Component assembling model and its application to quasi-brittle damage

Potential energy can be approximated by “pair-functional” potentials which is composed of pair potentials and embedding energy. Pair potentials are grouped according to discrete directions of atomic bonds such that each group is represented by an orientational component. Meanwhile, another kind of component, the volumetric one is derived from embedding energy. Damage and fracture are the changing and breaking of atomic bonds at the most fundamental level and have been reflected by the changing of these components’ properties. Therefore, material is treated as a component assembly, and its constitutive equations are formed by means of assembling these two kinds of components’ response functions. This material model is referred to as the component assembling model. Theoretical analysis and numerical computing indicate that the proposed model has the capacity of reproducing some results satisfactorily, with the advantages of physical explicitness and intrinsic induced anisotropy, etc.     

Gradient elasticity with surface energy: mode-III crack problem

In this paper an anisotropic strain-gradient dependent theory of elasticity is exploited, which contains both volumetric and surface energy gradient dependent terms. The theory is applied to the solution of the mode-III crack problem and is extending previous results by Aifantis and co-workers. The two boundary value problems corresponding to the “unclamped” and “clamped” crack tips, respectively, are solved analytically. It turns out that the first problem is physically questionable for some values of the surface energy parameter, whereas the second boundary value problem is leading to a cusping crack, which is consistent with Barenblatt's theory without the incorporation of artificial assumptions.     

DYNAMICS AND STABILITY OF PINNED–CLAMPED AND CLAMPED–PINNED CYLINDRICAL SHELLS CONVEYING FLUID

The paper examines the dynamics and stability of fluid-conveying cylindrical shells having pinned–clamped or clamped–pinned boundary conditions, where “pinned” is an abbreviation for “simply supported”. Flügge's equations are used to describe the shell motion, while the fluid-dynamic perturbation pressure is obtained utilizing the linearized potential flow theory. The solution is obtained using two methods — the travelling wave method and the Fourier-transform approach. The results obtained by both methods suggest that the negative damping of the clamped–pinned systems and positive damping of the pinned–clamped systems, observed by previous investigators for any arbitrarily small flow velocity, are simply numerical artefacts; this is reinforced by energy considerations, in which the work done by the fluid on the shell is shown to be zero. Hence, it is concluded that both systems are conservative.     

A “quasi-elastic” affine formulation for the homogenised behaviour of nonlinear viscoelastic polycrystals and composites

The derivation of the overall behaviour of nonlinear viscoelastic (or rate-dependent elastoplastic) heterogeneous materials requires a linearisation of the constitutive equations around uniform per phase stress (or strain) histories. The resulting Linear Comparison Material (LCM) has to be linear thermoviscoelastic to fully retain the viscoelastic nature of phase interactions. Instead of the exact treatment of this LCM (i.e., correspondence principle and inverse Laplace transforms) as proposed by the “classical” affine formulation, an approximate treatment is proposed here. First considering Maxwellian behaviour, comparisons for a single phase as well as for two-phase materials (with “parallel” and disordered morphologies) show that the “direct inversion method” of Laplace transforms, initially proposed by Schapery (1962), has to be adapted to fit correctly exact responses to creep loading while a more general method is proposed for other loading paths. When applied to nonlinear viscoelastic heterogeneous materials, this approximate inversion method gives rise to a new formulation which is consistent with the classical affine one for the steady-state regimes. In the transient regime, it leads to a significantly more efficient numerical resolution, the LCM associated to the step by step procedure being no more thermoviscoelastic but thermoelastic. Various comparisons for nonlinear viscoelastic polycrystals responses to creep as well as relaxation loadings show that this “quasi-elastic” formulation yields results very close to classical affine ones, even for high contrasts.     

Simply approximate estimation of local failure position of a free-free slender shell

Dynamic plastic failure characteristics of a space free-free slender shell subjected to intense dynamic loading of suddenly applied pressure unsymmetrical triangle distributed along its span was studied. Both rigid perfectly plastic (r-p-p) analytical method and finite element method based elastic perfectly plastic (e-p-p) material idealization and shell element model were adopted to predict the local failure position in the structure. It was shown that both r-p-p and e-p-p model could estimate a plastic “kink” taking place in the slender shell, which reflects the strain localization of deformation. The comparison for the position of “kink” predicted by using r-p-p and e-p-p methods is found to be reasonable good.     

