Non-associated Flow Research Articles

A multiaxial thermo-plasticity model for concrete in a transient fire condition

Lateral confinement and high temperature affect the load-carrying capacity of a concrete member significantly. In a fire condition, a concrete member exhibits not only mechanical deformation but also thermal deformation. Therefore, accurately modeling the fire behavior of confined structural concrete is challenging. In this paper, a new three-dimensional thermo-plasticity model for concrete is developed, taking both high temperature and confinement into account. A temperature-dependent yield surface and a non-associate flow rule are formulated. The hardening rules for concrete are proposed as a function of confinement and temperature. The load-induced strain of concrete at elevated temperatures is calculated by using a stress-triaxiality factor to consider the confinement effect. The proposed concrete model is implemented in the user-subroutine (UMAT) of Abaqus, in which Runge-Kutta-England scheme with sub-stepping is used to update stress increment. The accuracy of the proposed model is validated by experiments on concrete specimens, circular concrete-filled steel tubular (CFST) columns, double-skin CFST (DCFST) columns, and concrete-filled double steel tubular (CFDST) columns. It is shown that the developed thermo-plasticity model of concrete accurately captures the behavior of confined concrete at ambient and elevated temperatures and can be incorporated in nonlinear procedures for simulating the fire resistance of composite columns exposed to fire.

Numerical Investigation of the Slope Stability in the Waste Dumps of Romanian Lignite Open-Pit Mines Using the Shear Strength Reduction Method

Open-pit mining generates significant amounts of waste material, leading to the formation of large waste dumps that pose environmental risks such as land degradation and potential slope failures. The paper presents a stability analysis of waste dump slopes in open-pit mining, focusing on the Motru coalfield in Romania. To assess the stability of these dumps, the study employs the Shear Strength Reduction Method (SSRM) implemented in the COMSOL Multiphysics version 6 software, considering both associative and non-associative plasticity models. (1) Various slope angles were analyzed, and the Factor of Safety (FoS) was calculated, showing that the FoS decreases as the slope angle increases. (2) The study also demonstrates that the use of non-associative plasticity leads to lower FoS values compared to associative plasticity. (3) The results are visualized through 2D and 3D models, highlighting failure surfaces and displacement patterns, which offer insight into the rock mass behavior prior to failure. (4) The research also emphasizes the effectiveness of numerical modeling in geotechnical assessments of stability. (5) The results suggest that a non-associative flow rule should be adopted for slope stability analysis. (7) Quantitative results are obtained, with small variations compared to those obtained by LEM. (6) Dilatation angle, soil moduli, or domain changes cause differences of just a few percent and are not critical for the use of the SSRM in engineering.

Finite element analysis of large deformation for progressive failure of soil based on Cosserat continuum theory

The large deformation accompanied by strain softening and strain localization of the material is usually encountered in geotechnical engineering. Integrating the RITSS method and the Cosserat continuum theory, a large deformation Cosserat-RITSS finite element method is developed to tackle this issue. Based on the second development interfaces of UEL and SDVINI offered by the finite element software ABAQUS, the Cosserat-RITSS method adopting the MUEM interpolation and mapping method is realized automatically and used to simulate the problem of progressive failure and large deformation characterized by strain localization. The accuracy and effectiveness of the proposed method are verified by the comparison of the small deformation and the large deformation analysis of the penetration process of a rigid strip foundation. Further, the Cosserat-RITSS method is used to analyze the large deformation of a retaining wall resisting on the soil with non-associated plastic flow and strain-softening properties. Compared with the classical RITSS method, it is demonstrated that the proposed method has better performancy of simulating large deformation and overcoming the pathological mesh-dependent problem usually suffered in the classical FEA of large deformation accompanied by strain localization.

