Effective Stress Strain Research Articles

Design and analysis of extrusion die for T-shaped sheet materials

Abstract The study explores plastic deformation behavior of T-shaped plates using DEFORM™ 3D, a perfect plastic finite element analysis software that considers T-shaped and double T-shaped extrusion dies as rigid bodies and compares effective strain, effective stress, blank temperature, die wear and temperature conditions. Moreover, the study employed the machine learning step descent method to predict effective stress and effective strain. Furthermore, the Pearson product difference correlation was utilized to examine the relationship between effective stress, effective strain, and temperature in T-shaped extrusion. Lastly, META analysis was conducted to synthesize statistical data on effective stress and temperature from various research.

On the effect of deformation conditions on the metal flow behavior during upsetting process using finite element simulation DEFORM 3D software

AbstractThe study reports on the metal flow behaviour during upsetting or forging using the finite element method. Forging simulation studied the metal flow behaviour of a laboratory-sized specimen and a cylindrical engine connecting rod specimen of AISI 52100 high-chromium steel specified in the software database. The focus was to study the effect of deformation conditions (temperature and die velocity) on metal flow behaviour during forging. The simulation results showed heterogeneous metal flow behaviour during forging. Hence, this indicates that effective flow stress and flow strain, particle flow velocity, effective strain rate, damage and temperature distribution exhibited inhomogeneous deformation behaviour. As the temperature increased, the forging load decreased, thus a decrease in deformation resistance. The simulation of the engine connecting rod further confirmed inhomogeneous deformation during forging. Damage coefficient results show that the crack pin end had a higher damage probability during forging. This study clearly showed that finite element simulation can predict metal flow behaviour during the forging of AISI 52100 steel. The study output provides a basis for analysing and optimising most industrial metal forming processes using a numerical simulation approach. Hence, this method is effective in predicting flow behaviour.

Uniaxial material model with softening for simulating the cyclic behavior of steel tubes in concrete‐filled steel tube beam‐columns

AbstractThis paper presents a new uniaxial constitutive material formulation with softening for simulating the inelastic behavior of steel rectangular tubes in concrete‐filled steel tube (CFST) members. The primary behavioral characteristics of the steel tube in CFST members are isolated and pronounced through a carefully designed experimental campaign with CFST specimens subjected to uniaxial strain‐based loading protocols. The model is expressed in an effective stress–strain domain, where the effective uniaxial strain is defined as the uniaxial displacement within a dissipative zone over a predefined length. In the pre‐peak state, the proposed model can effectively capture the combined kinematic/isotropic hardening and Bauschinger effect—characteristic of mild structural steels—within the framework of rate‐independent plasticity. In the post‐peak state, the proposed model traces strength deterioration due to outward local buckling, which is a characteristic nonlinear geometric instability in CFST members due to the presence of the filled concrete in the steel tube. The proposed constitutive formulation incorporates a softening branch that exponentially decays to trace the stabilization of the outward buckling wave within the buckling region in successive inelastic loading cycles. Cyclic deterioration of the effective stress is explicitly considered via an energy‐based rule. The proposed model is calibrated to a CFST dataset. Regression equations are proposed for predicting the input model parameters. These equations cover a wide range of geometric parameters and structural steel materials in CFST members. Comparisons with prior tests on actual CFST beam‐columns under planar symmetric cyclic loading suggest that conventional 2‐dimensional displacement‐based beam‐column elements can predict the full‐range of the hysteretic behavior of the CFST members with the proposed constitutive formulation including cases where the post‐peak response of CFST members exhibits negative stiffness.

Notched Tensile Fracture of a Fe-15Mn-0.6C-2Al Twinning Induced Plasticity Steel at Room Temperature

