Strain Formulation Research Articles

A mesomechanical analysis of the stress–strain localisation in friction stir welds of polycrystalline aluminium alloys

A numerical analysis is presented of the microstructural effects on the deformation and fracture of friction stir welds in aluminium alloys. A dynamic boundary-value problem in a plane strain formulation is solved numerically by the finite-difference method. Experimental polycrystalline microstructures inherent in different weld zones—base material, weld nugget, and thermo-mechanically affected zones—were accounted for explicitly in the calculations. To simulate the mechanical response of individual grains, use was made of an elastic–plastic formulation of the problem accounting for isotropic strain hardening, including the Hall–Petch effect, and of a fracture model allowing for crack initiation and growth in the regions of maximum equivalent plastic strains. Plastic strain and fracture localisation is shown to depend on the strength of welded materials.

Microencapsulation of new probiotic formulations for gastrointestinal delivery: in vitro study to assess viability and biological properties.

The paper describes the preparation of new probiotic formulations based on chitosan-coated alginate microcapsules containing three different probiotic strains, Lactobacillus plantarum PBS067, Lactobacillus rhamnosus PBS070, and Bifidobacterium animalis subsp. lactis PBS075 taken individually and as a mixture of them. The effects of microencapsulation on the viability of the strains in conditions simulating the gastrointestinal tract and under industrial processes conditions were studied. In addition, an evaluation of their probiotic properties was also investigated by in vitro tests on the human intestinal cell line HT-29 to explore the effect of microencapsulation on health beneficial effect of the considered strains. Non-encapsulated cells were completely destroyed when exposed to simulated gastric juice and other stress conditions, while encapsulated cells exhibited a significantly higher resistance to artificial intestinal juice and heat and osmotic treatment. Moreover, in this study, the effect of the various microencapsulated probiotic strain formulations was compared with analogous formulations also containing the β-glucan Pleuran. The microencapsulation effectively protected the selected bacteria, as single strain and as a mixture of the three strains in both the formulations with and without Pleuran, from simulating gastrointestinal tract and industrial process conditions in delivering the viable cells without any significant adverse effect on their functionalities. The comparative study of the immunomodulatory properties of each single strain and the mixture of the three strains revealed a synergistic effect of the probiotic mixture, but no appreciable difference between the two kinds of formulations could be detected, as the effect of Pleuran is covered by the higher potential of the probiotic strains.

Finite volume approach for finite strain consolidation

SummaryThe paper presents the finite volume formulation and numerical solution of finite strain one‐dimensional consolidation equation. The equation used in this study utilises a nonlinear continuum representation of consolidation with varying compressibility and hydraulic conductivity and thus inherits the material and geometric nonlinearity. Time‐marching explicit scheme has been used to achieve transient solutions. The nonlinear terms have been evaluated with the known previous time step value of the independent variable, that is, void ratio. Three‐point quadratic interpolation function of Lagrangian family has been used to evaluate the face values at discrete control volumes. It has been shown that the numerical solution is stable and convergent for the general practical cases of consolidation. Performance of the numerical scheme has been evaluated by comparing the results with an analytical solution and with the piecewise piecewise‐linear finite difference numerical model. The approach seems to work well and offers excellent potential for simulating finite strain consolidation. Further, the parametric study has been performed on soft organic clays, and the influence of various parameters on the time ate consolidation characteristics of the soil is shown. Copyright © 2015 John Wiley & Sons, Ltd.

A preliminary investigation of dislocation cell structure formation in metals using continuum dislocation dynamics

A continuum dislocation dynamics model capable of capturing the cellular arrangements of dislocations in deformed crystals is presented. A small strain formulation of the model is given, followed by sample results of stress-strain behaviour, dislocation density evolution, dislocation cell pattern, lattice rotation, and geometrically necessary dislocation density and strain energy density distributions. An important finding of the current work is that dislocations form patterns under all circumstances due to their long range interactions. It is found, however, that the famous cell structure pattern forms when cross slip is activated. It is also found that cells are 3D sub-regions surrounded by dislocations walls in all directions, and they form, disappear, and reappear as a result of the motion of cell walls and formation of new walls by cross slip. It is further found that the average cell size is connected with the applied resolved shear stress according to the similitude principle observed in related experiments. The importance of these results is briefly discussed in the context of recrystallization.

