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We study the computational capabilities of a biologically inspired neural model where the synaptic weights, the connectivity pattern, and the number of neurons can evolve over time rather than stay static. Our study focuses on the mere concept of plasticity of the model so that the nature of the updates is assumed to be not constrained. In this context, we show that the so-called plastic recurrent neural networks (RNNs) are capable of the precise super-Turing computational power — as the static analog neural networks — irrespective of whether their synaptic weights are modeled by rational or real numbers, and moreover, irrespective of whether their patterns of plasticity are restricted to bi-valued updates or expressed by any other more general form of updating. Consequently, the incorporation of only bi-valued plastic capabilities in a basic model of RNNs suffices to break the Turing barrier and achieve the super-Turing level of computation. The consideration of more general mechanisms of architectural plasticity or of real synaptic weights does not further increase the capabilities of the networks. These results support the claim that the general mechanism of plasticity is crucially involved in the computational and dynamical capabilities of biological neural networks. They further show that the super-Turing level of computation reflects in a suitable way the capabilities of brain-like models of computation.

The contact behaviors of rough surfaces, which consist of asperities with random geometric properties at small length scale, have been extensively investigated on contact behaviors in engineering and scientific research. Due to the complexity of loading condition and surface topography, the limitation of traditional statistical model leads to the inaccuracy of prediction for rough surface contact behaviors. Starting from the multi-asperity contact theory, we release the restrictions of classical GW model and propose an elastic-plastic interacting model to investigate the coalescence effect of neighboring asperities in this paper. Through numerous simulations and analyses, the results show that the plasticity can be measured by material and morphology parameters. With the increasing of plasticity and the decreasing of asperity peak distance, the contact interface transits from interaction dominated to coalescence dominated contact relationships. With the increasing of loading, the shape of contact zone changes from two independent circles with expanding radius to a joint point, and finally the contact zone becomes a single ellipse. The coalescence status of neighboring asperities is influenced by the plasticity and the initial distance between asperity peaks. Our study provides some basis for establishing a statistical or discrete rough surface model considering merging, predicting the contact behaviors between solids, and revealing the evolution of contact spot information.

In the present study, the bending collapse of an elastoplastic cylindrical tube subjected to static pure bending is investigated using the finite element method (FEM). The moment of the elastoplastic cylindrical tube is controlled by the flattening rate of the tube cross-section. For a long tube, the flattening rate can be expressed in terms of the axial and circumferential stresses that, in turn, depend on the material and geometrical properties and the curvature of the tube. On the other hand, for a short tube, the boundary condition of the fixed walls prevents the flattening rate. In order to account for the length effect of tubes, we propose a new method in which flattening is considered as a deflection problem of a fixed curved beam. The proposed method was able to predict the change in the flattening rate as the curvature was increased. A rational prediction method is proposed for estimating the maximum bending moment of cylindrical tubes that accounts for the length effect. Its validity is demonstrated by comparing it predictions with numerical results obtained using the finite element method.

The strain path dependence of the compressive flow behavior of cast AZ31 magnesium alloy was investigated. Biaxial compression tests with linear strain paths were conducted using a unique biaxial compression device. It was found that the equivalent stress-strain relations varied according to the strain paths. The work contour for linear strain paths was well described by the Logan-Hosford yield criterion. Biaxial compressions with abrupt strain path change were also carried out to investigate the influences of the prestrain amplitude and angular relation of the sequential strain paths on the flow behavior. Rapid increase in the equivalent stress was observed just after the abrupt strain path change. These specific flow behaviors were discussed with regard to the plastic anisotropy, which showed rapid evolution in the early stage of the biaxial compressions.

Microscopic hardness on free surface of polycrystalline metal during plastic deformation is closely related to the inhomogeneous deformation in respective grains. Uniaxial tensile tests were carried out on annealed pure aluminum sheet specimens with different averaged grain size and also on annealed pure titanium sheet specimen. The microscopic hardness was measured with the Vickers type micro-hardness testing machine. The increase in micro-hardness is larger at the grain boundary area than the central area of grains. The increase in the hardness is dependent on the averaged grain size of polycrystalline metals. The experimental results are discussed in relation to Hall-Petch relation concerning the grain size dependence of the yield stress or the flow stress.