The tensile fracture behavior of an Al-bearing TWIP steel was investigated by conducting a series of tensile tests on smooth and notched specimens with different notch geometries, focusing on the effects of evolution of the stress triaxiality and the effective strain during deformation. The flow curve and digital image correlation (DIC) analysis evidenced suppression of dynamic strain aging due to Al addition, and therefore, the effects of local inhomogeneous deformation associated with Portevin-Le Chatelier (PLC) band on fracture could be excluded. The smooth specimen fractured with negligible necking despite the absence of PLC bands. As a result, the effective strain was uniform through the gage section and the stress triaxiality (<i>η</i>) of ~0.33 was nearly unchanged over the entire cross-section up to the maximum load. This led to the fracture surface of the smooth specimen being entirely covered with fine equiaxed dimples. For notched specimens, the fracture strain was drastically reduced with decreasing notch radius, indicating the high notch susceptibility of the steel. The effective strain of the notched specimens was the highest at the edge of the notch root, regardless of the notch radius, so cracks first developed at the surface of the notch root. Although the <i>η</i> at the center of the notched specimens (0.40~0.48 depending on the notch radius) was higher than that of the smooth one, the center of the fracture surface of all notched specimens exhibited dimple features that were very similar to the smooth one, even in size. In contrast, in spite of the same <i>η</i> of ~0.33, fractography at the edge of the notched specimens revealed a fracture mode transition from dimple fracture to void sheet fracture to quasi-cleavage fracture as the notch radius decreased. The present results were rationalized in terms of the local evolution of stress triaxiality and effective strain during deformation, which were analyzed using the finite elemental method and DIC technique. It can be said that the fracture mode of TWIP steel, showing limited necking, was more influenced by the distribution and/or gradient of stress traiaxiality and effective strain rather than their local absolute values - that is, the severer their gradient is, the easier the quasi-cleavage fracture occurs.

Anisotropy and cyclic loading characteristics of a stiff Bolders Bank glacial till at Cowden

Glacial tills are widespread across the world, common in northern Europe and found under the North and Baltic Seas. Their geological and geotechnical characterisation is important to the geotechnical design of a wide range of onshore and offshore structures. This paper reports outcomes from coordinated monotonic small-strain stress probing, cyclic and larger strain triaxial and hollow cylinder apparatus (HCA) testing on a natural low-to-medium plasticity, apparent highly over consolidated, stiff glacial clay till. Monotonic HCA and triaxial experiments investigated the till’s stiffness and shear strength anisotropy from its limited linear elastic range up to ultimate failure, showing that stiffnesses are higher in the horizontal direction than in the vertical and that higher undrained shear strengths develop under “passive” horizontal loading than “active” vertical loading. The cyclic triaxial tests revealed the impact of cycling on effective stress paths and strain development, and cyclic stiffness degradation. Stable, metastable and unstable patterns of behaviour are identified, along with different cyclic failure modes, which are related to the till’s static yielding behaviour. The experiment results provide the basis for developing, testing and calibrating monotonic and cyclic constitutive models and establishing simplified design procedures for piles installed in comparable tills to support offshore energy and other structures.

How to select discrete or continuous interfaces in biological materials to achieve a strength-toughness tradeoff

Many biological materials, such as nacre, bone and turtle shell cuticle, can successfully achieve a tradeoff between strength and toughness, which is attributed to the stacked microstructure formed by soft and hard phases. However, among these biological materials, the soft phase-formed interfaces of some biological materials are continuous, while those of some are discrete. In this paper, a shear lag model considering an elasto-plastic discrete interface is established to reveal the selection mechanism of two kinds of interfaces in different biological materials, thus solving the tradeoff between strength and toughness. Based on the shear lag model, theoretical solutions of the stress and displacement in the hard phase and the shear stress in the soft interfacial phase are obtained for a general case with any number of interfacial bonding segments. The relationship between the effective stress and effective strain of the representative volume element (RVE) is further achieved, with the help of which the strength and toughness of staggered bio-composites can be analyzed. Corresponding experiments based on 3D-printed samples are further performed to verify the theoretical predictions. It is found that, when the hard phase and soft phase have comparable mechanical properties, like those in turtle shell cuticle, the interface guarantees a high load transfer efficiency to generate the ultimate stress in the platelet, while its discrete distribution leads to a higher interfacial shear stress level than that in a continuously bonded interface. Such a material-structure co-action induces a hybrid damage mode of hard phase fracture and soft phase failure, consequently leading to an excellent strength-toughness tradeoff. However, if the mechanical properties of two phases differ significantly, like those in nacreous materials or bone, a discrete interface should result in a unique damage mode of interface failure and a low utilization efficiency of hard phase. Instead, a continuous interface in this case is more conducive to obtain a tradeoff between strength and toughness. All the results demonstrate that biological materials choose different interface structures to meet the requirements of strength and toughness matching, based on the differences in the mechanical properties of soft and hard phases. Such a selection mechanism provides a direct reference for the optimal design of artificial composites with an excellent strength-toughness match.