Stability analysis of unlined elliptical tunnel using finite element upper-bound method with rigid translatory moving elements

The stability of an unlined elliptical tunnel in cohesive-frictional soils is determined. The analysis has been performed with two methods: finite element upper-bound method with plastic deformation elements (UP-PDE) and finite element upper-bound method with rigid translatory moving elements (UP-RTME). UP-PDE has been used to study tunnel stability by many scholars. The UP-RTME in combination with a finite element approach and triangular rigid translator moving elements is presented in detail. In the proposed method, the node coordinates and velocities of rigid elements are treated as unknowns without considering the rotating freedom. A specific plane strain formulation is proposed using nonlinear programming, and the optimal slip lines are determined by automatically adjusting the velocity discontinuities. Solutions for the influence of a range of soil parameters, dimensionless depths C/D and dimensionless spans B/D on the stability numbers γD/c and collapse mechanisms are solved using this method. The γD/c values increase with ϕ and decrease with C/D and B/D. γD/c is less sensitive to C/D as ϕ increases. The collapse mechanisms of unlined elliptical tunnels comprising two groups of slip lines are also presented, and they explicitly reflect the relative movement of blocks. The results show that these two methods are in agreement with each other.

Numerical simulation of hollow steel profiles for lightweight concrete sandwich panels

The focus of the present study is to investigate both local and global behaviour of a precast concrete sandwich panel. The selected prototype consists of two reinforced concrete layers coupled by a system of cold-drawn steel profiles and one intermediate layer of insulating material. High-definition nonlinear finite element (FE) models,based on 3D brick and 2D interface elements, are used to assess the capacity of this technology under shear, tension and compression. Geometrical nonlinearities are accounted via large displacement-large strain formulation, whilst material nonlinearities are included, in the series of simulations, by means of Von Mises yielding criterion for steel elements and a classical total strain crack model for concrete; a bond-slip constitutive law is additionally adopted to reproduce steel profile-concrete layer interaction. First, constitutive models are calibrated on the basis of preliminary pull and pull-out tests for steel and concrete, respectively. Geometrically and materially nonlinear FE simulations are performed, in compliance with experimental tests, to validate the proposed modeling approach and characterize shear,compressive and tensile response of this system, in terms of global capacity curves and local stress/strain distributions. Based on these experimental and numerical data, the structural performance is then quantified under various loading conditions, aimed to reproduce the behaviour of this solution during production, transport, construction and service conditions.

Lateral soil–pipeline interaction in sand backfill: Effect of trench dimensions

Current analytical methodologies for the evaluation of soil pressures on laterally displaced pipelines, as in the case of differential (e.g. fault-induced) permanent ground movements, allow the use of sand fill material properties under the condition that the size of the trench is adequate so that the failure surface develops fully within the sand fill (i.e. “free field” response). The accuracy of this assumption is investigated in this paper by means of numerical analyses, which employ a number of advanced features, such as pipe-backfill interface elements, large strain formulation and mesh rezoning. Following verification against well-documented experimental data, the analyses investigate: (a) the shape and size of the failure mechanism, as well as, (b) the potential trench effects on soil pressures and pipeline strains in the case of a strike-slip fault rupture. It is shown that for small embedment depths soil failure extends to the ground surface, in the form of a general shear failure mechanism, while for larger depths it becomes progressively localized and surrounds the pipeline. It is also shown that, for most cases of pipeline diameter and embedment depth, common trench dimensions cannot contain the “free field” failure surface dimensions. Finally, analyses for limited trench dimensions, reveal that the ultimate soil pressure increases exponentially with decreasing trench width, leading to high bending strains in pipelines subjected to differential lateral ground displacements.