Convex plastic potentials of fourth and sixth rank for anisotropic materials

It is briefly reminded how the theory of dual plastic potentials has been used in the past to generate analytical expressions for plastic potentials of anisotropic polycrystalline materials with a known crystallographic texture. Such constitutive models are fairly general, and the identification of their parameters can readily be done on the basis of data obtained from a texture measurement. As a result, they are suitable for engineering applications such as elastic–plastic finite element models for forming processes. However, the yield loci generated in this way are not automatically convex. Therefore, a new variant of the method has now been developed, which preserves the advantages of the old method, but for which convexity can at least been tested by means of a mathematical criterion. In addition, it has turned out to be possible to slightly modify plastic potentials which do not satisfy the criterion, in order to achieve convexity. An example of a plastic potential modified in this way is discussed. After modification, it was still a good analytical approximation of the plastic potential directly derived from the Taylor–Bishop–Hill theory on the basis of the crystallographic texture of the material.     

An elastic-plastic analysis of an asymmetric cracked specimen subjected to longitudinal shear

Some recent elastic-plastic analyses of cracked specimens subjected to symmetric mode III loading are extended to include asymmetric loading and geometry. Solutions are given for arbitrary work hardening behaviour in any specimen that is amenable to a linear elastic analysis. It is shown that asymmetry has a major influence on the shape of the plastic zone, but does not affect the J-integral unil the loading is well into the large scale yielding range. In particular the “plastic zone corrected” estimate of J, obtained by elastically solving a problem for a crack longer than the actual one, is shown to remain a valid two-term asymptotic expansion in the presence of asymmetry. The general results are applied to a crack at an angle to a uniform stress field in a power law hardening material. The growth of the plastic zone is displayed graphically for various hardening exponents and crack orientations. No other asymmetric solution is available, but values of J are compared with those obtained from a fully plastic analysis in the symmetric case.     

Relativistic electron transport and confinement within charge-insulated, mass-limited targets

We present experimental results on the interaction of short-pulse ultra-high-intensity laser beams with small size (“mass-limited”) targets. Several diagnostics (X-ray spectroscopy, K_α and optical imaging of target rear side) have been simultaneously used in order to characterize the laser-generated fast electron transport and energy deposition into the target material. Our results show that fast electrons are effectively confined inside the target by the induced space charge. This electrostatic confinement opens new opportunities to create “Warm Dense Matter” states characterized by solid-state density and temperatures of the order of a few tens of eV.     

Experimental characterization of dynamic soil-track interaction on dry sand

A set of soil-track interaction relations was made developed for the morbility simulation of tracked or crawler system vehicles on dry, loose sand. These interaction relations were developed specifically for multibody mobility codes in which the soil-vehicle interaction is represented solely by soil-track interaction forces. By employing plate penetration and shear tests, an average pressure-sinkage relation, a shear force-slippage relation, and a sinkage-slippage relation were measured. These plate test data were sufficient only to describe the soil-track interaction on hard ground. On soft ground, however, it was found that intermittent sinkages induced by each passage of the road wheels become important. This dynamic contribution is called “agitation sinkage.” Based on this observation, the sinkage rate (velocity) was decomposed into elastic and plastic rates; the plastic part consists of normal force-induced, slip-induced, and agitation-induced components. Whereas the elastic and the first two components of the plastic sinkage rate were characterized by the conventional plate penetration and plate shear tests, the last term, agitation sinkage, required a new dynamic test in which the sinkage of the track after successive passages of moving road wheels was measured. It is recommended that this new field measurement technique be adopted to characterize the agitation sinkage for various terrains.     

