Size effects in the conical indentation of an elasto-plastic solid

The size effect in conical indentation of an elasto-plastic solid is predicted via the Fleck and Willis formulation of strain gradient plasticity (Fleck, N.A. and Willis, J.R., 2009, A mathematical basis for strain gradient plasticity theory. Part II: tensorial plastic multiplier, J. Mech. Phys. Solids, 57, 1045-1057). The rate-dependent formulation is implemented numerically and the full-field indentation problem is analyzed via finite element calculations, for both ideally plastic behavior and dissipative hardening. The isotropic strain-gradient theory involves three material length scales, and the relative significance of these length scales upon the degree of size effect is assessed. Indentation maps are generated to summarize the sensitivity of indentation hardness to indent size, indenter geometry and material properties (such as yield strain and strain hardening index). The finite element model is also used to evaluate the pertinence of the Johnson cavity expansion model and of the Nix-Gao model, which have been extensively used to predict size effects in indentation hardness. © 2012 Elsevier Ltd.

Tensile response of passivated films with climb-assisted dislocation glide

The tensile response of single crystal films passivated on two sides is analysed using climb enabled discrete dislocation plasticity. Plastic deformation is modelled through the motion of edge dislocations in an elastic solid with a lattice resistance to dislocation motion, dislocation nucleation, dislocation interaction with obstacles and dislocation annihilation incorporated through a set of constitutive rules. The dislocation motion in the films is by glide-only or by climb-assisted glide whereas in the surface passivation layers dislocation motion occurs by glide-only and penalized by a friction stress. For realistic values of the friction stress, the size dependence of the flow strength of the oxidised films was mainly a geometrical effect resulting from the fact that the ratio of the oxide layer thickness to film thickness increases with decreasing film thickness. However, if the passivation layer was modelled as impenetrable, i.e. an infinite friction stress, the plastic hardening rate of the films increases with decreasing film thickness even for geometrically self-similar specimens. This size dependence is an intrinsic material size effect that occurs because the dislocation pile-up lengths become on the order of the film thickness. Counter-intuitively, the films have a higher flow strength when dislocation motion is driven by climb-assisted glide compared to the case when dislocation motion is glide-only. This occurs because dislocation climb breaks up the dislocation pile-ups that aid dislocations to penetrate the passivation layers. The results also show that the Bauschinger effect in passivated thin films is stronger when dislocation motion is climb-assisted compared to films wherein dislocation motion is by glide-only. © 2012 Elsevier Ltd.

Reinforcement learning using a continuous time actor-critic framework with spiking neurons.

Animals repeat rewarded behaviors, but the physiological basis of reward-based learning has only been partially elucidated. On one hand, experimental evidence shows that the neuromodulator dopamine carries information about rewards and affects synaptic plasticity. On the other hand, the theory of reinforcement learning provides a framework for reward-based learning. Recent models of reward-modulated spike-timing-dependent plasticity have made first steps towards bridging the gap between the two approaches, but faced two problems. First, reinforcement learning is typically formulated in a discrete framework, ill-adapted to the description of natural situations. Second, biologically plausible models of reward-modulated spike-timing-dependent plasticity require precise calculation of the reward prediction error, yet it remains to be shown how this can be computed by neurons. Here we propose a solution to these problems by extending the continuous temporal difference (TD) learning of Doya (2000) to the case of spiking neurons in an actor-critic network operating in continuous time, and with continuous state and action representations. In our model, the critic learns to predict expected future rewards in real time. Its activity, together with actual rewards, conditions the delivery of a neuromodulatory TD signal to itself and to the actor, which is responsible for action choice. In simulations, we show that such an architecture can solve a Morris water-maze-like navigation task, in a number of trials consistent with reported animal performance. We also use our model to solve the acrobot and the cartpole problems, two complex motor control tasks. Our model provides a plausible way of computing reward prediction error in the brain. Moreover, the analytically derived learning rule is consistent with experimental evidence for dopamine-modulated spike-timing-dependent plasticity.

Changing the responses of cortical neurons from sub- to suprathreshold using single spikes in vivo.

