General Loading Conditions Research Articles

A loading-dependent model of critical resolved shear stress

A quantitative model is developed to describe the critical resolved shear stress (CRSS), which is required for homogeneous partial dislocation nucleation in Lennard−Jones single crystals under general loading conditions, and to predict the slip systems to be activated. In this model, CRSS depends on actual loading, i.e., hydrostatic and all deviatoric stress components, and has directionality. Systematic molecular dynamics simulations are conducted to validate the model under different loading conditions including pure shear, and uniaxial stress (compression and tension) without and with initial hydrostatic pressure applied, and demonstrate that this model predicts exact slip systems and CRSS accurately. The relative orientation between loading direction and slip direction plays an important role in the compression–tension asymmetry in yield strength. On the other hand, Schmid's law fails for some loading conditions, and a new definition of the Schmid factor is proposed.

Displacement Propagation in Fibrous Networks Due to Local Contraction.

The extracellular matrix provides macroscale structure to tissues and microscale guidance for cell contraction, adhesion, and migration. The matrix is composed of a network of fibers, which each deform by stretching, bending, and buckling. Whereas the mechanics has been well characterized in uniform shear and extension, the response to more general loading conditions remains less clear, because the associated displacement fields cannot be predicted a priori. Studies simulating contraction, such as due to a cell, have observed displacements that propagate over a long range, suggesting mechanisms such as reorientation of fibers toward directions of tensile force and nonlinearity due to buckling of fibers under compression. It remains unclear which of these two mechanisms produces the long-range displacements and how properties like fiber bending stiffness and fiber length affect the displacement field. Here, we simulate contraction of an inclusion within a fibrous network and fit the resulting radial displacements to ur ∼ r-n where the power n quantifies the decay of displacements over distance, and a value of n less than that predicted by classical linear elasticity indicates displacements that propagate over a long range. We observed displacements to propagate over a longer range for greater contraction of the inclusion, for networks having longer fibers, and for networks with lower fiber bending stiffness. Contraction of the inclusion also caused fibers to reorient into the radial direction, but, surprisingly, the reorientation was minimally affected by bending stiffness. We conclude that both reorientation and nonlinearity are responsible for the long-range displacements.

Generalized T-stress solutions for penny-shaped cracks in transversely isotropic piezoelectric media

A novel set of analytical and semi-analytical solutions is obtained for the generalized T-stress for both electrically impermeable and permeable penny-shaped cracks embedded in a transversely isotropic, linear piezoelectric, infinite medium under uniform far-field loading and general mechanical and electrical crack-face loading. The generalized stress field of the crack for two basic loading cases, viz. uniformly distributed self-equilibrated crack-face loading and a pair of crack-face self-equilibrated unit normal point forces and unit point electrical charges, are employed together with the asymptotic near-front expansion to establish fundamental solutions for the generalized T-stress. Such fundamental solutions are explicit and involve only elementary functions, and are then utilized to form an explicit integral formula for computing the generalized T-stress of a penny-shaped crack under general crack-face loading. The exact integration of the integral formula is also established for specific loading conditions, whereas its evaluation via an efficient quadrature for general loading conditions is also addressed. A selected set of numerical results is presented to verify the proposed quadrature and significant and useful findings are also reported.

Elastoplastic Model for Overconsolidated Clays with Focus on Volume Change under General Loading Conditions

Elastoplastic Model for Overconsolidated Clays with Focus on Volume Change under General Loading Conditions

Improved formulation for running torque in angular contact ball bearings

This paper presents an improved computational model for the angular contact ball bearing (ACBB) running torque. Considering the general loading condition, the friction torque formula of individual bearing balls was derived. Five friction components were considered: elastohydrodynamic lubrication (EHL) rolling resistance, elastic hysteresis friction, differential sliding loss, spinning friction, and lubricant viscous drag effect. The formulas for elastohydrodynamic lubrication rolling resistance and spinning friction, which contribute significantly to the ACBB running torque, were improved by investigating and re-formulating the contact related formulas. The friction coefficient between the ball and races was investigated in order to choose a suitable and reliable formula for the proposed model. The proposed model was verified through a comparison with formulas provided by a bearing manufacturer and with a set of experimental data.

Application of Three Nodded Finite Element Beam Model to Beam on Elastic Foundation

The convergence of numerical solution based on two nodded beam finite element require considerable number of iterations and time; and is also plagued with shear locking. To address these deficiencies a three nodded beam element is proposed in this study to simulate the behavior of beams on elastic foundation. The analytical formulation of the model and development of shape functions are achieved with assumption of Winkler hypothesis for beam on elastic foundation A Matlab programme was developed to determine the combined beam and foundation stiffness as well as the load vector. The proposed model reliably simulates the deformations and stress resultants of beam on elastic foundation under general loading conditions. The result showed faster convergence devoid of shear locking. The maximum deflection and bending moment differ from the classical solution by about 5 percent.