A generalized, computationally versatile plasticity model framework - Part II: Theory and verification focusing on shear anisotropy

Shear-dominated deformation (SHDD) is pivotal in sheet metal forming; however, comprehensive modeling of plastic anisotropy in SHDD, specifically shear anisotropy considering both yield stress and plastic flow, has been inadequately addressed in existing literature. In this work, a generalized constitutive framework is introduced on the basis of stress triaxiality-dependent state variable to accurately emulate plastic anisotropy and the physics-based shear constraint in SHDD. The framework is capable to seamlessly integrate with existing yield criteria, preserving computational efficiency and versatility. Notably, the yield function, anisotropic parameters, and their optimization or analytical determination for the non-shear deformation state remain unaltered. When integrated with the Hill48 yield function, featuring either one or two anisotropic parameters within the generalized constitutive framework, precise characterization of yield strength and plastic flow in SHDD is achieved. The applicability of the framework extends to various anisotropic yield functions such as the widely employed Yld2k-2d and the sixth-order polynomial (Poly6) function as a class of associated flow rule-based yield functions, and one non-quadratic yield function for non-associated flow rule scenarios. Experimental validation with two engineering sheet metals, high-strength dual-phase steel DP980 and high-strength aluminum alloy AA7075-T6, was conducted. Comparative analyses with several recently proposed yield criteria, especially Poly6-18p, highlighted the efficiency of the proposed constitutive framework. Furthermore, this study explores intrinsic shear constraints, particularly the absence of through-thickness strains under in-plane shear stress. Additionally, it offers an enhanced description of plastic anisotropy in shear yield stress within the general framework, providing valuable insights into the complexities of SHDD.

Asymptotic safe nonassociative quantum gravity with star R-flux products, Goroff–Sagnotti counter-terms, and geometric flows

Nonassociative modifications of general relativity, GR, defined by star products with R-flux deformations in string gravity consist an important subclass of modified gravity theories, MGTs. A longstanding criticism for elaborating quantum gravity, QG, argue that the asymptotic safety does not survive once certain perturbative terms (in general, nonassociative and noncommutative) are included in the projection space. The goal of this work is to prove that a generalized asymptotic safety scenario allows us to formulate physically viable nonassociative QG theories using effective models defined by generic off-diagonal solutions and nonlinear symmetries in nonassociative geometric flow and gravity theories. We elaborate on a new nonholonomic functional renormalization techniques with parametric renormalization group, RG, flow equations for effective actions supplemented by certain canonical two-loop counter-terms. The geometric constructions and quantum deformations are performed for nonassociative phase spaces modelled as R-flux deformed cotangent Lorentz bundles. Our results prove that theories involving nonassociative modifications of GR can be well defined both as classical nonassociative MGTs and QG models. Such theories are characterized by generalized G. Perelman thermodynamic variables which are computed for certain examples of nonassociative geometric and RG flows.

Anisotropic formability and deformation mechanism of near-α titanium alloy sheet under continuous nonlinear strain paths at high temperature

In the present study, the anisotropic formability and underlying deformation mechanism of near-α TA32 titanium alloy sheet under continuous nonlinear strain paths (CNSPs) at high temperature were investigated in depth. To achieve this goal, a new experimental method combining hot gas bulging with step-combined dies was proposed, and the hot CNSPs of metal sheets can be flexibly and conveniently realized by changing the number and shape of step-combined dies. Based on this method, the anisotropic deformation behavior and forming limits of TA32 sheet under fifteen CNSPs were tested at 800 ℃ with a strain rate of 0.001 s−1. Then, two advanced constitutive models with different scales were embedded into the classical Marciniak-Kuczyński (M-K) theory to predict the forming limits of TA32 sheet under different strain paths: the macro-scale viscoplastic model coupled with Hill48 yield criterion and non-associated flow rule (NAFR) as well as the meso-scale three-dimensional crystal plasticity finite element (CPFE) model coupled with cellular automata (CA). The results demonstrate that the CPFE-CA-MK coupled model exhibits higher accuracy in predicting the forming limits of TA32 sheet under linear and continuous nonlinear strain paths. Especially for the tension-tension strain paths, the CPFE-CA-MK coupled model improves accuracy by at least 3.1 % compared to macro-scale models. Due to the material anisotropy, the initial inclination angle of the groove in the CPFE-CA-MK model is closely related to the strain path and significantly affects the prediction accuracy. Based on the CPFE simulation, the effects of anisotropy and strain path change on the dislocation slip mode of different texture components was analyzed in depth, which provides a theoretical guidance for the optimization of hot forming process of TA32 titanium alloy complex components.