Action Potential (APs) patterns of sensory cortex neurons encode a variety of stimulus features, but how can a neuron change the feature to which it responds? Here, we show that in vivo a spike-timing-dependent plasticity (STDP) protocol-consisting of pairing a postsynaptic AP with visually driven presynaptic inputs-modifies a neurons' AP-response in a bidirectional way that depends on the relative AP-timing during pairing. Whereas postsynaptic APs repeatedly following presynaptic activation can convert subthreshold into suprathreshold responses, APs repeatedly preceding presynaptic activation reduce AP responses to visual stimulation. These changes were paralleled by restructuring of the neurons response to surround stimulus locations and membrane-potential time-course. Computational simulations could reproduce the observed subthreshold voltage changes only when presynaptic temporal jitter was included. Together this shows that STDP rules can modify output patterns of sensory neurons and the timing of single-APs plays a crucial role in sensory coding and plasticity.DOI:http://dx.doi.org/10.7554/eLife.00012.001.

Global analysis of dynamical decision-making models through local computation around the hidden saddle

Bistable dynamical switches are frequently encountered in mathematical modeling of biological systems because binary decisions are at the core of many cellular processes. Bistable switches present two stable steady-states, each of them corresponding to a distinct decision. In response to a transient signal, the system can flip back and forth between these two stable steady-states, switching between both decisions. Understanding which parameters and states affect this switch between stable states may shed light on the mechanisms underlying the decision-making process. Yet, answering such a question involves analyzing the global dynamical (i.e., transient) behavior of a nonlinear, possibly high dimensional model. In this paper, we show how a local analysis at a particular equilibrium point of bistable systems is highly relevant to understand the global properties of the switching system. The local analysis is performed at the saddle point, an often disregarded equilibrium point of bistable models but which is shown to be a key ruler of the decision-making process. Results are illustrated on three previously published models of biological switches: two models of apoptosis, the programmed cell death and one model of long-term potentiation, a phenomenon underlying synaptic plasticity. © 2012 Trotta et al.

Stiffness of clays and silts: Normalizing shear modulus and shear strain

An analysis is presented of a database of 67 tests on 21 clays and silts of undrained shear stress-strain data of fine-grained soils. Normalizations of secant G in terms of initial mean effective stress p9 (i.e., G=p9 versus log g) or undrained shear strength cu (i.e., G=cu versus log g) are shown to be much less successful in reducing the scatter between different clays than the approach that uses the maximum shear modulus,Gmax, a technique still not universally adopted by geotechnical researchers and constitutive modelers. Analysis of semiempirical expressions forGmax is presented and a simple expression that uses only a void-ratio function and a confining-stress function is proposed. This is shown to be superior to a Hardin-style equation, and the void ratio function is demonstrated as an alternative to an overconsolidation ratio (OCR) function. To derive correlations that offer reliable estimates of secant stiffness at any required magnitude of working strain, secant shear modulus G is normalized with respect to its small-strain value Gmax, and shear strain g is normalized with respect to a reference strain gref at which this stiffness has halved. The data are corrected to two standard strain rates to reduce the discrepancy between data obtained from static and cyclic testing. The reference strain gref is approximated as a function of the plasticity index.Aunique normalized shear modulus reduction curve in the shape of a modified hyperbola is fitted to all the available data up to shear strains of the order of 1%. As a result, good estimates can be made of the modulus reduction G/Gmax ±30% across all strain levels in approximately 90% of the cases studied. New design charts are proposed to update the commonly used design curves. © 2013 American Society of Civil Engineers.

Modelling and design of stress-induced martensite formation in metastable β Ti alloys

The temperature dependence of the stress-induced martensite (SIM) formation in a Ti-10V-2Fe-3Al (Ti-1023) alloy under compressive loading has been studied. At low temperatures, the stress level at which martensite starts to form increases linearly with the deformation temperature, while the stress at which the deformation switches to regular plastic deformation is roughly temperature independent. A thermostatistical model for dislocation evolution is employed to describe deformation twinning in martensite. Combined effects of twinning induced plasticity and solid solution strengthening are considered in terms of temperature variations. The SIM effect disappears on deformation at temperatures beyond ~ 233 ° C, which is close to the predicted Ms temperature of 240°C. The thermostatistical model predicts a transition from twinned martensite to pure slip at 250°C. By providing a model to predict the martensite formation, and by describing deformation twinning, the present work provides a number of tools that may be employed to conceive new titanium alloys combining improved strength and ductility. © 2013 Elsevier B.V.

