Stress Assumption Research Articles

Enhancement of Protocols for Simple Shear of Isotropic Soft Hyperelastic Samples

The classic deformation known as simple shear has been investigated within the framework of nonlinear elasticity for isotropic incompressible hyperelastic materials in a large variety of contexts, most notably in the analysis of the mechanical behaviour of soft matter. One of the major difficulties in providing a realistic physical interpretation of this idealised homogeneous deformation is the fact that the conventional mathematical model of simple shear using a plane stress assumption to determine the hydrostatic pressure implies that a normal traction must be applied to the slanted faces of the deformed specimen. However, such a traction is not applied in practice. To resolve this dilemma, we retain the classic plane stress assumption to determine the hydrostatic pressure but modify the basic kinematics to consider a simple shear deformation superposed on a uniform lateral extension or compression of the specimen. The amount of lateral stretch is treated as a stabilising factor determined so that the predicted normal traction is minimised and thus the fidelity of the model with experimental protocols is enhanced. This new approach is illustrated for a variety of classical strain-energy densities for isotropic hyperelastic materials that have been used to model the mechanical behaviour of soft matter.

Experimental investigation of the anchoring properties of special-shaped cross-section self-drilling bolts

This paper designed a special-shaped cross-section hollow self-drilling bolt with discharge grooves, in which Mindlin’s solution of displacement was used in the elastic solution of a wholly grouted bolt. Theoretically, the ultimate pulling force and the residual pulling force were analyzed by considering the average distribution assumption of residual stress. The bolts’ performance with 2, 3, and 4 discharge grooves was compared with circular cross-section bolts, which experimental results are consistent with the theoretical results. The ultimate pulling force and the residual pulling force of the special-shaped cross-section bolt improved significantly according to the circular bolt. The bonding properties of special-shaped cross-section bolts present significant difference to circular section bolts. The residual pulling strength was contributed both by the bar-grout and grout-grout frictions. Upgrading the grout strength may further enhance the pulling strength of special-shaped cross-section bolts.

The hysteresis model of the friction pendulum bearing based on the moment balance theory

The hysteresis model of the friction pendulum bearing (FPB) is very important for predicting its seismic performance. The previous hysteresis model is based on the horizontal force balance theory and cannot analyze the moment required when the FPB rotates. Because of this, this paper proposes a hysteresis model of the FPB based on the moment balance theory, which can be used to analyze the rotation performance of the FPB. In this paper, formulas of the hysteresis model of the FPB based on the moment balance theory are derived firstly. And it is found that the hysteresis loops calculated based on the moment balance theory is very close to those obtained from experiments. Then two main assumptions of the hysteresis model of the FPB based on the moment balance theory: Small rotation assumption and Normal stress assumption are introduced, and the expression of the hysteresis model of the FPB based on the moment balance theory without using the two assumptions is given. Finally, errors caused by the assumptions are analyzed in detail and the applicability of the simplified formula is verified.

3D finite element analysis of laminated composites under three-point bending

Delamination is considered as one of the most critical failure modes which occurs near the free edges in laminated composites due to high interlaminar stress. When the classical plate theory is used to determine the in plane stress, the interlaminar stresses cannot be assessed by this theory, as it adopts the plane stress assumption. For that, a three-dimensional finite element analysis is adopted to calculate in-plane stresses as well as out-of-plane stresses of laminated composites under three-point bending. 8-node linear brick elements C3D8R with reduced integration available in ABAQUS element library is used for meshing the laminated composite models. The flexural numerical response of two main lay-up arrangements is modelled: Unidirectional laminates ([0]12,[90]12, [45]12) and multidirectional laminates (cross-ply [0/90]3S , angle-ply [±45]3S and quasi-isotropic laminates [0/90/±452] S ). Comparing the current results to experimental methodologies accessible in the literature demonstrates the predictive capability of the present model. Therefore, this study shows that the present formulations can predict with a good accuracy the deflection of the test specimens. Whilst, a significant dispersion is only observed for the unidirectional laminates [0]12.

