Direct approach to elastic deformations and stability of thin-walled rods of open profile

A new geometrically nonlinear theory of thin-walled rods of open profile accounting for warping and bi-moment is developed. The direct approach we employ is based on the principles of Lagrangean mechanics. Linear equations for small deformations in the vicinity of a pre-stressed state are derived. These equations can be used in particular for stability analysis. Stability of a beam subjected to axial or transversal loading is considered as an example. Solutions with coupled bending and twisting mode of buckling are compared with the classical Euler’s solution, existing results for thin-walled rods and numerical solutions for a shell model.     

Non-linear programming for the plastic analysis of local deformations in shell structures

The paper presents an analysis of the response of plastic spherical and cylindrical shells subjected to loads applied through a rigid boss. Special emphasis is placed on following the load-deflection behaviour of these structures after the application of the yield-point load in order to predict the appearance of any snapping action. The method of analysis assumes that upper bound calculations are applicable and that the associated velocity fields can be represented by a series of piecewise continuous polynomials. The internal dissipation of energy for the structures are then written in terms of the coefficients of these polynomials and the values appropriate to the solution are found by using a non-linear programming routine. The results of this analysis are correlated with a non-dimensional boss size parameter p and compared with the results of experimental investigations. Mention is also made of the possible effects of initial imperfections.     

Distribution of local deformations in diamond crystals according to the analysis of Kikuchi lines profile intensities

The histogram method has been proposed to determine strains in diamond crystals by the analysis of reflection electron diffraction bands in Kikuchi patterns. The anisotropy has been defined of the local strain distribution on the surface of two diamond samples produced by the temperature gradient method in the Fe-Al-C system and by growing on a surface of a statically synthesized diamond single crystal (Ni-Mn-C) in the Mg-C + Bor system.     

Using the local approach to evaluate scaling effects in ductile fracture

This paper uses a local model to predict ductile fracture in geometrically similar structures of different sizes containing either sharp cracks or blunt stress concentrators. Simple theoretical considerations suggest that when fracture occurs by quasi-isotropic void growth, fracture initiation at blunt notches follows replica scaling, whereas fracture initiation at sharp cracks does not. Simulations with a local fracture model of fracture events in (1) fatigue precracked compact specimens and (2) three-point-bend bars containing blunt notches confirm these conclusions. However, a comparison of simulations with actual experimental results with HY-130 steel specimens leads to mixed conclusions. Predicted and observed behaviors for fracture at sharp cracks agree well, but the discrepancy is considerable for fracture initiating at blunt notches loaded in bending. Significant scaling effects are observed in the experiments for the conditions of fracture initiation at blunt notches. Fractographic analysis reveals that the reason for this discrepancy is a difference in the micromechanisms controlling fracture at sharp cracks as opposed to blunt notches. At sharp cracks, quasi-isotropic void growth dominates, whereas fracture initiates at blunt notches by a shear localization process and the nucleation, growth, and coalescence of voids in a mixed shear and tensile deformation field. The transition from one mode to the other may be governed by the hardening rate and, if so, is material dependent. Therefore, when using local fracture models for predicting fracture under generalized geometric and loading conditions, care must be taken, that the micromechanisms of ductile fracture invoked in the actual material match those assumed by the local fracture model. If this correspondence is verified, local fracture models can be used to predict fracture conditions and associated scaling effects for situations not amenable to treatment by classical elasto-plastic fracture mechanics. However, new or expanded models that can treat ductile fracture in localized shear zones should be developed to realize the full potential of these local fracture methodologies. This revised version was published online in August 2006 with corrections to the Cover Date.     

Coupling of FEM and DEM simulations to consider dynamic deformations under particle load

Coupled FEM–DEM simulations enable the direct analysis of the load, the deformation and the stresses inside machine parts which interact with bulk materials. The analysis of large deformations of elastic parts is interesting as the deformation will significantly influence the bulk material behaviour. In this paper a bidirectional coupling method for the FEM software \(\hbox {ANSYS}^\circledR \) Classic and the DEM software \(\hbox {LIGGGHTS}^\circledR \) is presented. The coupling algorithm was verified and validated using a modified draw down test rig. The results from the experimental investigations and the FEM–DEM simulations are compared. A very good correlation between experiments and simulations could be found.     

