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.

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.

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.

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.

Review of Proposed Stress-dilatancy Relationships and Plastic Potential Functions for Uncemented and Cemented Sands

Stress-dilatancy relationship or plastic potential function are crucial components of every elastoplastic constitutive model developed for sand or cemented sand.This is because the associated flow rule usually does not produce acceptable outcomes for sand or cemented sand.Many formulas have been introduced based on the experimental observations in conventional and advanced plasticity models in order to capture ratio of plastic volumetric strain increment to plastic deviatoric strain increment(i.e.dilatancy rate).Lack of an article that gathers these formulas is clear in the literature.Thus,this paper is an attempt to summarize plastic potentials and specially stress-dilatancy relations so far proposed for constitutive modelling of cohesionless and cemented sands.Stress-dilatancy relation is usually not the same under compression and extension conditions.Furthermore,it may also be different under loading and unloading conditions.Therefore,the focus in this paper mainly places on the proposed stress-dilatancy relations for compressive monotonic loading.Moreover because plastic potential function can be calculated by integration of stress-dilatancy relationship,more weight is allocated to stress-dilatancy relationship in this research.

A thermoviscoelastic finite deformation constitutive model based on dual relaxation mechanisms for amorphous shape memory polymers

This paper proposes a new thermoviscoelastic finite deformation model incorporating dual relaxation mechanisms to predict the complete thermo-mechanical response of amorphous shape memory polymers.The model is underpinned by the detailed microscopic molecular mechanism and effectively reflects the current understanding of the glass transition phenomenon.Novel evolution rules are obtained from the model to characterize the viscous flow,and a new theory named an internal stress model is introduced and combined with the dual relaxation mechanisms to capture the stress recovery.The rationality of the constitutive model is verified as the theoretical results agree well with the experimental data.Moreover,the constitutive model is further simplified to facilitate engineering applications,and it can roughly capture the characteristics of shape memory polymers.

A lightweight DDoS detection scheme under SDN context

Software-defined networking(SDN),a novel network paradigm,separates the control plane and data plane into dif-ferent network equipment to realize the flexible control of network traffic.Its excellent programmability and global view present many new opportunities.DDoS detection under the SDN context is an important and challenging research field.Some previous works attempted to collect and analyze statistics related to flows,usually recorded in switches,to address DDoS threats.In contrast,other works applied machine learning-based solutions to identify DDos and achieved promising results.Generally,most previous works need to periodically request flow rules or packets to obtain flow statistics or features to detect stealthy exceptions.Nevertheless,the request for flow rules is very time-consuming and CPU-consuming;moreover may congest the communication channel between the controller and the switches.Therefore,we present FORT,a lightweight DDoS detection scheme,which spreads the rule-based detection algorithm at edge switches and determines whether to start it by periodically retrieving the ports state.A time-series algorithm,ARIMA,is utilized to determine the port statistics adaptively,and an SVM algorithm is applied to detect whether a DDoS attack does occur.Representative experiments demonstrate that FORT can significantly reduce the controller load and provide a reliable detection accuracy.Referring to the false alarm rate of 1.24%in the comparison scheme,the false alarm rate of this scheme is only 0.039%,which significantly reduces the probability of false alarm.Besides,by introducing the alarm mechanism,this scheme can reduce the load of the southbound chan-nel by more than 60%in the normal state.

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.

FRACTIONAL ORDER MODELLING OF THE CUMULATIVE DEFORMATION OF GRANULAR SOILS UNDER CYCLIC LOADING

To model the cumulative deformation of granular soils under cyclic loading, a mathematical model was proposed. The power law connection between the shear strain and loading cycle was represented by using fractional derivative approach. The volumetric strain was characterized by a modified cyclic flow rule which considered the effect of particle breakage. All model parameters were obtained by the cyclic and static triaxial tests. Predictions of the test results were provided to validate the proposed model. Comparison with an existing cumulative model was also made to show the advantage of the proposed model.

Several basic problems in plastic theory of geomaterials

Based on the basic mechanical properties of geomaterials,it was proven that the Drucker Postulate and the classical theory of plasticity can not be applied to geomaterials.Moreover,several basic problems of plastic theory of geomaterials were discussed.Based on the strict theoretical analysis,the following have been proven:the single yield surface model based on the classical theory of plasticity is unsuitable for geomaterials whether the rule of associated flow is applied or not;the yield surface of geomaterials is not unique,and its number is the same as the freedoms of plastic strain increment;the yield surface is not convex;and the rule of associated flow is unsuitable for geomaterials.