Analytical Modeling of an Oblique Edge Crack in Rolling Contact Fatigue

Surface cracks represent a frequent cause of damage and even failure in rolling contacts, observed in gears, cams, rails, and so on. In the literature, different approaches have been applied to describe the crack behaviour by means of Fracture Mechanics parameters, such as the stress intensity factors (SIFs) and the J-integral. In this paper, a general procedure for dealing with plane problems is presented, which is based on Linear Elastic Fracture Mechanics hypotheses. It combines the Weight Function Method for evaluating the SIFs in a loading cycle with the Kolosov-Muskhelishvili complex variable approach for estimating the nominal stress field. In this way, a completely analytical procedure can be applied for a general loading condition, assuming that the real geometry can be simplified in a half-plane with an oblique edge crack. As test case, a travelling load has been considered representing a combination of three contributions: Hertzian pressure distribution, traction force due to friction, and pressurization of the crack faces. A comparison with literature results proved that the proposed approach can be an efficient tool for SIFs estimation and crack growth description.

Nonlinear analysis of ionic polymer–metal composite beams using the von Kármán strains

In this study, nonlinear analysis of ionic polymer–metal composite (IPMC) strips using the Euler–Bernoulli beam theory with the von Kármán nonlinear strain is presented. The governing equations are derived using a variational formulation based on a thermodynamic framework. The nonlinear extensions to the linear theory are made in such a way that the resulting form of the coupling between deformation and solvent concentration remains simple. A hybrid finite element–finite volume numerical solution and a operator-split time stepping scheme are formulated for obtaining numerical solutions of the transient electromechanical response. The model is phenomenological, but it is capable of simulating the transient response of IPMC strips under general loading conditions, and it would be useful in the design of mechanisms with IPMC strips as components. The results of the nonlinear analysis are compared with the corresponding linear results for a cantilever beam like IPMC strip. Significant differences in simulation results of tip deflection, solvent concentration, and beam configurations are observed between the linear and the nonlinear beam theory. The differences are due to coupling between the bending and the axial stiffness as properly formulated in the proposed nonlinear theory.

General surface loading over layered transversely isotropic pavements with imperfect interfaces

In this paper, we present an efficient and comprehensive approach to study the response of layered flexible pavements under general surface loading. Each layer can be transversely isotropic and the interface between the layers can be imperfect. Multiple surface loadings in both vertical and horizontal directions over circular regions can be applied. To handle efficiently multilayered pavements under very general loading and interface conditions, a new method called DVP (dual variable and position method) is proposed. The new method is computationally stable and can handle multiple imperfect interfaces very well in the multilayered pavement. The solution is further expressed in terms of the cylindrical system of vector functions so that the normal (dilatational) and shear (torsional) deformations can be separated and solved in terms of the LM- and N-types of this vector-function system. Various equivalent imperfect interface models are also investigated and their equivalence to the thin interface layer is further discussed.

Elastic Analysis of Steel Beams Strengthened with GFRP Plates Including Preexisting Loading Effects

The present study develops a theory for the elastic analysis of a preloaded wide flange steel beam, strengthened with two glass fiber-reinforced polymer (GFRP) plates bonded to both flanges, then subjected to additional loads. Starting with the principle of stationary potential energy, the governing equilibrium equations and corresponding boundary conditions are formulated prior to and after GFRP strengthening. The resulting theory involves four coupled equilibrium equations and 10 boundary conditions. A general closed form solution is then provided for general loading and boundary conditions. Detailed comparisons with three-dimensional finite-element solutions show that the theory provides reliable predictions for the displacements and stresses. A parametric study is then developed to quantify the effects of strengthening, GFRP plate thicknesses, and preexisting loads on the capacity of the strengthened beam.

Dual measurement self-sensing technique of NiTi actuators for use in robust control

Using a shape memory alloy actuator as both an actuator and a sensor provides huge benefits in cost reduction and miniaturization of robotic devices. Despite much effort, reliable and robust self-sensing (using the actuator as a position sensor) had not been achieved for general temperature, loading, hysteresis path, and fatigue conditions. Prior research has sought to model the intricacies of the electrical resistivity changes within the NiTi material. However, for the models to be solvable, nearly every previous technique only models the actuator within very specific boundary conditions. Here, we measure both the voltage across the entire NiTi wire and of a fixed-length segment of it; these dual measurements allow direct calculation of the actuator length without a material model. We review previous self-sensing literature, illustrate the mechanism design that makes the new technique possible, and use the dual measurement technique to determine the length of a single straight wire actuator under controlled conditions. This robust measurement can be used for feedback control in unknown ambient and loading conditions.