Il'iushin's postulate and resulting thermodynamic conditions on elasto-plastic coupling

Il'iushin's postulate is restated within a general thermodynamic strain space formulation of rate independent plasticity by means of plastic internal variables. This yields a general expression in terms of appropriate thermodynamic potentials. A combination of a thermodynamic condition, derived from the general development, with the results of Il'iushin's postulate, furnishes explicit conditions on elasto-plastic coupling. A specific example is presented, with the plastic work being the only plastic internal variable. Necessary and sufficient consitbns on the elastic moduli and their change with plastic deformation are derived, for the thermodynamic condition to be satisfied.     

Energy approach to crack growth in a fiber-reinforced brittle material modeled by an inclusion

Brittle materials randomly reinforced with a low volume fraction of strong, stiff and ductile fibers are considered, with specific reference to fiber-reinforced cements and concrete. Visible cracks in such materials are accompanied by a surrounding damage zone – together these constitute a very complex “crack system”. Enormous effort has been put into trying to understand the micromechanics of such systems. Almost all of these efforts do not deal with the “crack system” propagation behavior as a whole. The propagation process of such a “crack system” includes propagation of the visible crack and the growth of the damage zone. Propagation may take place by lengthening of the visible crack together with the concomitant lengthening of the surrounding damage zone, or simply by broadening of the damage zone while the visible crack length remains unchanged – or simultaneously by growth of both types. A phenomenological completely theoretical model (for an ideal material) is here proposed which can serve to examine the propagation process by means of energy principles, without recourse to the microscopic details of the process. An application of this theoretical approach is presented for the case of a damage zone evolving with a rectangular shape. This shape is chosen because it is expected that it will illustrate the nature of damage evolution and because the computational procedure necessary to follow the growth is the most straightforward.     

Molecular dynamics simulation of deformation and failure of nanocrystals of bcc metals

Simulations of uniaxial and hydrostatic tension of Fe and Mo nanocrystal are made by molecular dynamics method. Stress versus strain are obtained while regularities of lattice rearrangement during nanocrystal plastic deformation are considered. Local instability of nanocrystal lattice, which is the cause for transition from elastic to plastic deformation of nanocrystal, is found. It is shown that local shear stresses is a driving force of nanocrystal lattice rearrangements under the conditions of both uniaxial and hydrostatic tension, so, local instability of nanocrystal of bcc metals should be considered as shear instability. Realization of “orthorhombic” path of deformation at 1 0 0 tension of Mo nanocrystal is specific case of above effect. It is demonstrated that unlike covalent nanocrystal, metallic nanocrystals display “heterogeneous” mechanism of crack nucleation, which essence is that cracks nucleate not in homogeneous elastically deformed lattice but in shear bands or near their boundaries, i.e., after non-homogeneous plastic deformation of nanocrystal.     

The mechanism of sinkage of running gear on sand

This paper presents the results of an investigation into the mechanism of sinkage of running gear on sand. The results indicate that the main reasons for the sinkage on sand are its special mechanical properties as well as the spatial strength characteristics of the sand near the surface of the ground. Sinkage on sand is greatly influenced by the mode of interaction. The “flow confining” action of the running gear could change the flow of sand. If the lateral and upward components of displacement are decreased, the bearing capacity of the sand is increased.     

Dynamic plastic behavior of structures under impact loading investigated by the extended hamilton's principle

We propose the extended Hamilton's principle to investigate the dynamic plastic behavior of a beam or a plate under an impact loading. Material is assumed to be rigid perfectly plastic. The impact loading is given in the form of initial velocity. Good agreement between our numerical solutions and experimental results done by Parkes and Jones indicates that the proposed variational method is a powerful approximation method for the dynamic plasticity analysis. The effect of strain-rate sensitivity on the permanent deflection of a plate is investigated in some detail. Instead of nonlinear differential equations, nonlinear algebraic equations are solved in the proposed method.     

耦合条件下大脑皮层神经振子群的能量函数

探讨了局部脑皮层网络活动中,耦合条件下的大规模神经振子群的能量消耗与神经信号编码之间的内禀关系,得到了神经元集群在阈下和阈上互相耦合时神经元膜电位变化的函数. 这个能量函数能够精确地再现神经电生理学实验中的EPSP,IPSP,动作电位以及动作电流. 最近功能性核磁共振实验证明了神经信号的编码是与能量的消耗紧密地耦合在一起的,因此研究结果表明利用能量原理研究大脑在神经网络层次上是如何进行编码的这一重大科学问题的讨论是十分有益的. 可以预计得到的能量函数将是生物学神经网络动力学稳定性计算的基础.      