A study on anisotropic hardening of 7075 aluminum alloy based on non-associated flow rules

The accurate description of anisotropic plastic deformation is key to accurately predicting the stamping forming of metal sheets. The anisotropic yield criterion, when based on the assumption of isotropic hardening, often leads to significant inaccuracies. To address this issue, this paper observes the anisotropic hardening phenomenon through non-associated flow rules and evaluates the anisotropy of 7075-O aluminum alloy. Through a series of tensile tests, we determined the mechanical properties of 7075-O aluminum alloy in three distinct orientations. To describe the metal hardening behavior, we employed the Swift-Voce hardening criterion. From the hardening curves in three different directions, it was found that AA7075-O exhibits plastic anisotropy. Based on the VUMAT subroutine, finite element simulation of AA7075-O tensile tests was conducted through Abaqus. Compared with the Hill48 model, it was found that the simulated values of the S–Y2009 anisotropic hardening model have a higher degree of agreement with the experimental curves. The S–Y2009 anisotropic hardening model was adopted to predict the earing behavior of AA7075-O during circular cup deep drawing. The root mean square error between the predicted values of the S–Y2009 model and the experimental values was only 0.1795, which is far smaller than that of the Hill48 yield model. Therefore, the SY2009 model has important guiding significance for the stamping forming of metal sheets.

Neural network based rYld2004 anisotropic hardening model under non-associated flow rule for BCC and FCC metals

This paper extends the reduced Yld2004 (rYld2004) function to present the anisotropic hardening behavior for body-centered cubic and face-centered cubic metals under the proportional loading conditions based on neural network. The parameters of the rYld2004 anisotropic hardening model (AH_rYld2004) are determined by the uniaxial tensile yield stresses along 0°, 15°, 30°, 45°, 60°, 75° and 90° from the rolling direction as well as equibiaxial tension. The evolution of anisotropic parameters are described by the back propagation neural network optimized by ant colony optimization algorithm. The predicted data by AH_rYld2004 and some common anisotropic models are compared with the experimental results to verify the precision of the AH_rYld2004 in characterizing anisotropic hardening. The comparison proves that the AH_rYld2004 precisely characterize the anisotropic evolution with increasing plastic deformation for AA 3003-O and QP980. Simultaneously, the AH_rYld2004 function based on neural network is used to accurately simulate of circular cup deep drawing for AA 3003-O and uniaxial tension for QP980. The results indicate that the AH_rYld2004 model is capable to accurately represent the plastic anisotropic evolution for uniaxial tension along seven loading directions and equibiaxial tension.

Earing Prediction of AA5754-H111 (Al-Alloy) with Linear Transformation-Based Anisotropic Drucker Yield Function under Non-Associated Flow Rule (Non-AFR).

The yield behavior of aluminum alloy 5754-H111 under different stress conditions for three kinds of plastic work is studied using an anisotropic Drucker model. It is found that when the plastic work is 30 MPa, the anisotropic Drucker model has the most accurate prediction. Comparing the Hill48 and Yld91 models with the Drucker model, the results show that both the anisotropic Drucker and Yld91 models can accurately predict the yield behavior of the alloy. Cylinder drawing finite element analysis is performed under the AFR, but it is not possible to accurately predict the position and height of earing appearance. The anisotropic Drucker model is used to predict the earing behavior under the non-AFR, which can accurately predict the earing phenomenon. Numerical simulation is conducted using three different combinations of yield functions: the anisotropic yield function and the anisotropic plastic potential function (AYAPP), the anisotropic yield function and the isotropic plastic potential function (AYIPP), and the isotropic yield function and the anisotropic plastic potential function (IYAPP). It is concluded that the influence of the plastic potential function on predicting earing behavior is more critical than that of the yield function.