Grain-Scale Study of SAC305 Oligocrystalline Solder Joints: Anisotropic Elasto-Plastic Constitutive Properties of Single Crystals

Abstract This paper focuses on anisotropic elastic-plastic constitutive modeling of SAC (SnAgCu) solder grains because of their importance in modeling the behavior of oligocrystalline (few-grained) micron-scale solder joints that are increasingly common in heterogeneous integration. Such grain-scale anisotropic modeling approach provides more accurate assessment of the mechanical response of solder interconnects in terms of predicting different failure modes, failure sites, and variability in time-to-failure. Anisotropic plasticity is represented using Hill–Ramberg–Osgood (RO) continuum plasticity model, which utilizes Hill's anisotropic plastic potential along with a RO power-law plastic hardening flow rule. Mechanistically motivated empirical scaling factors are proposed to extrapolate the stress–strain response for different grain sizes/shapes and for different coarseness of microstructures within each grain (generated with different cooling rates). This scaling factor can therefore also capture the effects of microstructural coarsening due to isothermal aging. This goal is achieved by first conducting monotonic tensile and shear tests on monocrystalline and oligocrystalline SAC305 solder joints containing grains of various geometries and also intragranular microscale (dendritic and eutectic) structures of various coarseness. The grain structures are characterized for each tested specimen using electron backscattered diffraction (EBSD). The Hill–RO model constants and the empirical scaling factors are then estimated by matching grain-scale anisotropic elastic-plastic finite element models of each tested specimen to the measured stress–strain behavior, using an inverse-iteration process. Grain shape is seen to influence the sensitivity of the effective stress–strain curves to the applied stress state (i.e., to the orientation of the principal stress directions) relative to (i) the material principal directions and (ii) the geometric principal directions of grains with high aspect ratio. Limitations of the current results and opportunities for future improvements are discussed.

Modelling the viscoplastic behaviour of Callovo-Oxfordian claystone with consideration of damage effect

In order to evaluate the performance of deep geological disposal of radioactive waste, an underground research laboratory (URL) was constructed by Andra in the Callovo-Oxfordian (COx) claystone formation at the Meuse/Haute-Marne (MHM). The construction of URL induced the excavation damage of host formations, and the ventilation in the galleries desaturated the host formation close to the gallery wall. Moreover, it is expected that the mechanical behaviour of COx claystone is time-dependent. This study presents a constitutive model developed to describe the viscoplastic behaviour of unsaturated and damaged COx claystone. In this model, the unsaturation effect is considered by adopting the Bishop effective stress and the van Genuchten (VG) water retention model. In terms of the viscoplastic behaviour, the nonstationary flow surface (NSFS) theory for unsaturated soils is used with consideration of the coupled effects of strain rate and suction on the yield stress. A progressive hardening law is adopted. Meanwhile, a non-associated flow rule is used, which is similar to that in Barcelona basic model (BBM). In addition, to describe the damage effect induced by suction change and viscoplastic loading, a damage function is defined based on the crack volume proportion. This damage function contains two variables: unsaturated effective stress and viscoplastic volumetric strain, with the related parameters determined based on the mercury intrusion porosimetry (MIP) tests. For the model validation, different tests on COx claystone under different loading paths are simulated. Comparisons between experimental and simulated results indicated that the present model is able to well describe the viscoplastic behaviour of damaged COx claystone, including swelling/shrinkage, triaxial extension and compression, and triaxial creep.