It is well-known that the plasticity of magnesium and magnesium alloy is too low to be processed at low temperature. After normal hot extrusion, the plasticity of magnesium alloy can be improved, but not noticeably. In this paper, cold extrusion of commercial AZ31 magnesium alloy with severe plastic deformation was performed at room temperature with various extrusion ratios from 2:1 to 12.5:1 in order to refine the grain size of AZ31 magnesium alloy. Finally the grain size between 2~3 µm was obtained. And the influence of different grain size on the plasticity was further investigated. And the elongation of the initial billet with the grain size of 300 µm whose elongation is about 10.4%. After extrusion at room temperature with different extrusion ratios, the average grain size can be refined to below 10 µm, and the plasticity increased to 24%~30%. In order to study the effect of plasticity of AZ31 magnesium alloy under different processing techniques, we study the correspondence between plasticity and crystalline size at the same time. All results proved that, the increase in elongation could be mainly attributed to refining of the grain size of the magnesium crystalline. It also showed that, when the average grain size of AZ31 magnesium alloy was below 5 µm, the plasticity increased noticeably by cold extrusion.

Ti-based bulk metallic glasses (BMGs), Ti₄₀Zr₂₅Cu₉Ni₈Be₁₈, were prepared by phase transition cooling (PTC) and copper mould casting(CMC) technology. Ti₄₀Zr₂₅Cu₉Ni₈Be₁₈ glassy rod of more than 13 mm in diameter was prepared by PTC technology which shows the high cooling rate obtained by this technology. No obviously differences in thermal property were found between the BMGs prepared by the PTC and CMC technology. The compressive plasticity of the alloy was apparently changed, from 8% using CMC to 37% by using PTC technology. PTC technology is probably a promising method for preparing BMG and an effective way to increase the plasticity of BMGs.

In this study we have modeled the Berkovich indentation response of elastic-plastic thin films on elastic-plastic substrates, the modulus of film and substrate being equivalent, using FEM. The stimulus for this investigation was experimental indentation data of rapidly quenched nickel thin films on stainless steel substrates, for which depth-dependent, significantly low (>50% decrease) moduli were extracted via the Oliver-Pharr method. This was notable because both film and substrate had the same elastic modulus. Previous studies showed that differences in plastic behavior could elicit such a modulus drop, for extremely hard films on substrates. In this study, we performed further FEM models to explore the modulus decrease, using aspects of continuum plastic behavior that could be hypothesized from microstructural observations. Specifically, we used plastic anisotropy and significant delayed hardening that would be expected from the nano-scale, highly columnar grain structure as input, and results showed a significant modulus decrease for reasonable values of hardness.

The hardness properties of materials are tracked from early history until the present time. Emphasis is placed on the hardness test being a useful probe for determining the local elastic, plastic and cracking properties of single crystal, polycrystalline, polyphase or amorphous materials. Beginning from connection made between individual hardness pressure measurements and the conventional stress–strain properties of polycrystalline materials, the newer consideration is described of directly specifying a hardness-type stress–strain relationship based on a continuous loading curve, particularly, as obtained with a spherical indenter. Such effort has received impetus from order-of-magnitude improvements in load and displacement measuring capabilities that are demonstrated for nanoindentation testing. Details of metrology assessments involved in various types of hardness tests are reviewed. A compilation of measurements is presented for the separate aspects of Hertzian elastic, dislocation-mechanics-based plasticity and indentation-fracture-mechanics-based cracking behaviors of materials, including elastic and plastic deformation rate effects. A number of test applications are reviewed, most notably involving the hardness of thin film materials and coatings.