On perfectly plastic flow in porous material

Experimental observations suggest that for perfectly-plastic materials containing pores, the (small) strain at which significant macroscopic yielding occurs is relatively insensitive to porosity, for volume fractions below approximately 15–20% (although the yield stress drops significantly with increasing porosity). Another observation is that, at these porosity levels, the stress–strain curve remains approximately linear almost up to the yield point. Based on these observations, Sevostianov and Kachanov constructed yield surfaces that explicitly reflect the shapes of the pores and their orientation. The underlying microscale mechanism is that local plastic “pockets” near pores blunt the stress concentrations; as a result, they remain limited in size and well contained in the elastic field until they connect and almost the entire matrix plasticizes within a narrow interval of stresses that can be idealized as the yield point. The present paper provides direct insight into the micromechanics of poroplasticity through direct microscale numerical simulation. Besides confirming the basic microscale mechanism, these simulations reveal that the reduction of the macroscopic poroplastic yield stress is approximated quite closely by 1−v₂ times the dense nonporous yield stress, where v₂ is the volume fraction of the pores.     

Evolution of subsequent yield surfaces and elastic constants with finite plastic deformation. Part-I: A very low work hardening aluminum alloy (Al6061-T6511)

In the present study, the initial and subsequent yield surfaces in Al 6061-T6511, based on 10 με deviation from linearity definition of yield, are presented. The subsequent yield surfaces are determined during tension, free end torsion, and combined tension–torsion proportional loading paths after reaching different levels of strains. The yield surfaces are also obtained after linear, bi-linear and non-linear unloading paths after finite plastic deformation. The initial yield surface is very close to the von-Mises yield surface and the subsequent yield surfaces undergo translation and distortion. In the case of this low work hardening material, the size of the yield surfaces is smaller and negative cross-effect is observed with finite plastic deformation. The subsequent yield have a usual “nose” in the loading direction and flattened shape in the reverse loading direction; the observed nose is more dominant in the case of tension and combined tension–torsion loading than in torsional loading. The size of the yield surfaces after unloading is smaller than the initial yield surface but larger than subsequent yield surfaces obtained during prior loading, show much smaller cross-effect, and the shape of these yield surfaces depends strongly on the loading and unloading paths. Elastic constants (Young’s and shear moduli) are also measured within each subsequent yield surfaces. Evolution of these constants with finite deformation is also presented. The decrease of the two moduli is found to be much smaller than reported earlier in tension by Cleveland and Ghosh [Cleveland, R.M., Ghosh, A.K., 2002. Inelastic effects on springback in metals. Int. J. Plast. 18, 769–785]. Part-II and III [(Khan et al., 2009a) and (Khan et al., 2009b)] of the papers will include experimental results on annealed 1100 Al (a very high work hardening material) and on both Al alloys (Al6061-T6511 and annealed 1100 Al) in tension- tension stress space, respectively. The results for both cases are quite different than the ones that are presented in this paper.     

On structural safety assessment by load factor maximization in piecewise linear plasticity

The safety assessment of structures by the maximization of a load factor up to a critical threshold is considered in this paper and a procedure is developed which generalizes limit analysis by the static approach. The following issues are dealt with: (a) piecewise linear approximation of material models is adopted as a unifying framework; (b) a procedure is developed apt to reduce the computing effort by means of yield mode selection or “sifting”; (c) a method which combines limit and deformation analysis is presented, based on mathematical optimization under linear and complementarity constraints and apt to compute, also in the presence of nonassociativity and softening, the safety factor with respect to either plastic collapse or local fracture or unserviceability because of excessive deformations, alternatively. Classical limit analysis rooted in associative perfect plasticity has well-known limitations, which are substantially mitigated in its generalization represented by method (c) proposed herein.