The Cold Forming Analysis of Eccentric Parts

In this study, a multi-stage cold forming process for the manufacture of eccentric parts is studied numerically with low carbon steel AISI 1022. The forming processes through five stages and four stages include two-step forward extrusion, eccentric upsetting, and backward extrusion over a moving punch. The numerical simulations of cold forming are conducted using the code of DEFORM-3D. The formability of the workpiece is studied numerically, such as the effect on forging load responses, maximum forging loads, effective stress and effective strain distributions and metal flow pattern. The maximum effective stress of 819 MPa at the third stage is the largest among the stages. The maximum effective stresses of the last stages for the four-stage forming and five-stage forming are almost the same. The effective strain distributions of the last stages for the four-stage forming and five-stage forming are very similar. The flow line distributions of the last stages both for the four-stage forming and five-stage forming are also very similar. For the maximum axial forging force and forming energy, the third stage of eccentric upsetting at the upper end is the largest among the stages. The total maximum axial forging loads from the first to the last stages are 795.8kN for the five-stage forming and 590.4kN for the four-stage forming; and the total forming energies are about 0.751kJ for the five-stage forming and 0.671kJ for the four-stage forming. Although the total maximum axial forging loads and total forming energy of the four-stage forming are smaller than those of the five-stage forming, the maximum lateral forging force in the last stage of the four-stage forming is almost five times that of the last stage of the five-stage forming. Increasing lateral forging force may lead to wear and damage of the punch. Moreover, the inner surfaces of the hexagonal cavity at the upper end are relatively uneven because of simultaneous eccentric upsetting and backward extrusion in the last stage of the four-stage forming.

Infrared radiation constitutive model of sandstone during loading fracture

The significant increase in energy demand will inevitably boost the exploitation of natural resources. The exploitation of resources including coal, oil, geothermal, natural gas, shale gas, and other energy has to be extracted with deep mining to fulfill the industry energy demand. With the increase of mining depth and the utilization of deep rock mass, the problem of high ground stress has become increasingly prominent. During high ground stress conditions, the mechanical behavior of hard rock will change significantly. Constructing a reasonable stress–strain damage constitutive model of hard rock is the basis for the design of a resource mining construction scheme, numerical simulation analysis, more accurate acquisition of rock mechanical characteristics, and evaluation of engineering rock stability. This is very crucial that needs to be addressed in a better way to solve the scientific problems of rock engineering. In this research, the infrared radiation observation experiments of sandstone biaxial under different lateral stresses are carried out. It is found that the infrared radiation energy has a near power function relationship with the effective stress in loading and fracture process. The quantitative characterization method of infrared radiation of the first invariant of stress and the second invariant of deviator stress is established. The cumulative high-temperature point scale factor amplitude is proposed to characterize the plastic volumetric strain of sandstone. Based on the effective stress and plastic strain, the plastic and damage models are established respectively. The three-dimensional plastic damage constitutive model of loaded sandstone based on infrared radiation is constructed. The model has clear input parameters having physical significance, and the compaction stage of sandstone is considered. The stress prediction of sandstone during biaxial loading is realized through the secondary development of a finite element software subroutine. The research results can lay a theoretical foundation for the analysis and evaluation of the mechanical characteristics of hard rock in the process of deep energy exploitation.

The Study of Multi-Stage Cold Forming Process for the Manufacture of Relief Valve Regulating Nuts

Cold forging is widely used in many industries. Multi-stage cold forming is usually utilized in forging fasteners. In this study, numerical simulation and experimental investigations were carried out on a five-stage cold-forming process for the manufacturing of low-carbon steel AISI 1010 relief valve regulating nuts. The forming process through five stages included preparation and centering for backward extrusion, backward extrusion over die pin, upset, backward extrusion over a moving punch, and piercing. The formability of the workpiece was studied, such as the effects on forming force response, maximum forming force, effective stress and effective strain distributions, metal flow patterns, and strength. A comparison of the forming forces obtained in the forming experiment with the numerical simulation results of the five-stage cold forming showed a good agreement with the trend of the forming force growth. For the maximum forming force and forming energy, the fourth stage of backward extrusion over the moving punch at the upper face was the largest among the five stages. The total maximum forming forces from the first to the fifth stages were numerically 440.9 kN and experimentally 449.4 kN, meaning the FE simulation and experimental results were in good agreement. The numerically simulated effective strain distributions were consistent with the experimentally tested hardness distributions. Highly compacted grain flow lines also resulted in higher hardness. The overall hardness of the workpiece formed by five-stage cold forming increased by 31% compared to the initial billet. The hardness of the workpiece increased with the forming stages, and the strain-hardening effect was obvious. The strength of the workpiece was significantly increased by five-stage cold forming.