Prediction of interactive effects of CBM production, faulting stress regime, and fault in coal reservoir: Numerical simulation

The stress in coal reservoir is dynamic and redistributes during coalbed methane (CBM) production. It is abundantly evident in the literature that maximum and minimum horizontal stresses reduce with reservoir pressure depletion. This study aims to predict the change of Anderson's faulting (tectonic regimes) in anisotropic coal due to gas production. A series of fully coupled scenario-based numerical simulations are conducted to investigate the effects of anisotropic sorption and mechanical properties of coal reservoir and immediate underlying rock stratum, and faulting on stress redistribution and gas production. For this purpose, the common assumption of uniaxial strain condition and constant overburden stress together with the widely acceptable values for the mechanical properties of coal are used for the simulations. The simulation results show that initial faulting stress regime, anisotropy in coal, and sorption parameters such as modulus of solid expansion have a significant role in prediction of final stress regime. It was also observed that a permeable fault located parallel to a horizontal borehole may contribute to gas production for both cases of the borehole drilled in the horst and graben structures. The simulation results of this study offer implications on the impact of CBM production on stress redistribution, surface subsidence, and transition of faulting stress regime around horizontal boreholes and far-field.

DEM Analysis of Single-Particle Crushing Considering the Inhomogeneity of Material Properties

Crushing characteristics of single particles are the basis of granular material simulation with discrete element method (DEM). To improve the universality and precision of crushable DEM model, inhomogeneous stiffness and strength properties are introduced into the bonded particle method, with which the Weibull distribution and size effect of particle strength can be reproduced without deleting elementary balls. The issues of particle strength and carrying capacity under complex contact conditions are investigated in this work by symmetric loading tests, asymmetric loading tests, and ball–ball loading tests. Results of numerical experiments indicate that particle carrying capacity is significantly influenced by coordination numbers, the symmetry of contact points, as well as the relative size of its neighbors. Contact conditions also show impact on single-particle crushing categories and the origin position of inner particle cracks. The existing stress indexes and assumptions of particle crushing criterion are proved to be inappropriate for general loading cases. Both the inherent inhomogeneity and contact conditions of particles should be taken into consideration in the simulation of granular materials.

Adjoint Complement to the Universal Momentum Law of the Wall

The paper is devoted to an adjoint complement to the universal Law of the Wall (LoW) for fluid dynamic momentum boundary layers. The latter typically follows from a strongly simplified, unidirectional shear flow under a constant stress assumption. We first derive the adjoint companion of the simplified momentum equation, while distinguishing between two strategies. Using mixing-length arguments, we demonstrate that the frozen turbulence strategy and a LoW-consistent (differentiated) approach provide virtually the same adjoint momentum equations, that differ only in a single scalar coefficient controlling the inclination in the logarithmic region. Moreover, it is seen that an adjoint LoW can be derived which resembles its primal counterpart in many aspects. The strategy is also compatible with wall-function assumptions for prominent RANS-type two-equation turbulence models, which ground on the mixing-length hypothesis. As a direct consequence of the frequently employed assumption that all primal flow properties algebraically scale with the friction velocity, it is demonstrated that a simple algebraic expression provides a consistent closure of the adjoint momentum equation in the logarithmic layer. This algebraic adjoint closure might also serve as an approximation for more general adjoint flow optimization studies using standard one- or two-equation Boussinesq-viscosity models for the primal flow. Results obtained from the suggested algebraic closure are verified against the primal/adjoint LoW formulations for both, low- and high-Re settings. Applications included in this paper refer to two- and three-dimensional shape optimizations of internal and external engineering flows. Related results indicate that the proposed adjoint algebraic turbulence closure accelerates the optimization process and provides improved optima at no computational surplus in comparison to the frozen turbulence approach.

A contribution to numerical prediction of surface damage and residual stresses on die-sinking EDM of Ti6Al4V

A numerical simulation under plane-strain assumption of residual stresses and damage on titanium alloy Ti6Al4V in die-sinking electrical discharge machining (EDM) process is presented using Johnson–Cook (J–C) model and dynamic explicit temperature-displacement algorithm. A special attention is given to model the damaged thermo-mechanical behavior of EDMed Ti6Al4V alloy while considering the ductile damage evolution via a fully uncoupled damage formulation. A rigorous selection method including analytical and finite-element (FE) computations of tensile fracture behavior with thermal effect is proposed for suitable selection of J–C model parameters for the grade of Ti6Al4V alloy under investigation. The relationships between the machining parameters and both the heat flux density and the available sparking radius are considered for defining sparking analysis input. For a selected set of machining settings, the residual stresses and surface damage profiles were retrieved at the end of a cooling analysis. It has been concluded that J–C constitutive model can be used to describe material damaged thermo-plastic behavior under die-sinking EDM process conditions and thereby forecast temperature distribution, crater cavity shape, thermally induced residual stresses, white layer thickness and EDM thermal cracks formation. Unusually, an approach including damage criterion was proposed for assessment of both the geometry of crater cavity and the thickness of white layer and compared to based-on temperature criterion classical approach. Thus, numerical simulation of damage in die-sinking EDM offers a new insight into the mechanism of surface damage creation and helps to find out such phenomenon very precociously, which is otherwise difficult to access by experiment, such as surface crack formation due to damage mechanism as triggered in sparking phase and which was re-established in cooling. The numerical model yields reliable results for residual stresses profiles when compared with titanium alloy Ti6Al4V experimental results available in literature in the same machining conditions.

