Non-Associative Property of 123-Avoiding Class of Aunu Permutation Patterns

This paper presents the non-associative and non-commutative properties of the 123-avoiding patterns of Aunu permutation patterns. The generating function of the said patterns has been reported earlier by the author [1] [2]. The paper describes how these non-associative and non commutative properties can be established by using the Cayley table on which a binary operation is defined to act on the 123-avoiding and 132-avoiding patterns of Aunu permutations using a pairing scheme. Our results have generated larger matrices from permutations of points of the Aunu patterns of prime cardinality. It follows that the generated symbols can be used in further studies and analysis in cryptography and game theory thereby providing an interdisciplinary approach and applications of these important permutation patterns.

Two Dimensional Representation of the Dirac Equation in Non-Associative Algebra

In this note a simple extension of the complex algebra to higher dimension is proposed. Using the proposed algebra a two dimensional Dirac equation is formulated and its solution is calculated. It is found that there is a sub-algebra where the associative nature can be recovered.

Non-associative learning behavior in mixed proton and electron conductor hybrid pseudo-diode

With inherent ionic priorities, mixed ion and electron conductor hybrid devices have been proposed for brain-inspired neuromorphic system applications, demonstrating interesting neuromorphic functions. Here, mixed proton and electron conductor (MPEC) hybrid oxide neuromorphic transistor is proposed by adopting aqueous solution-processed mesoporous silica coating (MSC)-based electrolyte as gate dielec- tric. With optical and electrical synergetic coupling behaviors, the device demonstrates typical synap- tic responses and transition between short-term plasticity and long-term plasticity. With unique field- configurable proton self-modulation behaviors, a pseudo-diode operation mode is demonstrated on the MPEC hybrid transistor. Moreover, the device demonstrates interesting non-associative learning, including habituation and sensitization behavior. The results show that the proposed MPEC hybrid oxide neuromor- phic transistor has great potential in the field of neuromorphic engineering and would have potential in the bionic visual perception platform .

3-dimensional slope stability analyses using non-associative stress-strain relationships

The research work presented in this paper refers to a new slope stability analysis method used for landslide risk evaluations. It is an extension of the 3-dimensional upper-bound slope stability analysis method proposed by Chen et al. in 2001,which employs the Mohr-Coulomb's associative flow rule. It has been found that in a 3-dimensional area,a prism may not be able to move at friction angles to all its surrounding interfaces,as required by this associative rule,and convergence problems may occasionally arise. The new method establishes two velocity fields:(i) The plastic one that represents a non-associative and the best representative dilation behavior,and (ii) the virtual one that permits the solution for factor of safety in the work and energy balance equation. The new method can then allow any input value of dilation angle and thus solve the convergence problem. A practical application to a concrete dam foundation is illustrated.

Strain localization of Mohr-Coulomb soils with non-associated plasticity based on micropolar continuum theory

To address the problems of strain localization, the exact Mohr-Coulomb (MC) model is used based on second-order cone programming (mpcFEM-SOCP) in the framework of micropolar continuum finite element method. Using the uniaxial compression test, we focused on the earth pressure problem of rigid wall segment involving non-associated plasticity. The numerical results reveal that when mpcFEM-SOCP is applied, the problems of mesh dependency can be effectively addressed. For geotechnical strain localization analysis involving non-associated MC plasticity, mpcFEM-SOCP in conjunction with the pseudo-time discrete scheme can improve the numerical stability and avoid the unreasonable softening issue in the pressure-displacement curves, which may be encountered in the conventional FEM. It also shows that the pressure-displacement responses calculated by mpcFEM-SOCP with the pseudo-time discrete scheme are higher than those calculated by mpcFEM-SOCP with the Davis scheme. The inclination angle of shear band predicted by mpcFEM-SOCP with the pseudo-time discrete scheme agrees well with the theoretical solution of non-associated MC plasticity.

Finite element analyses of slope stability problems using non-associated plasticity

In recent years, finite element analyses have increasingly been utilized for slope stability problems. In comparison to limit equilibrium methods, numerical analyses do not require any definition of the failure mechanism a priori and enable the determination of the safety level more accurately. The paper compares the performances of strength reduction finite element analysis(SRFEA) with finite element limit analysis(FELA), whereby the focus is related to non-associated plasticity. Displacement-based finite element analyses using a strength reduction technique suffer from numerical instabilities when using non-associated plasticity, especially when dealing with high friction angles but moderate dilatancy angles. The FELA on the other hand provides rigorous upper and lower bounds of the factor of safety(FoS) but is restricted to associated flow rules. Suggestions to overcome this problem, proposed by Davis(1968), lead to conservative FoSs; therefore, an enhanced procedure has been investigated. When using the modified approach, both the SRFEA and the FELA provide very similar results. Further studies highlight the advantages of using an adaptive mesh refinement to determine FoSs. Additionally, it is shown that the initial stress field does not affect the FoS when using a Mohr-Coulomb failure criterion.