Modeling of cyclically loaded square thin-walled CSFT columns stiffened by diagonal ribs using OpenSees

Among various proposed stiffening forms, the diagonal binding ribs, made of thin-walled steel plates with circular holes and welded to the steel tube, were found to particularly effective in improve the cyclic-bending and cyclic-shear behavior of square thin-walled concrete-filled steel tubular (CFST) columns. Although the mechanical behavior can be obtained from the experiments, numerical models are still needed to expand the range of investigation beyond what was tested physically and to facilitate the practical design. A 3D model using shell and solid elements is able to explicitly show the influence of different parameters, and simulate the details including the holes in diagonal ribs and the contact interaction between different parts. However, such analyses are relatively complicated, time-consuming, and are susceptible to numerical issues that cause lack of convergence. By contrast, a 2D model using fiber-based beam–column elements is far more efficient thus allowing for a wider range of investigation. In this work, the fiber models of flexure-dominated diagonal ribs stiffened square thin-walled concrete-filled steel tubular (DSCFST) columns were firstly developed in OpenSees and validated based on the effective stress–strain relationships of steel tubes and moment–rotation curves of RC bases. The fiber models of shear-dominated DSCFST columns were further developed by defining the nonlinear shear force–deformation relationships at the section level. These models were verified by the test results, and then the effect of the deformable RC base, tube local buckling, shear effect, and types of beam–column elements was analyzed in detail. Based on extensive parametric analyses, the effective stress–strain relationships applicable to various square thin-walled steel tubes stiffened by diagonal ribs and infilled concrete were derived, and the simplified shear force–deformation relationships were proposed. These results facilitate understanding of the behavior of DSCFST columns and lay a foundation for further system-level analysis.

A multi-scale computational model for the passive mechanical behavior of right ventricular myocardium

We have previously demonstrated the importance of myofiber–collagen mechanical interactions in modeling the passive mechanical behavior of right ventricle free wall (RVFW) myocardium. To gain deeper insights into these coupling mechanisms, we developed a high-fidelity, micro-anatomically realistic 3D finite element model of right ventricle free wall (RVFW) myocardium by combining high-resolution imaging and supercomputer-based simulations. We first developed a representative tissue element (RTE) model at the sub-tissue scale by specializing the hyperelastic anisotropic structurally-based constitutive relations for myofibers and ECM collagen, and equi-biaxial and non-equibiaxial loading conditions were simulated using the open-source software FEniCS to compute the effective stress–strain response of the RTE. To estimate the model parameters of the RTE model, we first fitted a ’top-down’ biaxial stress–strain behavior with our previous structurally based (tissue-scale) model, informed by the measured myofiber and collagen fiber composition and orientation distributions. Next, we employed a multi-scale approach to determine the tissue-level (5 x 5 x 0.7 mm specimen size) RVFW biaxial behavior via ’bottom-up’ homogenization of the fitted RTE model, recapitulating the histologically measured myofiber and collagen orientation to the biaxial mechanical data. Our homogenization approach successfully reproduced the tissue-level mechanical behavior of our previous studies in all biaxial deformation modes, suggesting that the 3D micro-anatomical arrangement of myofibers and ECM collagen is indeed a primary mechanism driving myofiber–collagen interactions.

Coal permeability behaviors and non-uniform deformations under various boundary conditions: Part 1 – Experimental observations

Permeability is a key parameter to evaluate the ability of coal reservoir for transmitting coalbed methane (CBM). Deformations of internal components of coal caused by the variations of physical fields control the evolution of coal permeability. And there is obvious non-uniform in the deformations of coal bulk and fracture due to the heterogeneity of coal. However, at present, the evolution of non-uniform deformation and its relationship with coal permeability are unclear. In this study, first of a two-part series, we completed a series of experiments to measure the permeability, axial strain, radial strain, overall strain and fracture strain of a coal sample under different boundary conditions (constant confining pressure, constant effective stress and uniaxial strain) at different injection pressures of carbon dioxide (0.2 MPa, 1.0 MPa, 2.0 MPa, 3.0 MPa, 4.0 MPa and 5.0 MPa). And we defined the comprehensive non-uniform deformation index (CNDI) as the ratio of the fracture strain to the overall strain to quantify the degree of the non-uniform deformation between coal bulk and fracture. The experimental results show that the deformation of the coal sample in the longitudinal joint direction is smaller than that in the transverse joint direction, which indicates that the mechanical properties of the coal sample is anisotropic in different directions. And there are obvious differences between the deformations of coal bulk and fractures. When the gas pressure is in the range of 0.2 ∼ 5.0 MPa, the non-uniform deformations are vaguely related to the change of gas pressure, but closely related to the type of boundary conditions. The influence of gas pressure under displacement-controlled boundary condition (uniaxial strain) on the CNDI is greater than that under stress-controlled boundary conditions (constant confining pressure, constant effective stress). In addition, we also observed the phenomenon by the experimental results of the constant effective stress group: the permeability decreases gradually with the gas pressure even after removing the influence of gas slip effect, which is inconsistent with the traditional theoretical solution under the constant effective stress condition. Based on the fact that coal sample is a heterogeneous body, we tentatively believe that one of the reasons for this inconsistency may be that the traditional definition of effective stress does not include the effect of gas adsorption.