04.18: Determination of the plastic limit load for a cylindrical shell under general loading conditions using FEA

This article is not available for publication.

Cyclic plasticity behaviors of steam turbine rotor subjected to cyclic thermal and mechanical loads

In this paper, shakedown and ratchet analyses are performed to investigate the cyclic plasticity behaviors of the steam turbine rotor subjected to cyclic thermal and mechanical loads by employing Linear Matching Method (LMM). Traditionally, the shakedown or ratchet analysis mainly focus on the structure under general cyclic loading condition composed by constant mechanical load and cyclic thermal load, but the investigated steam turbine rotor here is subjected to cyclic mechanical load and cyclic thermal load that vary in phase and out of phase throughout the practical operation load cycle. The failure behaviours of structure under practical operation load cycle is studied and discussed. The novel shakedown and ratchet failure diagrams are plotted by calculating different combinations of cyclic mechanical load and cyclic thermal load. The innovative equation to acquire plastic strain range of the structure under steady state cycle is fitted, which is vital for low cycle fatigue (LCT) assessment. Moreover, detailed step-by-step inelastic analyses are also performed to verify the applicability and effectiveness of the limit boundaries calculated by the LMM. All the investigations demonstrate that the proposed LMM technique is capable of handling practical industrial application with complicated cyclic loads.

A consistent anisotropic damage model for laminated fiber-reinforced composites using the 3D-version of the Puck failure criterion

This paper presents a consistent anisotropic damage model for laminated fiber-reinforced composites relying on the 3D-version of the Puck failure criterion. The current model is based on ply failure mechanisms (fiber and inter-fiber failures) incorporating energetic considerations into the progressive damage evolution. The proposed formulation is implemented into the implicit FE commercial package ABAQUS using the user-defined capability UMAT. Additionally, the current damage model is combined with a locking-free solid shell formulation via the user-defined subroutine UEL in order to account for geometrical nonlinear effects in thin-walled applications. The reliability of the current formulation is first examined by means of several benchmark applications, and subsequently, the obtained numerical predictions are compared with experimental data corresponding to an open hole tension test. These applications show the practicability and accuracy of the proposed methodology for triggering damage in composite laminates, providing a robust modeling framework suitable for general specimens and loading conditions.

Centres of rigidity in multi-storey asymmetric diaphragm systems for general lateral static loading

In this paper a general methodology for calculating the centres of rigidity in multi-storey asymmetric buildings is proposed, which is applicable to orthogonal as well as to non-orthogonal diaphragm systems with complex topology and possible coupling of diaphragms along with consideration of very general load conditions, including gravity and modal loads. The methodology is presented in two alternative forms: (a) In the standard form, matrix relations have been developed which can be directly included to any new or existing programming codes for analysis of building structures, (b) In the alternative form the methodology can use the results of any standard programs for static analysis of building structures, in addition with a small post-processing effort that can be achieved by only few hand calculations, thus becoming significantly simpler than the methodologies that currently exist. A numerical example presents the individual steps of a comparative application of the standard and alternative forms of the methodology, while two additional numerical examples demonstrate the simplicity and efficiency of its alternative form.

On short cracks that depart from elastoplastic notch tips

The behavior of short cracks that depart from elastoplastic notch tips is modeled to estimate the stresses required to initiate and to propagate cracks in notched structural components, and to evaluate the size of tolerable crack-like defects under general loading conditions. This analysis can model both fatigue and environmentally assisted cracking problems; can evaluate notch sensitivity in both cases; and can as well be used to establish design or acceptance criteria for tolerable non-propagating crack-like defects in such cases. The growth of short cracks is assumed driven by the applied stresses and by the stress gradient ahead the notch tip, and supported by the material resistances to crack initiation and to long crack propagation by fatigue or EAC. In the elastoplastic case, the stress gradient ahead of the notch tip is quantified by a J-field to consider the short crack behavior. The tolerable short crack predictions made by this model are evaluated by suitable fatigue and EAC tests of notched specimens specially designed to start nonpropagating cracks from the notch tips, both under elastic and elastoplastic conditions.

