Material Constitutive Relations Research Articles

Concrete target quasi-static resistance to a penetrating projectile considering the material constitutive relationships

The well-known Forrestal's semi-empirical approach for a rigid projectile penetration into s thick concrete targets is based on an empirical term of the target quasi-static resistance that is calibrated from test data and is assumed to depend on the concrete uniaxial compressive strength.The present paper aims at deriving a theoretically based method for determining the quasi-static resistance term that is independent of test data. Considering the triaxial state of stress in the target around the projectile and the high magnitude of stresses and associated large deformations, the target material is described by an arbitrary non-linear pressure–volumetric strain relationship and a non-linear pressure dependent shear strength plasticity envelope.The major advantage of the new proposed approach is the theoretical sound basis and the clear dependence on the constitutive properties of the concrete target. The deceleration and penetration depth time histories obtained using the calculated theoretical value of the quasi-static resistance term are compared with measured data and very good agreement with test data is observed. Major parameters of the equation of state and of a shear strength plasticity envelope are investigated to clarify their effect on the magnitude of the quasi-static resistance term.

Numerical study on the seismic performance of precast UHPC bridge columns considering the buckling behavior of replaceable energy dissipaters

This paper aims to explore the seismic performance of a novel earthquake-resilient bridge column with replaceable elements, including external ultra-high-performance concrete (UHPC) cover plates and internal steel dissipaters, based on a numerical model including local and overall levels. The overall model was established to assess the seismic behavior of the bridge columns considering the buckling behavior of steel dissipaters adopting the modified material constitutive relationship, of which the parameters were determined according to the results of the local model. The numerical model was verified with reported experimental results. A parametric analysis was conducted to investigate the effects of three parameters. The results show that the numerical model can effectively evaluate the seismic performance of the bridge columns. The buckling behavior of steel dissipaters dominates lateral deformation capacity of the bridge columns. The steel dissipater's initial defect direction and gap gradient can accelerate the failure of cover plates. Reasonable upper and lower limits are required for the length-to-diameter ratio of the fuse part as well as the gap between the fuse part and surrounding concrete, while only a suitable lower limit is needed for the thickness of cover plate to ensure the superior seismic performance of the bridge columns.

Design of graded porous bone-like structures via a multi-material topology optimization approach

Graded porous structures combine robustness of porous structures and high stiffness of bulk designs. This study aims to design optimized graded porous bone-like structures through a novel multi-material topology optimization approach, which generalizes the concept of multiple materials. Namely, each material can have not only distinct material property but also a different level of local porosity, or a combination of both, thus allowing the realization of multiple levels of porosity. With separated density and material/porosity fields, we propose two types of multi-porosity local volume constraints to enable graded porosity considering linear and bi-linear material constitutive relations. Through the proposed framework, single- and multi-material structures can be obtained with a natural transition between the bulk and multiple levels of porous regions. We adopt the Bi-value Coding Parameterization (BCP) scheme combined with the Solid Isotropic Material with Penalization (SIMP) method to interpolate the stored energy functions. Through several examples with multiple porosity levels and various material properties, we demonstrate the effectiveness of the proposed framework with two novel constraints to generate optimized multi-material and multi-porosity structures. We further investigate the interactions among material properties, multiple porosity levels, structural stiffness, and robustness. Compared with conventional bulk designs, the optimized bone-like structures with multi-level graded porosity, although less stiff, are found to be more robust, i.e., their structural stiffness is less influenced by the load variations and material deficiency. The resulting graded porous composite designs showcase the capability of the proposed multi-material formulation to optimize the distributions of not only different types of materials but also multiple levels of porosity.

Analysis of Finite Element Mechanism of Axial Compressive Behavior of T-Shaped Stiffened Concrete-Filled Steel Tubular Stub Columns After Uniform Fire Exposure

Based on the reasonable determination of material constitutive relationship and interaction model between concrete and steel tube, a finite element model of T-shaped stiffened concrete-filled steel tube (TSCFST) stub column exposed to uniform fire was established, and model reliability was verified. Through the FE model, the working mechanism of the model in the whole process of loading was analyzed in detail. In the process of axial compression, the load distributions of steel tube and concrete, and the interaction between steel tube and concrete were discussed. This paper analyzed the effects of the main factors on residual bearing capacity of TSCFST stub columns, and put forward the calculation formula of the residual bearing capacity of TSCFST stub columns after uniform fire exposure.

Finite Element Analysis of Welding Residual Stress in Longdistance Gas Pipeline

This paper takes L415 pipeline steel as the research object. The temperature field and stress field of the gas pipeline welding process are numerically simulated by using ANSYS finite element analysis software. Gradient meshing is adopted by the finite element model. The simulation of the welding heat source is realized by the band heat source model, and ANSYS is used to load the heat source in a APDL command program. In the simulation process, the element birth and death technology is used to simulate the generation of weld material, and the material constitutive relationship is a bilinear follow-up strengthening elastoplastic model that changes with temperature. The simulation results show that applying the heat source in the form of heat generation rate with a belt-shaped heat source can realize effective calculation of the residual stress field of multi-layer and multi-pass welding. The calculation results in this paper provide a mechanical reference for pipeline installation and operation.