Effects of Strain Rate on Stress-Strain Curves in 2024 Aluminum Alloy After Solution Heat Treatment

Strain rate sensitivity of effective stress and fracture strain of aluminum alloy 2024 were examined considering the period from solution heat treatment. Notched round bar tensile test specimens were employed for obtaining stress-strain curves. Because the necking area of tensile tests is under multiaxial stress, effective stresses of aluminum alloy 2024 were corrected by an optimization method using experimental and simulation results. In the optimization, the experimental and finite element method simulation results of tensile force–true strain of the notched area in the tensile direction were compared. After stress correction, the effective stresses at a true strain of 0.002 were almost the same or showed a small strain rate sensitivity. The effective stresses at a true strain of 0.15 and 0.20 clearly decreased with increasing strain rate and clearly increased at a high strain rate. Fracture strain also decreased clearly with increasing strain rate and clearly increased at a high strain rate.

A double-phase field method for mixed mode crack modelling in 3D elasto-plastic solids with crack-direction-based strain energy decomposition

Crack-direction-based decomposition of elastic strain energy could effectively control the propagation of tensile and shear cracks in a phase field modelling context. The objective of the proposed double-phase field model is to extend the crack-direction-based decomposition strategy from 2D brittle fracture to complex mixed-mode crack modelling in a 3D setting, with plastic deformation incorporated. Both effective (undamaged) stress and plastic strain are split in the crack-orientation-based coordinate system. The decomposed tensile/shear stress contribute to tensile/shear damage evolution, respectively. The plastic contribution is coupled by relating the decomposed tensile/shear plastic strain to the corresponding tensile/shear crack energy release rates. Crack surface normal direction, represented by two orientation variables in 3D spatial domains, is determined by the F-criterion. The proposed model is implemented via ABAQUS subroutines with a staggered scheme for two phase field variables and crack direction. The simulation of a single-edge notch specimen under shear loading demonstrates that the ratio between shear and tensile crack energy release rates plays a significant role in the crack mode and mechanical response. Numerical results of a group of uniaxial tension, simple shear and tension shear specimens show good agreement with the experimental data in terms of the force–displacement curve and crack path, exhibiting the validity of the proposed model for capturing different crack modes. This model has also been proven effective for complex 3D problems via the third Sandia Challenge example.

Refined nonlinear micromechanical models using artificial neural networks for multiscale analysis of laminated composites subject to low-velocity impact

The parametric high fidelity generalized method of cells (PHFGMC) is an advanced micromechanical method that can be used for the nonlinear and failure analysis of several composite materials. The computational effort required for studying the nonlinear and damage multiaxial behavior is relatively small, depending on the size of the discretized repeating unit cell (RUC). However, it is computationally challenging, if not impossible, to integrate refined nonlinear micromechanical models within a multiscale analysis of composite structures. This is due to the thousands or more RUC models required at the integration points within a multiscale finite-element (FE) model of laminated structures. To that end, we propose a new artificial neural network (ANN) based micromechanical modeling framework, termed ANN-PHFGMC, for exploring the nonlinear behavior of fiber-reinforced polymeric (FRP) materials. Pre-simulated mechanical stress–strain responses and behaviors are determined using the PHFGMC to generate a multiaxial training database for the ANN micromodel. The simulated training data is founded on the PHFGMC-RUC results based on a hexagonal RUC. The PHFGMC effective stress–strain responses for different applied multiaxial strain paths are divided into two sets of data; one for the training and the other for verifying the trained ANN-PHFGMC model. The resulting trained ANN-PHFGMC is accurate, with less than 5% error in the verified predictions. The ANN-PHFGMC can be used as a stand-alone or embedded as a surrogate proxy model within a multiscale analysis of composite structures. Next, the ANN-PHFGMC model is integrated within a commercial explicit FE code for low-velocity impact (LVI) analysis of laminated composite plates. Multiscale LVI analyses are performed for two composite plates with different layups. Further, results are compared to experimental data to demonstrate the new model's ability to integrate refined nonlinear micromechanical models within a multiscale analysis.