Strain Gradient Theory Based Dynamic Mindlin-Reissner and Kirchhoff Micro-Plates with Microstructural and Micro-Inertial Effects

In this study, a dynamic Mindlin–Reissner-type plate is developed based on a simplified version of Mindlin’s form-II first-strain gradient elasticity theory. The governing equations of motion and the corresponding boundary conditions are derived using the general virtual work variational principle. The presented model contains, apart from the two classical Lame constants, one additional microstructure material parameter g for the static case and one micro-inertia parameter h for the dynamic case. The formal reduction of this model to a Kirchhoff-type plate model is also presented. Upon diminishing the microstructure parameters g and h, the classical Mindlin–Reissner and Kirchhoff plate theories are derived. Three points distinguish the present work from other similar published in the literature. First, the plane stress assumption, fundamental for the development of plate theories, is expressed by the vanishing of the z-component of the generalized true traction vector and not merely by the zz-component of the Cauchy stress tensor. Second, micro-inertia terms are included in the expression of the kinetic energy of the model. Finally, the detailed structure of classical and non-classical boundary conditions is presented for both Mindlin–Reissner and Kirchhoff micro-plates. An example of a simply supported rectangular plate is used to illustrate the proposed model and to compare it with results from the literature. The numerical results reveal the significance of the strain gradient effect on the bending and free vibration response of the micro-plate, when the plate thickness is at the micron-scale; in comparison to the classical theories for Mindlin–Reissner and Kirchhoff plates, the deflections, the rotations, and the shear-thickness frequencies are smaller, while the fundamental flexural frequency is higher. It is also observed that the micro-inertia effect should not be ignored in estimating the fundamental frequencies of micro-plates, primarily for thick plates, when plate thickness is at the micron scale (strain gradient effect).

A two-layer beam model with interlayer slip based on two-dimensional elasticity

The objective of this paper is the computation of the Airy stress function of a two-layer composite beam with interlayer slip. For the calculation of the upper and lower layer stress functions an iterative solution procedure from Boley-Tolins is adapted, which was originally introduced for isotropic single layer beams under plane stress assumptions. Considering the continuity equations for the interface stress, for the vertical deflection and a linear law between the interlayer slip and the shear stress, Boley-Tolins’ method may be extended to derive an ordinary differential equation for the slip. The order of the ordinary differential equation depends on the number of iterations and the desired accuracy, ranging from an elementary, second order ordinary differential equation for the slip to a more refined, fourth order ordinary differential equation for the slip. Finally the derived slip models are compared by considering a thick simply-supported two-layer beam subjected to a sinusoidal transverse load. The results from the iterative approaches are compared to two-dimensional results under plane stress assumptions for two limit cases: a perfectly bonded beam and a composite beam without bonding. It is found that the refined higher order slip model almost coincides with the elasticity solution, even for very thick composite beams, whereas the elementary slip model only yields accurate results for a thin beam.

Development length of glass fibre reinforced polymer (GFRP) rebar based on non-uniform bond stress

Due to the assumption of uniform bond stress, the development length of fibre reinforced polymer (FRP) bars by design standards can be unnecessarily long and difficult to provide in practice. Hence, the bond stress distribution and required development length of a glass fibre reinforced polymer (GFRP) rebar is investigated. Four beam-bond specimens, two following RILEM specifications and two based on a procedure by ACI are tested to evaluate the effect of test method on bond strength. Ten pullout tests are also performed using the same bar. The two test methods yield similar results, but the ACI test is easier to perform. The bond stress distribution in the beams is highly nonlinear but in the pullout tests approaches uniformity. The actual development length is found to be 50% to 250% less than that required by the aforementioned standards. Consequently, a new equation is proposed based on the logistic growth function to model the non-uniform bond stress distribution and estimate the required development length.