Paenibacillus polymyxa A26 Sfp-type PPTase inactivation limits bacterial antagonism against Fusarium graminearum but not of F. culmorum in kernel assay.

Fusarium graminearum and F. culmorum are the causing agents of a destructive disease known as Fusarium head blight (FHB). FHB is a re-emerging disease in small grain cereals which impairs both the grain yield and the quality. Most serious consequence is the contamination of grain with Fusarium mycotoxins that are severe threat to humans and animals. Biological control has been suggested as one of the integrated management strategies to control FHB. Paenibacillus polymyxa is considered as a promising biocontrol agent due to its unique antibiotic spectrum. P. polymyxa A26 is an efficient antagonistic agent against Fusarium spp. In order to optimize strain A26 production, formulation and application strategies traits important for its compatibility need to be revealed. Here we developed a toolbox, comprising of dual culture plate assays and wheat kernel assays, including simultaneous monitoring of FHB causing pathogens, A26, and mycotoxin production. Using this system we show that, besides generally known lipopeptide antibiotic production by P. polymyxa, biofilm formation ability may play a crucial role in the case of stain A26 F. culmorum antagonism. Application of the system for effective strain selection and maintenance is discussed.

Modeling the Si-Current Collector Interface in Li-Ion Battery

Si is a promising anode material for Li-ion batteries (LIB) due to its high energy density. Nevertheless, the large volume variation of Si during lithiation/delithiation cycles presents a great challenge to its structural integrity in LIBs. To this end, a wide variety of Si electrode designs have been attempted. It has been shown that reducing its size to nano scale can effectively prevent the fracture of the Si electrode itself. However, failure may still occur at interfacial regions between the Si electrode and other components such as the current collector due to deformation mismatch. The detached Si becomes isolated from the electronic pathway and hence the cell capacity degrades. Understanding the deformation and stress-strain relationship at the Si-current collector interface is an important step in engineering durable, high capacity LIBs. In this work, a multiphysics microstructure-resolved model [1] was used to simulate the deformation of Si nanorods on a Ni substrate reported by Bella et al [2]. The Si was described by an elasto-plastic law with a finite strain formulation. The Li concentration dependence of the Young’s modulus and yield strength was considered. Ni was modeled as an elasto-plastic material. The interface between Si and Ni was modeled as a region with unique properties. The results revealed that the interfacial properties not only affect the deformed shape of the Si nanorod and Ni substrate but also the stress triaxiality in the system. To reproduce the deformation as in the experiment, a parameter study with different interfacial properties was carried out. The interfacial properties resulting in the best correlation with the experiment were identified. The microstructure-resolved model will then be used to investigate the structure design of LIBs with Si anode. Wu, Wei, Xinran Xiao, Miao Wang, and Xiaosong Huang. “A Microstructural Resolved Model for the Stress Analysis of Lithium-Ion Batteries.” Journal of The Electrochemical Society 161, no. 5 (January 1, 2014): A803–A813.Berla, Lucas A., Seok Woo Lee, Ill Ryu, Yi Cui, and William D. Nix. “Robustness of Amorphous Silicon during the Initial Lithiation/delithiation Cycle.” Journal of Power Sources 258 (July 15, 2014): 253–59.

Traveling waves and their tails in locally resonant granular systems

In the present study, we revisit the theme of wave propagation in locally resonant granular crystal systems, also referred to as mass-in-mass systems. We use three distinct approaches to identify relevant traveling waves. The first consists of a direct solution of the traveling wave problem. The second one consists of the solution of the Fourier tranformed variant of the problem, or, more precisely, of its convolution reformulation (upon an inverse Fourier transform) in real space. Finally, our third approach will restrict considerations to a finite domain, utilizing the notion of Fourier series for important technical reasons, namely the avoidance of resonances, which will be discussed in detail. All three approaches can be utilized in either the displacement or the strain formulation. Typical resulting computations in finite domains result in the solitary waves bearing symmetric non-vanishing tails at both ends of the computational domain. Importantly, however, a countably infinite set of anti-resonance conditions is identified for which solutions with genuinely rapidly decaying tails arise.