Static liquefaction as a form of material instability in element test simulations of granular soil

Static liquefaction is a form of unstable behaviour of granular soil. It is most common in saturated loose sands under monotonically loaded undrained conditions. Predicting static liquefaction using an elastic-plastic model that incorporates the non-associated plastic flow rule and strain hardening is possible. The article briefly describes the unstable behaviour of saturated sand in undrained conditions under a monotonic load. A simple elastic-plastic model with deviatoric hardening and a Drucker–Prager load surface is presented. The constitutive relationships were programmed in a Python script. Simulations of triaxial tests under mixed stress-strain control demonstrated the model’s ability to predict various undrained sand responses, including fully stable responses (no liquefaction) and partial and complete liquefaction under triaxial compression and tension. Predicting static liquefaction is possible by properly selecting the proportions of the parameters involved in plastic potential and loading functions and the parameter A used in the deviatoric hardening rule of hyperbolic type.

User friendly FE Formulation for anisotropic distortional hardening model based on non-associated flow plasticity and its application to springback prediction

Based on non-associated flow plasticity, a newly developed anisotropic distortional hardening model developed by Hu and Yoon [15] is implemented in finite element analysis in a user-friendly manner. The derivatives of complex hardening models are calculated using the Finite Difference Method (FDM), which is much more convenient than using the analytical derivatives. To further improve the accuracy of the proposed method, the step size analysis in FDM is performed by analyzing the derivative formation. To evaluate the accuracy and computational efficiency of a proposed step size for FDM, single element simulations are performed under different loading paths. It has been found that the maximum absolute error of the flow curves between the simulation and the theoretical result is less than 0.3%. The U-bending tests for DP600 and TRIP1180 are used to verify the ability of the distortional hardening model for springback prediction. The simulation result of the strain hardening model is in good agreement with the experiment. The computational efficiency is also increased by 24% due to the improved convergence rate.

Expansion of a Spherical Cavity in an Infinite Dilatant Medium Obeying the Drucker–Prager Yield Criterion and a Non-Associated Plastic Flow Rule

Expansion of a Spherical Cavity in an Infinite Dilatant Medium Obeying the Drucker–Prager Yield Criterion and a Non-Associated Plastic Flow Rule

Predicting plastic behavior of magnesium alloy tube bending with comprehensive constitutive models

This paper aims to predict defects occurring in magnesium alloy tube bending through finite element simulations. Deformation tests were conducted to identify and characterize plastic anisotropy, tension-compression asymmetry, and anisotropic hardening behaviors of extruded Mg–Al–Zn-RE alloy rectangular tubes. Limited by size, the deformation tests along the wall thickness of specimens were conducted through crystal plasticity analysis. To thoroughly investigate the material constitutive features affecting bending, two constitutive models, Yoon2014 and Hill48, were established and calibrated. The non-associative flow rule was adopted, and anisotropic hardening was depicted using the yield-surface interpolation method. In comparison, the Yoon2014 model accurately predicted the strain distribution and tube shape collapse of the bent tube with negligible deviation from the experimental data, prior to the Hill48 model. This underscores the necessity of considering comprehensive plasticity models in tube bending simulations.

A thermoplastic clay constitutive model with temperature dependent evolution of stress anisotropy

This paper presents a thermomechanical constitutive model that captures temperature dependent evolutions of preconsolidation stress and stress anisotropy in normally consolidated and lightly overconsolidated saturated clays. Following a non-associative flow rule, the model was formulated to account for the rate of evolution of stress anisotropy as a function of temperature. A temperature-dependent rotational hardening parameter was introduced and calibrated employing a simple optimization algorithm for four different clays. The developed model was further implemented in a finite element (FE) analysis software for use in boundary value problems. Success of such numerical implementation and predictive performance of the constitutive model was further verified through FE simulations of drained and undrained triaxial tests on saturated clays at reference and elevated temperature. FEA results obtained from these simulations agreed very well with test data reported in the literature.