Effect of Plastic Anisotropy on the Collapse of a Hollow Disk under Thermal and Mechanical Loading

Plastic anisotropy significantly affects the behavior of structures and machine parts. Given the many parameters that classify a structure made of anisotropic material, analytic and semi-analytic solutions are very useful for parametric analysis and preliminary design of such structures. The present paper is devoted to describing the plastic collapse of a thin orthotropic hollow disk inserted into a rigid container. The disk is subject to a uniform temperature field and a uniform pressure is applied over its inner radius. The condition of axial symmetry in conjunction with the assumption of plane stress, permits an exact analytic solution. Two plastic collapse mechanisms exist. One of these mechanisms requires that the entire disk is plastic. According to the other mechanism, plastic deformation localizes at the inner radius of the disk. Additionally, two special solutions are possible. One of these solutions predicts that the entire disk becomes plastic at the initiation of plastic yielding (i.e., plastic yielding simultaneously initiates in the entire disk). The other special solution predicts that the plastic localization occurs at the inner radius of the disk with no plastic region of finite size. An essential difference between the orthotropic and isotropic disks is that plastic yielding might initiate at the outer radius of the orthotropic disk.

Causes analysis of shield tunnel cracks in deep stratum with high water pressure

In the process of shield tunneling, there is a risk of cracks and diseases caused by geological changes, construction process, design and other factors, and leads to the construction process and even engineering accidents. This paper analyzes the cracks on the top of the segment under the geological conditions of deep burial and high water pressure by analyzing the cracks of a traffic rail project in Shenzhen, and analyzes the reasons for the cracks under normal construction. Based on the conventional stress model of segment and the screening of surrounding geological and hydrological conditions, the model assumption of local stress of integral segment is made, and the modified idiom and beam method are adopted- The results show that under the geological condition of fractured water stratum, the sudden change of water pressure caused by rainstorm and the joint action of broken rock block and segment floating will lead to the reduction of segment top space and direct contact with rock stratum, which will exceed the normal pressure range of segment and lead to cracks in the top segment.

Probabilistic treatment of pipe girth weld residual stress in fracture assessment

This study examines the influence of probabilistic treatment of transverse residual stress in a structural integrity assessment. Pipe girth weld measurement data gathered from numerous studies was statistically interpreted to provide realistic through-thickness stress distributions for use in fracture assessments. The database measurements are shown to follow a normal distribution which is capable of evaluating a probabilistic interpretation of weld residual stress within a fracture assessment. A comparison between deterministic upper bounds, provided by various standards, and probabilistic interpretation was undertaken. The presented results propose a 42% reduction in the estimated probability of failure of the case study using a probabilistic assumption of residual stress. Direct implications include a more realistic model for treatment in fracture assessments which can in turn improve acceptance criteria and avoid unnecessary weld repairs.

Asymptotic Analysis for Plane Stress Problems

In this classroom note, the old and well-known plane-stress elastic class of problems is revisited, using an analysis technique which is different than that commonly found in the literature, and with a pedagogical benefit. An asymptotic analysis is applied to problems of thin linear elastic plates, made of a homogeneous and rather general anisotropic material, under the plane stress assumption. It is assumed that there are no body forces, that the boundary conditions are uniform over the thickness, and that the material (hence also the solution) is symmetric about the middle plane. The small parameter in this analysis is $\epsilon =t/D$ where $t$ is the (uniform) thickness of the plate and $D$ is a measure of its overall size. The goal of this analysis is to show how the three-dimensional (3D) problem of this type is reduced asymptotically to a sequence of essentially two-dimensional (2D) problems for a small $\epsilon $ . As expected, the leading problem in this sequence is shown to be the classical plane-stress problem. The solutions of the higher-order problems are corrections to the plane-stress solution. The analysis also shows that all six 3D compatibility equations are satisfied as $\epsilon $ goes to zero, and that the error incurred by the plane stress assumption is $O(\epsilon ^{2})$ . For the special case of an isotropic in-the-plane material, the second-order solution is shown to be the exact solution of the 3D problem, up to an $O(\epsilon ^{2})$ error in the close vicinity of the edge (which agrees with a well-known result for an isotropic material).

Effects of sliding and debonding of the pile-soil interface on the soil reaction to laterally loaded piles

An analytical model is proposed to analyze the effects of sliding and debonding of the interface between the pile and the surrounding soil on the soil reaction under a lateral load. Based on the approximate three-dimensional analytical model, the vanishing stress assumption is also employed to satisfy the stress-free soil surface condition. Referring to the distribution of stresses on the pile-soil interface, the interface in the proposed model is divided into three parts—the bonding, sliding, and debonding areas. The behaviors of sliding and debonding are considered by incorporating the hypothesis of mixed boundary conditions on the pile-soil interface. Those behaviors were not considered in earlier analytical studies, which led to an overestimation of the soil reaction. Influence functions are adopted to define the relationship between the stresses and the displacements on the pile-soil interface. Then, the radiant stress method and the convolution of Fourier series are employed to solve the mixed boundary conditions occurring at the pile-soil interface. The validity of the proposed model is demonstrated by comparison with experimental data. Parametric studies are also presented to show the effects of predefined parameters on the behaviors of sliding and debonding.