X-FEM modeling of dynamic ductile fracture problems with a nonlocal damage-viscoplasticity model

In this paper, the dynamic large deformation X-FEM method is presented for modeling the full process of dynamic ductile fracture based on a nonlocal damage visco-plasticity model. The effect of inertia is modeled using an explicit central difference scheme which is enhanced through the use of mass lumping, reduced integration with hourglass control, and numerical damping. The material nonlinearity and the flow stress dependency on strain rate, hardening and temperature are modeled with the Johnson–Cook visco-plastic model. The micro-void nucleation, growth and coalescence are modeled macroscopically with an isotropic damage model. The localization phenomenon due to the damage and thermal softening is suppressed by using the visco-plastic regularization in combination with the nonlocal visco-plastic model. The large deformation and large strain formulations are implemented within the X-FEM framework to model the macro crack discontinuities using an updated Lagrangian approach. Crack propagation and crack direction criteria are presented and the issues relating to the combination of X-FEM with the damage visco-plasticity model are addressed. Finally, the robustness and accuracy of the proposed method are verified through several numerical examples.

Reaction–Diffusion–Stress Coupling Effect in Inelastic Oxide Scale During Oxidation

Stress is induced in a thermally grown oxide scale during high-temperature oxidation. Under certain conditions, the oxidation causes plastic deformation. An inhomogeneous growth strain formulation is proposed based on evolution equations. Using the inhomogeneous growth strain, a reaction–diffusion–stress coupling elastic–plastic model, which accounts for factors, such as the chemical reaction, kinetics of the oxide scale and diffusion of reactant species, is developed for the analysis of stress and effects of stress on these factors in the oxide scale during high-temperature oxidation. Numerical results reveal large compressive stresses and a significant stress gradient in the oxide scale with the largest compressive stress at the oxide/substrate interface and the lowest compressive stress at the oxygen/oxide interface, which is consistent with experimental observations. The stress developed in the oxide scale has an influence on the oxidation reaction rate and distribution of the reactant species concentration, which in return affects the stress distribution.

Comparison of Experimentally Measured Temperature Gradient and Finite-Element-Method Simulations for Two Continuously Cast Bloom Heating Strategies

This paper deals with the comparison of experimentally measured temperature gradients and finite-element-method (FEM) simulations of two heating strategies that were used for continuously cast bloom soaking. The temperature gradient between the bloom surface and center was measured by two thermocouples incorporated directly into the bloom. Scanning electron microscopy equipped by energy dispersive X-ray spectroscopy analysis, hot tensile tests, and interdendritic solidification software was used for modeling of steel thermophysical properties with respect to the alloying-elements macrosegregation. The model of the bloom was programmed in the Fortran language. The FEM software MARC/MENTAT 2012 was used for simulation of two heating strategies (plane strain formulation). The first heating model was fitted to the commonly used heating strategy when internal defects grew above the critical limit. The second heating model was a newly proposed strategy that consisted of slower heating up to 1073 K when the first warming-through period occurred. The FEM simulations included determinations of the temperature gradient, the equivalent of stress, the equivalent of elastic strain, the equivalent of plastic strain, and the equivalent of total strain. The simulation results were in good agreement with experimental observations. The new heating strategy based on the FEM simulations led to significantly lower occurrence of internal defects in hot-rolled billets that are used for cylinder production.