SYMMETRIC FORMULATION OF TANGENTIAL STIFFNESSES FOR NON-ASSOCIATED VISCOPLASTICITY WITH AN IMPLICIT TIME INTEGRATION SCHEME

A numerical scheme is presented which enables the use of symmetric equation solvers in tangential stiffness programs for non-associated viscoplastic materials.

Modified Burzynski criterion with non-associated flow rule for anisotropic asymmetric metals in plane stress problems

The Burzynski criterion is developed for anisotropic asymmetric metals with the non-associated flow rule （NAFR） for plane stress problems. The presented pressure depending on the yield criterion can be calibrated with ten experimental data, i.e., the tensile yield stresses at 0°, 45°, and 90°, the compressive yield stresses at 0°, 15°, 30°, 45°, 75°, and 90° from the rolling direction, and the biaxial tensile yield stress. The corresponding pressure independent plastic potential function can be calibrated with six experimental data, i.e., the tensile R-values at 0°, 15°, 45°, 75°, and 90° from the rolling direction and the tensile biaxial R-value. The downhill simplex method is used to solve these ten and six high nonlinear equations for the yield and plastic potential functions, respectively. The results show that the presented new criterion is appropriate for anisotropic asymmetric metals.

Artificial synaptic behavior of the SBT-memristor

The synapse of human brain neurons is not only the transmission channel of information,but also the basic unit of human brain learning and information storing.The artificial synapse is constructed based on the Sr_(0.97)Ba_(0.03)TiO_(3-x)(SBT)memristor,which realizes the short-term and long-term plasticity of the synapse.The experiential learning and non-associative learning behavior in accordance with human cognitive rules are realized by using the SBT-memristor-based synapse.The process of synaptic habituation and sensitization is analyzed.This study provides insightful guidance for realization of artificial synapse and the development of artificial neural network.

STUDY ON THE MATHEMATICAL MODEL FOR FABRIC WEAVE DESIGN AND ITS APPLICATIONS

In the light of the mapping between[0,1]matrixes of fab-ric weaves,we establish in this paper a mathematical modelfor fabric weave design- One type of non- associative al-gebra composed of 7 basic transformations in a 2- elementfield.In view of practice,we expand the generative set ofmapping of this matematical model to cover the generaltransformation methods in traditional weave design.Takingthe algorethm of" Kronecker product" as an example,wefurthermore illustrate applied potentialities of the generativeset of mapping in the CAD of fabic weaves.

Combined influence of nonlinearity and dilation on slope stability evaluated by upper-bound limit analysis

The combined influence of nonlinearity and dilation on slope stability was evaluated using the upper-bound limit analysis theorem.The mechanism of slope collapse was analyzed by dividing it into arbitrary discrete soil blocks with the nonlinear Mohr–Coulomb failure criterion and nonassociated flow rule.The multipoint tangent(multi-tangent) technique was used to analyze the slope stability by linearizing the nonlinear failure criterion.A general expression for the slope safety factor was derived based on the virtual work principle and the strength reduction technique,and the global slope safety factor can be obtained by the optimization method of nonlinear sequential quadratic programming.The results show better agreement with previous research result when the nonlinear failure criterion reduces to a linear failure criterion or the non-associated flow rule reduces to an associated flow rule,which demonstrates the rationality of the presented method.Slope safety factors calculated by the multi-tangent inclined-slices technique were smaller than those obtained by the traditional single-tangent inclined-slices technique.The results show that the multi-tangent inclined-slices technique is a safe and effective method of slope stability limit analysis.The combined effect of nonlinearity and dilation on slope stability was analyzed,and the parameter analysis indicates that nonlinearity and dilation have significant influence on the result of slope stability analysis.

Elastoplastic homogenization of particulate composites complying with the Mohr–Coulomb criterion and undergoing isotropic loading

This work aims at determining the overall response of a two-phase elastoplastic composite to isotropic loading. The composite under investigation consists of elastic particles embedded in an elastic perfectly plastic matrix governed by the Mohr-Coulomb yield criterion and a non-associated plastic flow rule. The composite sphere assemblage model is adopted, and closed-form estimates are derived for the effective elastoplastic properties of the composite either under tensile or compressive isotropic loading. In the case when elastic particles reduce to voids, the composite in question degenerates into a porous elastoplastic material. The results obtained in the present work are of interest, in particular, for soil mechanics.

A FRACTURE-ENERGY-BASED ELASTO-SOFTENING-PLASTIC CONSTITUTIVE MODEL FOR JOINTS OF GEOMATERIALS

On the basis of plasticity and fracture mechanics for quasi-brittle materials, this article presented a constitutive model for gradual softening behavior of joints of geomaterials. Corresponding numerical tests are carried out at the local level. Characteristics of the model proposed are 1) plastic softening and dilatancy behavior are directly related to the fracture process of joint, and much less material and model parameters are required compared with those proposed by references; 2) the process of decohesion coupled with frictional sliding at both micro-scale and macro-scale is described.