A finite-strain homogenization model for viscoplastic porous single crystals: I – Theory

This paper presents a homogenization-based constitutive model for the finite-strain, macroscopic response of porous viscoplastic single crystals. The model accounts explicitly for the evolution of the average lattice orientation, as well as the porosity, average shape and orientation of the voids (and their distribution), by means of appropriate microstructural variables playing the role of internal variables and serving to characterize the evolution of both the “crystallographic” and “morphological” anisotropy of the porous single crystals. The model makes use of the fully optimized second-order variational method of Ponte Castañeda (2015), together with the iterated homogenization approach of Agoras and Ponte Castañeda (2013), to characterize the instantaneous effective response of the porous single crystals with fixed values of the microstructural variables. Consistent homogenization estimates for the average strain rate and vorticity fields in the phases are then used to derive evolution equations for the associated microstructural variables. The model is 100% predictive, requiring no fitting parameters, and applies for porous viscoplastic single crystals with general crystal anisotropy and average void shape and orientation, which are subjected to general loading conditions. In Part II of this work (Song and Ponte Castañeda, 2017a), results for both the instantaneous response and the evolution of the microstructure will be presented for porous FCC and HCP single crystals under a wide range of loading conditions, and good agreement with available FEM results will be shown.

Coupled axial-shear numerical model for CLT connections

A new coupled axial-shear numerical model is proposed to simulate the response of typical Cross Laminated Timber (CLT) connections under general loading conditions. The general model is then specialized for hold-down connections. To this aim, a series of experimental tests was first designed and performed at University of Bologna, in order to provide for the necessary data for the characterization of the numerical model. The main parameters required to define the constitutive law of the model are here evaluated by means of linear regression analyses performed on the experimental data. Both monotonic and cyclic test series are taken into account to calibrate and then validate the proposed numerical model, demonstrating its effectiveness in representing the coupled response of hold-down connections under simultaneous application of axial and shear forces. Finally, the response of a whole CLT panel subjected to a cyclic top displacement history is studied, confirming the need of considering axial-shear interaction in modelling of numerical connections.

ДИНАМИЧЕСКАЯ ОСЕСИММЕТРИЧНАЯ ЗАДАЧА ПРЯМОГО ПЬЕЗОЭФФЕКТА ДЛЯ КРУГЛОЙ БИМОРФНОЙ ПЛАСТИНЫ

The dynamic axisymmetric problem for a round bimorph structure consisting of the metal substrate and the axially polarized piezoceramic plate is considered. Its bending modes are caused by the action of the mechanical loading (normal tension) on the side surface; the loading is a function of the radial coordinate and time. The rigid and hinge supports of the plate are considered. The initial design relations are formulated for the piezoceramic material with the hexagonal crystal lattice of the 6 mm class. In order to solve the problem of the theory of electrodynamics in a three-dimensional formulation, the finite integral Hankel transformations along the axial coordinate and a generalized transformation (FIT) over the radial variable is used. At each stage, the standardization is carried out which allows implementing an appropriate transformation algorithm. In the first case the boundary conditions are presented in a mixed form; and in the second case they are homogeneous by introducing auxiliary functions. This approach allows gaining precise (within the used models) calculated ratios in a most general form. The built closed solution allows defining the frequency range of the axisymmetric oscillations, the stress-strain state and the nature of the changing induced electric field of the bimorph plate. This makes it possible to establish the conventional solutions of the designed devices, determine a way of fixing the electrical signal, pick up all the geometrical and physical characteristics of the typical elements of the piezoceramic transducers Also, the developed solution allows solving the problems of the elasticity and electroelasticity theory for circular thick and thin plates with an arbitrary number of layers under most general loading conditions without the use of kinematic hypotheses.

Semi-analytical model based on generalized plane strain assumption for unidirectional composites with matrix micro cracks

ABSTRACTGeneralized plane strain state is assumed and stress-based finite strip method is formulated for analysis of unidirectional laminates with matrix microcracks. Total complementary potential energy is minimized and fourth-order Euler Lagrange governing equations are presented. This stress-based generalized plane strain approach analyzes general layup and loading conditions. It provides flexibility to control the number of finite strip nodal lines within each lamina; hence, stress behavior can be predicted across each lamina at the desired location of the structure. Along with all of the capabilities which are common with finite strip methodology based on plane strain assumption, this current work has extended the analysis of the cracked laminate. For example, by incorporating behavior of the out of the plane shear stress, boundary conditions including natural boundary conditions are imposed appropriately to solve governing Euler's equations. Results are compared with previously developed displacement-based formulation in the literature for cracked laminates. It has already been shown that a stress-based plane strain approach enhances variation-based cracked laminate analysis where only the case of cross-ply laminate under tension is considered. This current work applies generalized plane strain-based finite strip methodology to carry out analysis under different loading conditions.