An analysis of competing toughening mechanisms in layered and particulate solids

The relative potency of common toughening mechanisms is explored for layered solids and particulate solids, with an emphasis on crack multiplication and plasticity. First, the enhancement in toughness due to a parallel array of cracks in an elastic solid is explored, and the stability of co-operative cracking is quantified. Second, the degree of synergistic toughening is determined for combined crack penetration and crack kinking at the tip of a macroscopic, mode I crack; specifically, the asymptotic problem of self-similar crack advance (penetration mode) versus 90 ° symmetric kinking is considered for an isotropic, homogeneous solid with weak interfaces. Each interface is treated as a cohesive zone of finite strength and toughness. Third, the degree of toughening associated with crack multiplication is assessed for a particulate solid comprising isotropic elastic grains of hexagonal shape, bonded by cohesive zones of finite strength and toughness. The study concludes with the prediction of R-curves for a mode I crack in a multi-layer stack of elastic and elastic-plastic solids. A detailed comparison of the potency of the above mechanisms and their practical application are given. In broad terms, crack tip kinking can be highly potent, whereas multiple cracking is difficult to activate under quasi-static conditions. Plastic dissipation can give a significant toughening in multi-layers especially at the nanoscale. © 2013 Springer Science+Business Media Dordrecht.

Finite Element studies on indentation size effect using a higher order strain gradient theory

In this work, a Finite Element implementation of a higher order strain gradient theory (due to Fleck and Hutchinson, 2001) has been used within the framework of large deformation elasto-viscoplasticity to study the indentation of metals with indenters of various geometries. Of particular interest is the indentation size effect (ISE) commonly observed in experiments where the hardness of a range of materials is found to be significantly higher at small depths of indentation but reduce to a lower, constant value at larger depths. That the ISE can be explained by strain gradient plasticity is well known but this work aims to qualitatively compare a gamut of experimental observations on this effect with predictions from a higher order strain gradient theory. Results indicate that many of the experimental observations are qualitatively borne out by our simulations. However, areas exist where conflicting experimental results make assessment of numerical predictions difficult. © 2012 Elsevier Ltd. All rights reserved.

Optimal recall from bounded metaplastic synapses: predicting functional adaptations in hippocampal area CA3.

A venerable history of classical work on autoassociative memory has significantly shaped our understanding of several features of the hippocampus, and most prominently of its CA3 area, in relation to memory storage and retrieval. However, existing theories of hippocampal memory processing ignore a key biological constraint affecting memory storage in neural circuits: the bounded dynamical range of synapses. Recent treatments based on the notion of metaplasticity provide a powerful model for individual bounded synapses; however, their implications for the ability of the hippocampus to retrieve memories well and the dynamics of neurons associated with that retrieval are both unknown. Here, we develop a theoretical framework for memory storage and recall with bounded synapses. We formulate the recall of a previously stored pattern from a noisy recall cue and limited-capacity (and therefore lossy) synapses as a probabilistic inference problem, and derive neural dynamics that implement approximate inference algorithms to solve this problem efficiently. In particular, for binary synapses with metaplastic states, we demonstrate for the first time that memories can be efficiently read out with biologically plausible network dynamics that are completely constrained by the synaptic plasticity rule, and the statistics of the stored patterns and of the recall cue. Our theory organises into a coherent framework a wide range of existing data about the regulation of excitability, feedback inhibition, and network oscillations in area CA3, and makes novel and directly testable predictions that can guide future experiments.

First principles interatomic potential for tungsten based on Gaussian process regression

An accurate description of atomic interactions, such as that provided by first principles quantum mechanics, is fundamental to realistic prediction of the properties that govern plasticity, fracture or crack propagation in metals. However, the computational complexity associated with modern schemes explicitly based on quantum mechanics limits their applications to systems of a few hundreds of atoms at most. This thesis investigates the application of the Gaussian Approximation Potential (GAP) scheme to atomistic modelling of tungsten - a bcc transition metal which exhibits a brittle-to-ductile transition and whose plasticity behaviour is controlled by the properties of $\frac{1}{2} \langle 111 \rangle$ screw dislocations. We apply Gaussian process regression to interpolate the quantum-mechanical (QM) potential energy surface from a set of points in atomic configuration space. Our training data is based on QM information that is computed directly using density functional theory (DFT). To perform the fitting, we represent atomic environments using a set of rotationally, permutationally and reflection invariant parameters which act as the independent variables in our equations of non-parametric, non-linear regression. We develop a protocol for generating GAP models capable of describing lattice defects in metals by building a series of interatomic potentials for tungsten. We then demonstrate that a GAP potential based on a Smooth Overlap of Atomic Positions (SOAP) covariance function provides a description of the $\frac{1}{2} \langle 111 \rangle$ screw dislocation that is in agreement with the DFT model. We use this potential to simulate the mobility of $\frac{1}{2} \langle 111 \rangle$ screw dislocations by computing the Peierls barrier and model dislocation-vacancy interactions to QM accuracy in a system containing more than 100,000 atoms.