An overview of recent work on the interaction of elastic waves with dislocations is given. The perspective is provided by the wish to develop nonintrusive tools to probe plastic behavior in materials. For simplicity, ideas and methods are first worked out in two dimensions, and the results in three dimensions are then described. These results explain a number of recent, hitherto unexplained, experimental findings. The latter include the frequency dependence of ultrasound attenuation in copper, the visualization of the scattering of surface elastic waves by isolated dislocations in LiNbO₃, and the ratio of longitudinal to transverse wave attenuation in a number of materials.

Specific results reviewed include the scattering amplitude for the scattering of an elastic wave by a screw, as well as an edge, dislocation in two dimensions, the scattering amplitudes for an elastic wave by a pinned dislocation segment in an infinite elastic medium, and the wave scattering by a sub-surface dislocation in a semi-infinite medium. Also, using a multiple scattering formalism, expressions are given for the attenuation coefficient and the effective speed for coherent wave propagation in the cases of anti-plane waves propagating in a medium filled with many, randomly placed screw dislocations; in-plane waves in a medium similarly filled with randomly placed edge dislocations with randomly oriented Burgers vectors; elastic waves in a three-dimensional medium filled with randomly placed and oriented dislocation line segments, also with randomly oriented Burgers vectors; and elastic waves in a model three-dimensional polycrystal, with only low angle grain boundaries modeled as arrays of dislocation line segments.

Quasi-static problems of the flow theory of elastoplasticity are formulated in strain space by means of a variational inequality. Continuous dependence of the resulting stress tensor on some input data (coefficients, initial condition and loading) is proved. Employing a worst scenario method for uncertain data, we prove the existence of "worst" admissible input data with regard to three given criteria.

We present a finite element implementation of a Cosserat elasto-plastic model and provide a rigorous numerical analysis of the introduced time-incremental algorithm. The model allows the use of standard tools from convex analysis as known from classical Prandtl–Reuss plasticity. We derive the dual stress formulation and prove that for vanishing Cosserat couple modulus μ_c → 0 the classical problem is approximated. Our numerical results show the robustness of the approximation. Notably, for positive couple modulus μ_c > 0 there is no need for a safe-load assumption. For small μ_c the response is numerically indistinguishable from the classical response.

We study microstructure formation in two nonconvex singularly-perturbed variational problems from materials science, one modeling austenite–martensite interfaces in shape-memory alloys, the other one slip structures in the plastic deformation of crystals. For both functionals we determine the scaling of the optimal energy in terms of the parameters of the problem, leading to a characterization of the mesoscopic phase diagram. Our results identify the presence of a new phase, which is intermediate between the classical laminar microstructures and branching patterns. The new phase, characterized by partial branching, appears for both problems in the limit of small volume fraction, that is, if one of the variants (or of the slip systems) dominates the picture and the volume fraction of the other one is small.

Gradient plasticity at large strains with kinematic hardening is analyzed as quasistatic rate-independent evolution. The energy functional with a frame-indifferent polyconvex energy density and the dissipation is approximated numerically by finite elements and implicit time discretization, such that a computationally implementable scheme is obtained. The nonself-penetration as well as a possible frictionless unilateral contact is considered and approximated numerically by a suitable penalization method which keeps polyconvexity and simultaneously bypasses the Lavrentiev phenomenon. The main result concerns the convergence of the numerical scheme toward energetic solutions. In the case of incompressible plasticity and of nonsimple materials, where the energy depends on the second derivative of the deformation, we derive an explicit stability criterion for convergence relating the spatial discretization and the penalizations.

This paper is concerned with an abstract inf-sup problem generated by a bilinear Lagrangian and convex constraints. We study the conditions that guarantee no gap between the inf-sup and related sup-inf problems. The key assumption introduced in the paper generalizes the well-known Babuška–Brezzi condition. It is based on an inf-sup condition defined for convex cones in function spaces. We also apply a regularization method convenient for solving the inf-sup problem and derive a computable majorant of the critical (inf-sup) value, which can be used in a posteriori error analysis of numerical results. Results obtained for the abstract problem are applied to continuum mechanics. In particular, examples of limit load problems and similar ones arising in classical plasticity, gradient plasticity and delamination are introduced.