Modeling machining of particle-reinforced aluminum-based metal matrix composites using cohesive zone elements

Finite element modeling for the machining of heterogeneous materials like particle-reinforced metal matrix composites has not been much successful as compared to homogeneous metals due to several issues. The most challenging issue is to deal with severe mesh distortion due to nonuniform deformation inside the workpiece. Other problems are related to the modeling of the interface between reinforcement particles and matrix and tool-reinforcement particle interaction. In this study, different strategies are adopted for finite element models (FEM) to cope with the above issues and comparative analyses have been performed. These 2D FE models are based on plane strain formulations and utilize a coupled temperature displacement method. The workpiece is modeled using reinforcement particle size and volume fraction inside the base matrix. The interface between the reinforcement particles and the matrix is modeled by using two approaches, with and without cohesive zone elements, and the chip separation is modeled with and without using a parting line. This allows models to simulate the local effects such as tool-reinforcement particle interaction and reinforcement particle debonding. In addition, the models can predict cutting forces, chip morphology, stresses, and temperature distributions. The effects of different methodologies on the model development, simulation runs, and predicted results have been discussed. The results are compared with experimental data, and it has been found that the utilization of cohesive zone elements (CZE) with the parting line approach seems to be the best one for the modeling of metal matrix composite (MMC) machining.

A Finite Element Based on the Strain Approach Using Airy’s Function

Plane membrane elements of class \({C^{\circ}}\) provide poor deflection and stress for problems where bending is dominant. They also encountered problems of continuity and compliance when connected to plate elements (elements of class C1). The scope of this paper is to overcome these problems by developing a new triangular plane elastic element based on a strain formulation. The developed membrane element, denoted T43_Eq, has three nodes at the vertices of the triangle and the fourth one at its barycenter. Each node has three degrees of freedom, two translations and one rotation around the normal. The coefficients related to the degrees of freedom at the internal node are subsequently removed from the element stiffness matrix by using the static condensation technique. Interpolation functions of strain, displacements and stresses fields are developed from equilibrium conditions. These polynomial bi-harmonics functions are selected from the development of the Airy function solutions. The elementary stiffness matrix is evaluated by applying the variational principle and the analytical integration method. The results of the validation test show that the developed T43_Eq element is very efficient for treating bending problems. They are competitive compared to the triangular or rectangular elements available in the literature in terms of accuracy and convergence. The performance of T43_Eq element is observed in the presence of both regular and distorted meshes.

Production and Testing of Biopesticide for Control of Postharvest Mold Infections on Fresh Fruits of Apple and Pear

The present research aimed at producing a biopesticide with proper formulation of invert emulsion (water-in-oil type) and effective strain of Trichoderma harzianum then, testing it against pathogens of postharvest mold infections(Botrytis cinerea & Penicillium expansum) on fresh fruits of apple and pear. The proper formulation of invert emulsion (IE#3) used for biopesticide production has the following ingredients (100% w/w): soybean oil (28.50%), coconut oil (19.50%), oil-soluble emulsifier: Tween 20 (2.0%), glycerine (4.25%), water-soluble emulsifier: dehymuls k (0.75%), sterile distilled water (22.5%) and conidial suspension of the effective strain ofT. harzianum “TrichoPAL1” in water (22.5%, concentration 1 × 107 conidia/ml). Testing efficacy of the produced biopesticide has indicated a significant reduction in the disease lesion diameter of mold infections on wounded apple and pear fruits stored at 20℃ ± 1℃ compared to the untreated fruits or control (reduction from up to 38.75 to about 7.50 mm, respectively, according to the type of mold infections and fruit type). Also, the treatment with the produced biopesticide has resulted in a long protection period from mold infections on wounded and un-wounded fresh fruits of apple and pear stored under controlled and semi-commercial conditions(up to 2.5 months according to the type of mold infections and fruit type). In conclusion, the overall results have demonstrated the effectiveness of produced biopesticide on stored fruits under controlled and semi-commercial conditions therefore, it is recommended to test this effectiveness on marketed fruits stored under variable conditions before applying it at a large scale.