Characterizing the class of local metal sheet thickening processes

The need to create high-value products for specialist applications, and the search for efficient forming routes that obviate the need for some machining steps, is driving Interest In a novel class of forming processes aiming to create locally thickened features within sheet work- pieces. A number of novel forming processes have been proposed to meet this need, but it is as yet unclear which processes will be most effective in creating local thickening of various geometries, and many process configurations have yet to be tried. This paper aims to provide some basic principles for designing and characterising process behaviour. A simplified generic description of sheet thickening processes is provided, with two tools of variable operating on a sheet workpiece in plane strain, with different tool separations and motions parameterised. A comprehensive numerical study of the behaviour of this class of processes is conducted in Abaqus to predict the main characteristics of the material flow in each configuration. The results are used to classify the different basic behaviours that can be achieved by the sheet-bulk thickening processes and to give guidance on future process development, capability and applicability. © 2011 Wiley-VCH Verlag GmbH & Co. KGaA. Weinheim.

Tool-path design for metal spinning

Toolpath design in spinning is an open ended problem, with a large number of solutions, and remains an art acquired by practice. To be able to specify a toolpath without the need for experimental trials, further understanding of the process mechanics Is required. At the moment, the mechanics of the process Is not completely understood, due to the complex deformation and because long solution times required for accurate numerical modelling of the process Inhibit detailed study. This paper proposes and applies a new approach to modelling the process and aims to contribute to the understanding of process mechanics, In particular with respect to the mechanisms of failure and and to apply this understanding for toolpath design In spinning. A new approach to numerical modelling Is proposed and applied to Investigate the process. The findings suggest that there are two different causes and two different modes of wrinkling In spinning, depending on the stage In the process and direction of roller movement. A simple test Is performed to estimate the limits of wrinkling and provide a guideline for toolpath design In a typical spinning process. The results show that the required toolpath geometry in the early stages of the process is different from that In later stages. © 2011 Wiley-VCH Verlag GmbH & Co. KGaA. Weinheim.

The forming of variable cross-section I-beams by hot rolling

A process is presented for the forming of variable cross-section I-beams by hot rolling. Optimized I-beams with variable cross-section offer a significant weight advantage over prismatic beams. By tailoring the cross-section to the bending moment experienced within the beam, around 30% of the material can be saved compared to a standard section. Production of such beams by hot rolling would be advantageous, as It combines high volume capacity with high material yields. Through controlled variation of the roll gap during multiple passes, beams with a variable cross-section have been created using shaped rolls similar to those used for conventional I-beam rolling. The process was tested experimentally on a small scale rolling mill, using plasticine as the modelling material. These results were then compared to finite element simulations of individual stages of the process conducted using Abaqus/Standard. Results here show that the process can successfully form a beam with a variable depth web. The main failure modes of the process, and the limitations on the achievable variations In geometry are also presented. Finally, the question of whether or not optimal beam geometries can be created by this process Is discussed. © 2011 Wiley-VCH Verlag GmbH & Co. KGaA. Weinheim.

Steel and aluminium in a low carbon future

Production of steel and aluminium creates 10% of global carbon emissions from energy and processes. Demand is likely to double by 2050, but climate scientists are recommending absolute reductions of at least 50% and these are Increasingly entering law. How can reductions of this order happen? Only 10-20% savings can be expected in liquid metal production, so the primary industry is pursuing carbon sequestration as the main solution. However, this Is as yet unproven at scale, and as well as carrying some risk, the capital and operating costs are likely to be high, but are as yet unknown. In parallel with these strategies we can also examine whether we can reduce demand for liquid metal. 'Material efficiency' may allow delivery of existing services with less requirement for metal, for instance through designing products that use less metal, reducing process scrap, diverting scrap for other use, re-using components or delaying end of life. Overall demand reduction could occur if goods were used more intensely, alternative means were used to deliver the same services, or total demand were constrained. The paper analyses all possible options, to define and evaluate scenarios that meet the 2050 target, and discuss the steps required to bring them about. The paper concludes with suggestions for key areas where future research In metal forming can support a future low carbon economy. © 2011 Wiley-VCH Verlag GmbH & Co. KGaA. Weinheim.