Fracture Closure Empirical Model and Theoretical Damage Model of Rock under Compression.

The rock or rock mass in engineering often contains joints, fractures, voids, and other defects, which are the root cause of local or overall failure. In response to most of the current constitutive models that fail to simulate the nonlinear fracture compaction deformation in the whole process of rock failure, especially brittle rocks, a piecewise constitutive model was proposed to represent the global constitutive relation of rocks in this study, which was composed of the fracture compaction empirical model and the damage statistical constitutive model. The fracture empirical compaction model was determined by fitting the expressions of fracture closure curves of various rocks, while the rock damage evolution equation was derived underpinned by the fracture growth. According to the effective stress concept and strain equivalence hypothesis, the rock damage constitutive model was deduced. The model parameters of the fracture compaction empirical model and damage statistical constitutive model were all calculated by the geometrical characteristics of the global axial stress-strain curve to guarantee that the models are continuous and smooth at the curve intersection, which is also simple and ready to program. Finally, the uniaxial compression test data and the triaxial compression test data of different rocks in previous studies were employed to validate the models, and the determination coefficient was used to measure the accuracy. The results showed great consistency between the model curves and test data, especially in the pre-peak stage.

Fiber-based model for simulating strength and stiffness deterioration of high-strength steel beams

This paper focuses on the behavior, modeling, and evaluation of high-strength steel beams used as girders in moment resisting frame systems (MRFs). The results of the evaluation have led to the development and calibration of effective (phenomenological) stress–strain curves and fiber-based finite element approaches for modeling the behavior of high-strength steel beams. The key parameters influencing the cyclic behavior of high-strength steel beams are: (i) shape/geometric details, (ii) flange and web slenderness ratios, (iii) material stress–strain behavior, and (iv) fracture/damage failure criteria. This paper summarizes prior experimental results on the cyclic behavior of high-strength steel beams and develops 3D finite element models to simulate their behavior. The models are developed cognizant of the parameters (i)–(iv) listed above. The models are validated against experimental data and then used to conduct parametric studies to evaluate the effects of material and geometric parameters on the cyclic behavior and ductility of high-strength steel beams. The developed effective stress–strain relationships hold the key to developing potential design methods based on allowable strain criteria and/or continuous strength methods recently developed by other researchers.

Investigation of mechanical properties of laser welded dual-phase steels at macro and micro levels

The current automotive industry uses new technology in materials processing and lightweight materials to minimize vehicle weight and fuel consumption. As a result, Tailor-Welded Blanks (TWB) are used in regions where additional strength or stiffness is necessary in body-in-white, thus decreasing weight. In this paper, TWB were produced by joining DP600 with 1.8 mm and DP800 with 0.8 mm and 1.5 mm using CO2 laser welding. The effects of laser power and welding speed on the mechanical properties of TWB were investigated. The flow behaviors of the TWB were obtained from tensile tests. The microstructures of the weld zones of the base materials and TWB were revealed, and the numerical analyzes of the microstructures were performed by micromechanical modeling with a 2D representative volume element (RVE). Effective stress and plastic strain distributions in the microstructures and macroscopic flow curves of the base materials and the weld zones were obtained. The uniaxial tensile tests of the samples were modeled, and the flow behaviors of the TWB were obtained with micromechanical modeling. The results showed a significant change in stress distribution and strain localization depending on the grain size of constituents and the thickness ratios of the TWB at micro and macro scales, respectively. The numerical flow curves obtained using the RVE method were in good agreement with those of the experimental.