Elastic buckling analysis of 3-D trusses and frames with thin-walled members

 A finite element method is presented for the determination of the elastic buckling load of three-dimensional trusses and frames with rigid joints. The beam element stiffness matrix is constructed on the basis of the exact solution of the governing equations describing the coupled flexural-torsional buckling behaviour of a three-dimensional beam with an open thin-walled section in the framework of a small deformation theory. Large deformation effects are taken into account approximately through consideration of P−Δ effects. The structural stiffness matrix is obtained by an appropriate superposition of the various element stiffness matrices. The axial force distribution in the members is obtained iteratively for every value of the externally applied loading and the vanishing of the determinant of the structural stiffness matrix is the criterion used to numerically determine the elastic buckling load of the structure. The effect of initial member imperfections is also included in the formulation. Comparisons of accuracy and efficiency of the present exact finite element method against the conventional approximate finite element method are made. Cases where the axial force distribution determination can be done without iterations are also identified. The effect of neglecting the warping stiffness of some mono-symmetric sections is also investigated. Numerical examples involving simple and complex three-dimensional trusses and frames are presented to illustrate the method and demonstrate its merits. Received: 2 May 2000 / Accepted: 15 July 2002     

An analytical approach for local buckling analysis of initially delaminated composite thin-walled columns with open and closed sections

Local buckling of intact thin-walled columns is generally performed by modeling the wall segments as long plates and by assuming that edges common to two or more plates remain straight. Thus, the buckling load can be determined by considering the wall segments as individual plates rotationally restrained by the adjacent wall segments. This technique is combined with plate theories as a new analytical method to predict the buckling load of an initially delaminated column with any arbitrary sections (open or closed). First, moments at the rotationally restrained edges of delaminated segment (web or flange) are obtained from the curvature and stiffness of the adjacent laminates. Then, the strain energy of this delaminated segment with distributed moment at edges is calculated based on the first-order shear deformation theory. Using the principal of minimum potential energy, the governing equations are obtained and solved by the Rayleigh–Ritz approximation technique. Results of the present approach are compared with three-dimensional finite-element results obtained from eigenvalue buckling analysis in ANSYS software for both box- and channel-section columns with cross-ply and angle-ply stacking sequences. Finally, the effects of delamination size and location are investigated on the buckling loads.     

A hybrid approach to multi-scale modelling of cancer

In this paper, we review multi-scale models of solid tumour growth and discuss a middle-out framework that tracks individual cells. By focusing on the cellular dynamics of a healthy colorectal crypt and its invasion by mutant, cancerous cells, we compare a cell-centre, a cell-vertex and a continuum model of cell proliferation and movement. All models reproduce the basic features of a healthy crypt: cells proliferate near the crypt base, they migrate upwards and are sloughed off near the top. The models are used to establish conditions under which mutant cells are able to colonize the crypt either by top-down or by bottom-up invasion. While the continuum model is quicker and easier to implement, it can be difficult to relate system parameters to measurable biophysical quantities. Conversely, the greater detail inherent in the multi-scale models means that experimentally derived parameters can be incorporated and, therefore, these models offer greater scope for understanding normal and diseased crypts, for testing and identifying new therapeutic targets and for predicting their impacts.     

A multi-scale approach to the propagation of non-adiabatic premixed flames

Flame propagation involves physico-chemical processes that occur over a range of temporal and spatial scales. By use of a multi-scale analysis it is shown that diffusion processes occurring on relatively small scales can be resolved analytically when the overall activation energy of the chemical reactions is large, thus providing, by asymptotic matching, explicit conditions for the state of the gas and for the flow field across the flame zone. The mathematical formulation on the larger hydrodynamic scale reduces to a free-boundary problem, with the free surface being the flame front. The front propagates into the fresh unburned gas at a rate that depends on both the local strain that it experiences and the local curvature, with coefficients that depend on the diffusion rates of heat and mass, the equivalence ratio of the mixture and the chemical kinetic parameters. The simplified model, properly termed a hydrodynamic model, involves the solution of the Navier Stokes equations with different densities and viscosities for the burned and unburned gas. The present work extends earlier studies by including volumetric heat loss, such as radiative loss, which affects the dynamics and may lead to flame extinction.     

A multi-scale analysis of local stresses development during the cure of a composite tooling material

This paper is dedicated to the cure of an in-plane isotropic carbon-epoxy tooling material presenting a specific mesostructure. Eshelby-Kröner self-consistent model (EKSC) is used to achieve a two-steps scale transition procedure, allowing relating microscopic to macroscopic properties of the material, and estimating its multi-scale mechanical states. This procedure is used to predict the local residual stresses due to thermal and chemical shrinkage of the resin, depending on the manufacturing process conditions. An experimental investigation provides the BMI resin cure kinetics and mechanical properties as a function of the temperature and conversion degree. The consequences of these evolutions on the local mechanical states are investigated and discussed.     

Radiation embrittlement modelling in multi-scale approach to brittle fracture of RPV steels

The purpose of the present article is to develop a multi-scale brittle fracture modelling for irradiated RPV materials. For this development, applicability of local brittle fracture criteria for radiation embrittlement modelling is analysed through comparison of the predicted and test results on radiation embrittlement of RPV steels in terms of ductile-to-brittle transition temperature and fracture toughness. The influence of radiation-induced defects on the processes of cleavage microcrack nucleation and propagation is clarified. The physical-and-mechanical models of the effect of irradiation-induced defects on cleavage microcrack nucleation are developed on the basis of dislocation and brittle fracture theories. Stress-and-strain controlled fracture criterion is developed that allows the adequate prediction of radiation embrittlement by various mechanisms. The differences and commonalities are revealed in the nature of material embrittlement due to cold work and neutron irradiation. The mechanism is explained of significant recovery of fracture resistance properties with simultaneous increase of fraction of intercrystalline fracture after post-irradiation annealing. Engineering approach for prediction of the temperature dependence of fracture toughness as a function of neutron fluence is justified.     