Element-Free Galerkin Method Modeling of Thermo-Elastic-Plastic Behavior for Continuous Casting Round Billet

When solving the coupled thermal-mechanical problem of the metal solidification, the mesh-based numerical methods suffer from the inconsistency of mesh lines and curved boundaries. Furthermore, the mesh should be continually reconstructed to comply with the interface when dealing with the moving boundary such as phase transition, which brings great difficulties to the numerical calculation. Based on the plane stress assumption, the present work establishes a two-dimensional thermo-elastic-plastic calculation model for continuous casting round billets using the Element-Free Galerkin method, and the correction scheme of elastoplastic transition region has been explored. The results show that the correction scheme has a slight effect on magnitude of the equivalent stress and no impact on the subsequent plastic deformation zone. The elastoplastic transition region of shell surface appears in the range of 100 to 200 mm below the meniscus, and the averaged plastic stress is about 2.27 times of the elastic stress at the mold outlet. Near the interface region of liquid–solid phase exhibits an elastic deformation behavior, while far from the interface region appears plastic deformation in which the elastic stress remains invariable. The Element-Free Galerkin method is discretized by a series of arbitrary nodes, which exhibits high accuracy and great flexibility in dealing with moving interface problems. It provides a powerful approach to calculate and analyze the heat transfer/mechanical behavior with complex geometric boundaries such as round billet, chamfered billet, and beam blank.

Grandfamilies and the Opioid Epidemic: A Systemic Perspective and Future Priorities.

As a result of the devastating impact of the opioid epidemic, increased numbers of children are being raised by their grandparents in what are known as grandfamilies. Despite these children and their families experiencing difficult environmental circumstances, numerous adverse life events, and challenging family dynamics, empirical examinations of the opioid epidemic, as it relates to grandfamilies, remain limited. The purpose of this review is to advance the understanding of how grandfamilies have been impacted by the opioid epidemic by using a systemic perspective to highlight themes and major conclusions within the existing conceptual and empirical literature. The review reveals five systemically informed themes including the assumption of caregiving responsibilities, grandparent stress and well-being, caring for vulnerable grandchildren, navigating relationships with parents, and contextual stressors of societal stigma and barriers to service. To extend this work, systemically informed recommendations for clinical intervention and future priorities for research and policy are discussed.

Large deformation analysis of fully incompressible hyperelastic curved beams

The aim of this contribution is to develop a nonlinear formulation for modelling the large deformation of elastic curved beams made of fully incompressible hyperelastic materials. The basic idea is to apply the incompressibility constraint besides the plane stress assumption in the directions perpendicular to the centreline of the beam. Accordingly, a system of three nonlinear algebraic equations for the hydrostatic pressure as well as normal strain components in the beam cross section are obtained. By solving the system of equations, either analytically or numerically, it is possible to propose constitutive equations for the force and moment resultants present in the formulation. The main advantage of this strategy is that it allows for using three-dimensional incompressible constitutive equations. Due to highly nonlinear nature of the differential equations, a Total Lagrangian finite element formulation is developed. Performance and accuracy of the formulation are investigated through several numerical examples.

Elastic Analysis for Rotating Functionally Graded Annular Disk with Exponentially-Varying Profile and Properties

Functionally graded materials have been widely used in engineering and human health applications. The issues about mechanical behavior of functionally graded material have received considerable attention. However, because of the complexity of material property, geometric profile, and mechanical load, there is still lack of proper analytic solutions about deformation and stress in many articles. The principal goal of this research is to study the effect of mechanical load on deformation and stress in rotating thin-walled functionally gradient material annular disk with exponentially-varying profile and properties. The inner and outer surfaces of annular disk are subjected to different pressures simultaneously. For this purpose, the infinitesimal theory of elasticity and axisymmetric plane stress assumptions has been proposed to formulate the governing equation. The governing equation is a generalized confluent hypergeometric differential equation, based on Whittaker’s functions; this is the first time that closed-form solutions of mechanical behaviors are revealed about proposed functionally gradient material model. Besides, another four boundary conditions are also discussed, i.e., the inner and outer surfaces of the annular disk are considered to be the combinations of free and clamped conditions. Numeric examples of two different functionally graded material properties are given to demonstrate displacement and stress solutions. Moreover, uniform disks made of homogeneous material under different boundary conditions are investigated, which are special cases of the proposed rotating functionally gradient material disks. Finally, some conclusions are made at the end of the present paper.