Elastic–plastic criterion solution of deep roadway surrounding rock based on intermediate principal stress and Drucker–Prager criterion

AbstractExcavation‐induced rock failure and deformation near an underground opening boundary is closely associated with the intermediate principal stress, strain softening and rock mass dilation. By combining theoretical analysis and numerical simulation to explore the mechanical evolution of the roadway surrounding rock during excavation. The elastic–plastic criterion solutions for surrounding rock stress, displacement, and the plastic zone of a circular roadway were deduced by including the intermediate principal stress, strain softening and rock mass dilation, based on the Drucker–Prager criterion and the nonassociated flow rule. Furthermore, ABAQUS finite element software was utilized for numerical simulations to scrutinize the influence of mechanical parameters on stress redistribution, surface displacement, and plastic range. The results of the numerical simulations verify the reliability of the theoretical analysis and affirm the high consistency of the results with the theoretical solution. The research findings indicate that the strength of surrounding rock is significantly influenced by the intermediate principal stress, and the deformation and failure of rock mass are primarily impacted by rock mass dilation, while strain softening mainly affects the thickness of the fractured zone. Moreover, the study reveals that enhancing the residual strength of the surrounding rock can improve its resistance to deformation and failure. Furthermore, the excavation of the roadway is observed to increase the original rock stress in the surrounding rock, but increasing the ground support strength effectively controls the deformation and failure of surrounding rock. Ultimately, the research outcomes offer valuable references for engineering calculations and ground support design of surrounding rock in deep roadways.

On the development of a constitutive model for steel subjected to fire and explosion

The behavior of steel under thermal and mechanical loading including high transient temperatures and strain rates (e.g., fire, creep or explosion) is extremely complex. To study this behavior, we propose a constitutive model accordance with the laws of thermodynamic, the principle of virtual power and experimental results. The thermodynamic framework considers the Clausius-Duhem inequality and maximum dissipation rate principle, as well as the theory of finite deformations, linear isotropic viscoelasticity, nonlinear isotropic and kinematic hardening, local and non-local viscoplasticity, local and non-local anisotropic viscodamage and parameters associated to material behavior dependent on loadings. The components of the thermodynamic conjugate forces are defined from the Helmholtz free energy function and the rate of energy dissipation, which are postulated considering the creep phenomenon, thermal-mechanical transient phenomenon, cyclic phenomenon and plastic wave propagation phenomenon. The balance of microforces is defined based on the principle of virtual power. A novel rule of non-associated thermo-viscoplastic flow of the Perzyna type and a novel rate dependent local and non-local damage evolution law are introduced from constitutive model. The verification of the model was carried out in two benchmark studies composed of fire tests. The predictions of the model have shown in according with the results of the experiments. A sensitivity study was also performed with a view to analysis the influence of the parameters in achieved results. From this study a simplified constitutive model is presented. Benchmark studies composed of explosion tests are part of future work.

Rock slope stability analysis under Hoek–Brown failure criterion with different flow rules

The stability analysis of homogeneous rock slope following the Hoek–Brown failure criterion under the hypothesis of different flow rules is performed based on limit equilibrium and finite element methods. The applied failure criterion is the generalized Hoek–Brown that can be introduced as a shear/normal function in analysis applying different flow rules. The results are compared with those obtained by the application of equivalent shear strength parameters of the Mohr–Coulomb criterion, considering that this is still the most widely used criterion in rock slope stability analysis and is still the base for the shear strength reduction method applied in finite element modelling. Different proposals for estimating the equivalent strength parameters based on confining stress level are evaluated. The limitation of stress-dependent linear Mohr–Coulomb parameters is emphasized by analysing the vertical cut problem, for which, depending on the chosen stress level, different critical heights are obtained for the same material. Sensitivity analysis of geotechnical parameters used as input for failure criterion is performed to determine their influence on slope stability. Probabilistic analysis is conducted to determine the probability of failure when different flow rules are applied. If slope stability analysis is performed with an assumption of associative flow rule, the probability of failure is within the acceptable limits for the considered case study, while employing non-associative flow rule, the probability of failure is rather high. The chart is presented that could be readily used to estimate the combination of σci, GSI, and mi values that produce failure for the analysed case study.