Finite strain formulation of viscoelastic damage model for simulation of fabric reinforced polymers under dynamic loading

The use of fabric reinforced polymers in the automotive industry is growing significantly. The high specific stiffness and strength, the ease of shaping as well as the great impact performance of these materials widely encourage their diffusion. The present model increases the predictability of explicit finite element analysis and push the boundaries of the ongoing phenomenological model. Carbon fibre composites made up various preforms were tested by applying different mechanical load up to dynamic loading. This experimental campaign highlighted the physical mechanisms affecting the initial mechanical properties, namely intra- and interlaminar matrix damage, viscoelasticty and fibre failure. The intralaminar behaviour model is based on the explicit formulation of the matrix damage model developed by the ONERA as the given damage formulation correlates with the experimental observation. Coupling with a Maxwell-Wiechert model, the viscoelasticity is included without losing the direct explicit formulation. Additionally, the model is formulated under a total Lagrangian scheme in order to maintain consistency for finite strain. Thus, the material frame-indifference as well as anisotropy are ensured. This allows reorientation of fibres to be taken into account particularly for in-plane shear loading. Moreover, fall within the framework of the total Lagrangian scheme greatly makes the parameter identification easier, as based on the initial configuration. This intralaminar model thus relies upon a physical description of the behaviour of fabric composites and the numerical simulations show a good correlation with the experimental results.

Contact Stresses between Two Cylindrical Bodies – Cylinder and Cylindrical Cavity with Parallel Axes – Part II: 2D and 3D FEA Comparative Study

Abstract This paper presents the results of a study carried out using the Finite Element Method, on the contact stresses between two bodies: cylindrical body in a cylindrical cavity. The results are compared, following the analysis, to the results calculated on basis of the relations in H. Hertz's theory. The analyzed situation is: cylindrical body of radius R1 in a cylindrical cavity of radius R2, both bodies having parallel axes. Considering the cylinder - cylindrical cavity assembly presents identical cross sections along the cylinder axis, both from the geometrical and loading point of view, this part of the paper models the problem with 2D elements using the plane strain formulation. The results are compared to the ones obtained on the spatial model and presented in the first part of the paper.

Formulation of a representative plastic strain and representative plastic strain rate by using a conical indentation on a rigid visco-plastic material

• Concepts of representative strain and strain rate in indentation are investigated. • These concepts are compared with the ones proposed in literature. • New formulations of representative strain and strain rate are proposed. • These formulations describe the changes on the whole space of mechanical properties. The indentation test consists in pressing an indenter on the surface of a tested material and in measuring continually the load F in function of the displacement h of the indenter. In order to analyze the indentation curve F ( h ) and extract material properties, one method among others uses the notion of the representative strain. The first aim of this paper is to investigate a new concept of a representative plastic strain as well as a new concept of a representative plastic strain rate. The second aim is to couple the effect of work hardening and strain rate to define the corresponding representative plastic strain and the corresponding representative plastic strain rate. It is shown that there are respectively two representative plastic strains and a plastic strain rate: the former obtained using the hardness of indentation and the latter obtained using the loading curve. Then, it is shown that the values of the representative strain and of the strain rate depend on the material behavior and its constitutive parameters.

Nonlinear finite element analysis of functionally graded structures by enhanced assumed strain shell elements

In this work, large elastic deformation of structures made of functionally graded materials (FGMs) is investigated. Due to highly nonlinear nature of the problem, a total Lagrangian finite element formulation for a seven-parameter shell model is developed. The model accounts explicitly for thickness change, as well as normal stress and strain components through the thickness of the structure. The Green–Saint Venant strain tensor in conjunction with the Kirchhoff–Saint Venant constitutive equation is used to capture the geometric nonlinearity. To circumvent locking phenomenon at large distortions, an enhanced assumed strain formulation is adopted. Five different examples have been analyzed and the effect of enhanced strains and that of FGM exponent is investigated.