-1212/Hg-1223 and Hg-1223/Hg-1234. The congruence relationships for these intergrowth structures are respectively: 〈1 1 0〉 Hg-1212|〈1 1 0〉 Hg-1223, {0 0 1} Hg-1212|{0 0 1} Hg-1223; and 〈1 1 0〉 Hg-1223|〈1 1 0〉 Hg-1234, {0 0 1} Hg-1223|{0 0 1} Hg-1234. For a stable intergrowth structure, the total strain energy density should have a minimum value. The strain energy density consists of two parts: the tensile strain energy density U t and the shear strain energy density U s. The tensile strain energy density U t stored in the crystal can be expressed in terms of the ratio between the numbers of matching slabs, i.e. f i = N i/ N, where N i is the number of slabs corresponding to Hg-12( n i−1) n i, and N is the number of slabs corresponding to the matrix, i.e. Hg-12( n−1) n. The plots of U t vs. f i = 1.2498 and f i = 0.8272 for intergrowth structures of Hg-1212/Hg-1223 and Hg-1234/Hg-1223, respectively. As was observed from the TEM micrograph, two immobile dislocations can be created by an appropriate combination of intergrowth structures of Hg-1212/Hg-1223 and Hg-1223/Hg-1234. A model for the formation of these immobile dislocations is presented.

Thermomechanical postbuckling of multilayered composite panels with cutouts

The results of a study of the detailed thermomechanical postbuckling response characteristics of flat unstiffened composite panels with central circular cutouts are presented. The panels are subjected to combined temperature changes and applied edge loading (or edge displacements). The analysis is based on a first-order shear deformation plate theory. A mixed formulation is used with the fundamental unknowns consisting of the generalized displacements and the stress resultants of the plate. The postbuckling displacements, transverse shear stresses, transverse shear strain energy density, and their sensitivity coefficients are evaluated. The sensitivity coefficients measure the sensitivity of the post-buckling response to variations in the different lamination and material parameters of the panel. Numerical results are presented showing the effects of the variations in the hole diameter, laminate stacking sequence, fiber orientation, and aspect ratio of the panel on the thermomechanical postbuckling response and its sensitivity to changes in panel parameters.

Bond shear strength for adhesive bonded double-lap joints

For adhesively bonded double-lap joints with an arbitrarily nonlinear shear stress-strain property, a simple formula is developed for predicting the bond shear strength developable between the adherends for the cohesive shear failure mode. In this formula, the bond shear strength is characterized by the maximum shear strain energy density of the adhesive. The thermal mismatch effect is highlighted in terms of reducing the bond shear strength for balanced joints, and in terms of either decreasing or increasing the bond shear strength for the stiffness unbalanced joints.

Shape Optimization Analysis of Flow Field. (Growth-Strain Method Approach).

A new analytical approach for optimizing shapes of the flow field is presented. The reshaping is accomplished by the growth-strain method which was first developed using the finite-element calculation of the deformation of shapes by generating bulk strain for solid problems. The generation law of the bulk strain is given as a function of a distributed parameter to be made uniform. For solid problems, the validity of the use of the shear strain energy density to maximize the strength based on the Mises criterion or the strain energy density to maximize the stiffness for the distributed parameter has been confirmed. In the present paper, we propose the use of the dissipation energy density for the distributed parameter to minimize the total energy dissipated due to the viscosity of the fluid. Numerical results for abruptly enlarged channel problems in steady state assuming low Reynolds number and incompressible viscous fluid shows the validity of the present approach.

Shape Optimization Analysis of Flow Field. (Approach by the Growth-Strain Method).

A new analytical approach to optimize shapes of the flow field is presented. The reshaping is accomplished by the growth-strain method which was developed as a method using finite-element calculation of the deformation of shapes by generating bulk strain of swelling and contracting to the solid problems first. The generation law of the bulk strain is given as a function of a distributed parameter to be uniformized. To the solid problems, the validity of the use of the shear strain energy density to maximize the strength based on the Mises criterion or the strain energy density to maximize the stiffness for the distributed parameter has been confirmed. In the present paper, we propose to use the dissipation energy density for the distributed parameter to minimize the total dissipation energy by viscosity to the fluid problem. Numerical results for abrupt enlargement channel problems in steady state assuming low-Reynolds-number and noncompressible viscous fluid show the validity of the present approach.