A finite deformation formulation for amorphous glassy polymers under moderate and impact strain rates: Application to adhesive films

This work describes a novel finite strain hypo-elastic formulation for amorphous thermoset polymers working in the glassy regime. The constitutive formulation is able to describe time and pressure-dependent behaviour under loading rates ranging from quasi-static to impact-type loading conditions and to account for thermo-mechanical coupling effects. A non-linear pressure dependent potential function is introduced to capture the non-associative visco-plastic potential flow for volumetric plastic strain control. The formulation also incorporates an internal state or deformation resistance variable to enable the description of the polymer hardening — softening behaviour, as well as a novel relation for the dissipative fraction of the plastic work in terms of the equivalent accumulated plastic strain. The constitutive model is formulated within a finite strain kinematics framework, and full details of its numerical implementation into the finite element method using a fully implicit Euler Backward algorithm are given. Model calibration is carried out for three different thermosetting resins (PR520 and RTM6 Epoxies, and MMA adhesives).To illustrate the model capabilities, two case studies are investigated: (i) the de-formation behaviour of epoxy under moderate and impact-type loading conditions under isothermal and fully adiabatic conditions, and (ii) the fracture behaviour of adhesive layers used to bond stiff metallic substrates. Results on RTM6 epoxy show that at, e.g., 60% true strain, 48.5% of the rate of plastic work is dissipative, and that the corresponding predicted increase in temperature due to the locally dissipated heat is consistent with published calorimetry data on a similar thermoset polymer. It was also found that, by coupling the proposed constitutive model with a cohesive zone model, it was possible to predict accurately the effect of an MMA adhesive layer thickness and pressure-dependency on the growth of an interfacial crack between the MMA adhesive and the metallic substrates. The proposed model should constitute a generic phenomenological formulation for the mechanical behaviour prediction of a wide range of thermoset polymers under confined and quasi-adiabatic conditions such as in composites and adhesive joints.

Assessing Mechanical Properties and Response of Expansive Soft Rock in Tunnel Excavation: A Numerical Simulation Study.

This study investigates the dynamics of moisture absorption and swelling in soft rock during tunnel excavation, emphasizing the response to support resistance. Utilizing COMSOL numerical simulations, we conduct a comparative analysis of various strength criteria and non-associated flow rules. The results demonstrate that the Mohr-Coulomb criterion combined with the Drucker-Prager model under compressive loads imposes stricter limitations on water absorption and expansion than when paired with the Drucker-Prager model under tensile loads. Restricted rock expansion leads to decreased horizontal displacement and ground uplift, increased displacement in the tunnel's bottom arch, and significantly reduced displacement in the top arch. The study also considers the effects of shear dilation, burial depth, and support resistance on the stress and displacement of the surrounding rock. Increased shear dilation angles correlate with greater rock expansion, resulting in increased horizontal displacement and ground uplift. The research study concludes that support resistance is critical in limiting the movement of the tunnel's bottom arch and impacting the stability of the surrounding rock. Additionally, the extent of rock damage during the excavation of expansive soft rock tunnels is found to be minimal. Overall, this study provides valuable insights into the processes of soft rock tunnel excavation and contributes to the development of more efficient support systems.

Smoothed Particle Hydrodynamics (SPH) Analysis of Slope Soil–Retaining Wall Interaction and Retaining Wall Motion Response

The occurrence of slope instability disasters seriously endangers the safety of people’s lives and property in China. Therefore, it is essential to study the slope instability process and the interaction between soil and retaining walls. In this paper, the smoothed-particle hydrodynamics (SPH) method, based on the elastoplastic constitutive model of rock and soil, was used to simulate the entire process of slope instability and the interaction between soil and retaining walls. The model, based on the classical elastic–plastic theory, includes linear elastic deformation and plastic deformation following the non-associated flow rule under the Drucker–Prager (DP) yield criterion. By considering the plastic characteristics of geotechnical materials, this method can accurately simulate the slope movement process. The model was established, calculated, and compared with a slope example, thus verifying its feasibility. Furthermore, the motion response of the retaining wall under different conditions was studied, which provides a new numerical simulation platform for the stability checking of the retaining wall and motion analysis after the interaction between the retaining wall and slope soil.