This paper presents a simplified approximate analysis of the overall collapse of the towers of World Trade Center in New York on September 11, 2001. The analysis shows that if prolonged heating caused the majority of columns of a single floor to lose their load carrying capacity, the whole tower was doomed. Despite optimistic simplifying assumptions, the structural resistance is found to be an order of magnitude less than necessary for survival.

This paper deals with the dynamics of a single-degree-of-freedom elastoplastic oscillator. The model adopted herein is useful for understanding the dynamic behavior of civil engineering structures, such as steel structures, especially when plastic inelasticity is of concern. Using appropriate internal variables, the dynamic hysteretic system can be written as a singular autonomous system. The free vibration of such a nonlinear system reduces to periodic motion. The harmonic forced oscillator can exhibit periodic or quasi-periodic behaviors. A bifurcation diagram is numerically computed, which indicates that periodic elastoplastic limit cycles exist for some ranges of structural parameters. The bifurcation boundary separates the shakedown from other alternating plasticity phenomena.

A plasticity-based approach has been proposed for reinforced concrete (RC) subjected to impact and blast loading. The proposed approach includes a new failure surface together with modified descriptions related to equation of state, strain rate effect and damage taken from literature. These selective descriptions in numerical analysis have been found to give better results than the existing models. A user-defined UMAT subroutine for the commercial software LS-DYNA has been developed for the proposed model. Dynamic analysis for both blast and impact type of loading on RC slabs are performed. The results are compared with an in-built material model in commercial software LS-DYNA, namely the Winfrith concrete model (WCM) and with experimental results taken from literature. A parametric study is carried out by analyzing the mechanical and damage response by varying parameters such as concrete strength, slab thickness and reinforcement ratio. The proposed approach is found to be effective in predicting the behavior under both impact and blast analysis.

Long-lasting, activity-dependent changes in synaptic efficacy at excitatory synapses are critical for experience-dependent synaptic plasticity. Synaptic plasticity at excitatory synapses is determined both presynaptically by changes in the probability of neurotransmitter release, and postsynaptically by changes in the availability of functional postsynaptic glutamate receptors. Two kinds of synaptic plasticity have been described. In homosynaptic or Hebbian plasticity, the events responsible for synaptic strengthening occur at the same synapse as is being strengthened. Homosynaptic plasticity is activity-dependent and associative, because it associates the firing of a postsynaptic neuron with that of the presynaptic neuron. Heterosynaptic plasticity, on the other hand, is activity-independent and the synaptic strength is modified as a result of the firing of a third, modulatory neuron. It has been suggested that long-term changes in synaptic strength, which are associated with gene transcription, can only be induced with the involvement of heterosynaptic plasticity. The neuromodulator adenosine plays an elaborated pre- and postsynaptic control of glutamatergic neurotransmission. This paper reviews the evidence suggesting that in some striatal excitatory synapses, adenosine can provide the heterosynaptic-like modulation essential for stabilizing homosynaptic plasticity without the need of a "third, modulatory neuron".

The hippocampal formation is critically involved for the long-term storage of various forms of information, and it is widely believed that the phenomenon of long-term potentiation (LTP) of synaptic transmission is a molecular/cellular mechanism participating in memory formation. Although several high level models of hippocampal function have been developed, they do not incorporate detailed molecular information of the type necessary to understand the contribution of individual molecular events to the mechanisms underlying LTP and learning and memory. We are therefore developing new technological tools based on mathematical modeling and computer simulation of the molecular processes taking place in realistic biological networks to reach such an understanding. This article briefly summarizes the approach we are using and illustrates it by presenting data regarding the effects of changing the number of AMPA receptors on various features of glutamatergic transmission, including NMDA receptor-mediated responses and paired-pulse facilitation. We conclude by discussing the significance of these results and providing some ideas for future directions with this approach.