Critical state model for structured soil

Structure is an evident determinant for macroscopic behaviors of soils.However,this is not taken into account in most constitutive models,as structure is a rather complex issue in models.For this,it is important to develop and implement simple models that can reflect this important aspect of soil behavior.This paper tried to model structured soils based on well-established concepts,such as critical state and sub-loading.Critical state is the core of the classic Cam Clay model.The sub-loading concept implies adoption of an inner(sub-loading)yield surface,according to specific hardening rules for some internal strain-like state variables.Nakai and co-workers proposed such internal variables for controlling density(p)and structure(ω),using a modified stress space,called tij.Herein,similar variables are used in the context of the better-known invariants(p and q)of the Cam Clay model.This change requires explicit adoption of a non-associated flow rule for the sub-loading surface.This is accomplished by modifying the dilatancy ratio of the Cam Clay model,as a function of the new internal variables.These modifications are described and implemented under three-dimensional(3D)conditions.The model is then applied to simulating laboratory tests under different stress paths and the results are compared to experiments reported for different types of structured soils.The good agreements show the capacity and potential of the proposed model.

Characterization of the asymmetric evolving yield and flow of 6016-T4 aluminum alloy and DP490 steel

6016-T4 aluminum alloy and DP490 steel were systematically tested under 24 proportional loading paths,including uniaxial tensile tests with a 15°increment,uniaxial compressive and simple shear tests with a 45°increment,and biaxial tensile tests using cruciform specimens.Cruciform specimens in the rolling/transverse and 45°/135°sampling directions were tested with seven and four different stress ra-tios,respectively.The normal and diagonal planes plastic work contours and the yield stresses under uniaxial tension and compression were measured to investigate the anisotropic yield.Meanwhile,the normal and diagonal planes directions of plastic strain rate and the rα-values under uniaxial tension and compression were characterized to confirm the plastic flow.Several existing asymmetric yield crite-ria under the associated and non-associated flow rules were comprehensively evaluated to describe the asymmetric plastic anisotropy of 6016-T4 aluminum alloy and DP490 steel.The results suggest that in the investigated yield criteria,the non-associated models can predict the tension and compression asym-metry of materials more accurately than the associated models,and the function of stress triaxiality can more effectively describe the asymmetric yield behavior than the first stress invariant.In addition,the pure shear stress states are helpful in assessing the validity and applicability of advanced asymmetric yield stress functions,and the inspection of diagonal plane plastic work contours containing more pure shear stress states should prioritized over that of normal plane plastic work contours.The evaluation of plastic potential functions should not only consider the prediction accuracy of the normal plane di-rections of plastic strain rate,but also further check the diagonal plane directions of plastic strain rate.Expressing mechanical properties as a function of equivalent plastic strain to calibrate parameters of the yield criterion allows the continuous capture of anisotropic evolution of the asymmetric yield surface and the changes in the asymmetric plastic potential surface.

Non‑associated and Non‑quadratic Characteristics in Plastic Anisotropy of Automotive Lightweight Sheet Metals

Lightweight sheet metals are highly desirable for automotive applications due to their exceptional strength-to-density ratio.An accurate description of the pronounced plastic anisotropy exhibited by these materials in finite element analysis requires advanced plasticity models.In recent years,significant efforts have been devoted to developing plasticity models and numeri-cal analysis methods based on the non-associated flow rule(non-AFR).In this work,a newly proposed coupled quadratic and non-quadratic model under non-AFR is utilized to comprehensively investigate the non-associated and non-quadratic characteristics during the yielding of three lightweight sheet metals,i.e.,dual-phase steel DP980,TRIP-assisted steel QP980,and aluminum alloy AA5754-O.These materials are subjected to various proportional loading paths,including uniaxial tensile tests with a 15°increment,uniaxial compressive tests with a 45°increment,in-plane torsion tests,and biaxial tensile tests using laser-deposited arm-strengthened cruciform specimens.Results show that the non-AFR approach provides an effective means for accurately modeling the yield behavior,including yield stresses and the direction of plastic strain rates,simultaneously,utilizing two separate functions and a simple calibration procedure.The introduction of the non-quadratic plastic potential reduces the average errors in angle when predicting plastic strain directions by the quadratic plastic potential function.Specifically,for DP980,the average error is reduced from 3.1°to 0.9°,for QP980 it is reduced from 6.1°to 3.9°,and for AA5754-O it is reduced from 7.0°to 0.2°.This highlights the importance of considering the non-quadratic characteristic in plasticity modeling,especially for aluminum alloys such as AA5754-O.