Evaluation of corrections due to local deformations in contact measurements of the thickness of low-modulus articles

Translated from Izmeritel'naya Tekhnika, No. 3, pp. 17–18, March, 1990.     

A massively multi-scale approach to characterizing tissue architecture by synchrotron micro-CT applied to the human placenta

Multi-scale structural assessment of biological soft tissue is challenging but essential to gain insight into structure–function relationships of tissue/organ. Using the human placenta as an example, this study brings together sophisticated sample preparation protocols, advanced imaging and robust, validated machine-learning segmentation techniques to provide the first massively multi-scale and multi-domain information that enables detailed morphological and functional analyses of both maternal and fetal placental domains. Finally, we quantify the scale-dependent error in morphological metrics of heterogeneous placental tissue, estimating the minimal tissue scale needed in extracting meaningful biological data. The developed protocol is beneficial for high-throughput investigation of structure–function relationships in both normal and diseased placentas, allowing us to optimize therapeutic approaches for pathological pregnancies. In addition, the methodology presented is applicable in the characterization of tissue architecture and physiological behaviours of other complex organs with similarity to the placenta, where an exchange barrier possesses circulating vascular and avascular fluid spaces.     

Fatigue analysis and the local stress–strain approach in complex vehicular structures

In the last 20 years the `strain-life' fatigue analysis philosophy has achieved the status of industry standard in the automotive, truck and earth moving industries in North America. Although the fundamental concepts of the method are quite simple, the recent massive computerization of the techniques, and their incorporation into large dynamically loaded body and chassis durability calculation models, has resulted in new capabilities and insights for engineers, but also has meant new challenges for the creators of fatigue simulation software.This paper gives a brief history of the evolution of this type of calculation software in the vehicular industry from the observation of stress–strain hysteresis behavior, through the early development of computer versions of the stress–strain shape and memory models, to their evolution into routines that are closely linked to vehicle dynamics models that calculate loads in structures, finite element models that transform the loads into local stresses, and subsequent plasticity correction and damage evaluation routines which yield expected life color contour plots for vehicle body and chassis.     

An object‐oriented programming approach to the Lagrangian FEM analysis of large inelastic deformations and metal‐forming processes

The general deformation problem with material and geometric non‐linearities is typically divided into a number of subproblems including the kinematic, the constitutive, and the contact/friction subproblems. These problems are introduced for algorithmic purposes; however, each of them represents distinct physical aspects of the deformation process. For each of these subproblems, several well‐established mathematical and numerical models based on the finite element method have been proposed for their solution. Recent developments in software engineering and in the field of object‐oriented C++ programming have made it possible to model physical processes and mechanisms more expressively than ever before. In particular, the various subproblems and computational models in a large inelastic deformation analysis can be implemented using appropriate hierarchies of classes that accurately represent their underlying physical, mathematical and/or geometric structures. This paper addresses such issues and demonstrates that an approach to deformation processing using classes, inheritance and virtual functions allows a very fast and robust implementation and testing of various physical processes and computational algorithms. Here, specific ideas are provided for the development of an object‐oriented C++ programming approach to the FEM analysis of large inelastic deformations. It is shown that the maintainability, generality, expandability, and code re‐usability of such FEM codes are highly improved. Finally, the efficiency and accuracy of an object‐oriented programming approach to the analysis of large inelastic deformations are investigated using a number of benchmark metal‐forming examples. Copyright © 1999 John Wiley & Sons, Ltd.     

Quantifying the effects of strains on the conductivity and porosity of LiFePO4 based Li-ion composite cathodes using a multi-scale approach

The effects of the lithium concentration-induced and external load-induced strains on the porosity and electrical conductivity of a LiFePO₄ based Li-ion composite cathode are within the focus of this paper. A micro finite element analysis is first performed considering the arrangement and interaction of the particles in a representative volume element (RVE) of a LiFePO₄–PVDF mixture. The aim is to capture the deformation behavior under different levels of local state of charge (SOC) in lithium concentration, and external loads. Subsequently, apparent conductivities and porosities as a function of SOC and apparent macroscopic volumetric strains are extracted. A larger macro-scale cathode sample is then analyzed, using macro finite element simulations and the extracted apparent properties. Estimated representative spatial SOC profiles under different external pressures are supplied as input. It is found that external assembly loads should not have a considerable influence on the electrochemical performance, since the changes in porosity and conductivity are negligible. Nevertheless, lithium concentrations could account for up to 5% alteration in porosity and conductivity. Even though relatively small, such levels could be meaningful in situations of high rate and poor cell heat dissipation, which is typical in electrified vehicles applications. These strain effects could be considered in a rigorous electrochemical–thermal framework by using porosities and conductivities as a function of local Li concentrations and apparent volumetric strains.