Plastic analysis of steel arches and framed structures with various cross sections

This paper presents a displacement-based numerical methodology following the Euler-Bernoulli theory to simulate the 2 nonlinear behavior of steel structures. It is worth emphasizing the adoption of co-rotational finite element formulations considering large displacements and rotations and an inelastic material behavior. The numerical procedures proposed considers plasticity concentrated at the finite elements nodes, and the simulation of the steel nonlinear behavior is approached via the Strain Compatibility Method (SCM), where the material constitutive relation is used explicitly. The SCM is also applied in determining the sections bearing capacity. Moreover, the present numerical approach is not limited to a specific structural member cross-sectional typology, with the residual stress models introduced explicitly in subareas of steel cross-sections generated by a 2D discretization. Finally, results consistent with the literature and with low processing time are presented.

A Continuum Damage Mechanics Approach for Reliability Analysis of Composite Laminates Containing a Central Circular Hole

This paper discusses the topic of probabilistic analysis of composite laminates rectangular plates containing a central circular hole under static tensile load. First, According to the continuum damage mechanics (CDM) approach, structural analysis models, the definition of damage and the treatment of random variables will be explored. Then, the matrix cracking and fiber/matrix debonding damage is modeled and the material constitutive relationships are implemented in the ABAQUS software by the subroutine. The probabilistic methods, first order reliability method (FORM) and second order reliability method (SORM) have been used to analyze the composite plates’ system failure probability. The failure functions and random variables have been obtained according to the CDM approach. Issues arising out of the use of composite material structures, in applications, due to non-homogeneity and anisotropic characteristics, and manufacturing defects will be highlighted, and uncertainties related to the material properties, loads, and boundary conditions will be discussed through examples. It is shown that the scatter in parameter values has a significant effect on damage development in the model.

Analysis of the Shear Capacity of Ultrahigh Performance Concrete Beams Based on the Modified Compression Field Theory

An analysis model of the shear capacity of prestressed ultrahigh performance concrete (UHPC) beams under the combined action of bending and shearing was established in this paper based on the modified compression field theory and by considering the unique material constitutive relation of UHPC. Shear tests were performed using three prestressed UHPC‐T beams with different shear‐span ratios to verify the correctness of the model. The results showed that the shear‐span ratio greatly influenced the shear capacity and failure modes of UHPC‐T beams. Upon increasing the shear‐span ratio, the failure modes of the three beams were inclined compression failure, shear compression failure, and diagonal tension failure, successively. When the shear‐span ratio changed from 1.04 to 2.12, the shear bearing capacity decreased greatly; however, when the shear‐span ratio changed from 2.12 to 3.19, the decrease of the shear bearing capacity was very small. In addition, the MCFT analysis model was used to analyze the experimental data, and the predicted results were in good agreement, which proved the applicability of the model. Finally, according to the existing shear test results of UHPC beams and based on the main influencing factors, a simplified formula for predicting the shear capacity of UHPC beams was obtained by fitting. Comparing the MCFT model with the results of other pieces of literature, this formula accurately predicted the shear capacity of UHPC beams. The MCFT model and the simplified formula presented in this paper provide a powerful tool for predicting the shear performance of UHPC‐T beams, which will contribute to the design and analysis of UHPC‐T beams.

Effect of Support Conditions on Performance of Continuous Reinforced Concrete Deep Beams

While continuous reinforced concrete deep beams with fixed and hinged support conditions are every so often found in structures, little research has focused on their performance. This, in part, can be attributed to the demanding nature of ensuring fixed supports in experimentally testing such members. Nonetheless, conducting numerical analysis in comparison with experimental study has been a typical technique for producing a reliable numerical model as an alternative to destructive tests. This paper is aimed at numerically investigating the impact of different support conditions in the performance of two-span continuous reinforced concrete deep beams. A numerical model of three experimentally tested beams with two exterior rollers and interior hinge support conditions was generated. Good comparison, with an acceptable variation between numerical and experimental results, was achieved by tuning a few parameters in the numerical model, including element type, mesh size, and material constitutive relations. The refined numerical model was used as an alternative to destructive tests to conduct a parametric study to further investigate the impact of different sets of support conditions in the performance of two-span continuous reinforced concrete deep beams. This study highlights the potentially serious consequences of the support conditions in the performance of such deep beams.

Nonlinear Finite Element Analysis of Shear Strength for Steel Fiber Reinforced Concrete I-Section Beams

This research presents a numerical model of I-section fiber reinforced concrete beams to evaluate the shear strength and complete behavior of the beams using the numerical formulation, which compared with the results of (twenty-three) tested I-section beams taken from previous investigations which are varying in shear span to effective depth ratio and volume fraction of steel fibers. Models using finite element method having the same dimensions and properties as the experimental test specimens. It was shown that the behavior of SFRC I-section beams could be modeled well using the proposed material constitutive relationships and there was a good agreement between the experimental and numerical failure load, crack pattern load deflection curves obtained from this study. The finite element model shows slightly more stiffness results than the test data ranges. The average ratio of the experimental to the calculated results is (1.027).

A Methodology for the Statistical Calibration of Complex Constitutive Material Models: Application to Temperature-Dependent Elasto-Visco-Plastic Materials.

The calibration of any sophisticated model, and in particular a constitutive relation, is a complex problem that has a direct impact in the cost of generating experimental data and the accuracy of its prediction capacity. In this work, we address this common situation using a two-stage procedure. In order to evaluate the sensitivity of the model to its parameters, the first step in our approach consists of formulating a meta-model and employing it to identify the most relevant parameters. In the second step, a Bayesian calibration is performed on the most influential parameters of the model in order to obtain an optimal mean value and its associated uncertainty. We claim that this strategy is very efficient for a wide range of applications and can guide the design of experiments, thus reducing test campaigns and computational costs. Moreover, the use of Gaussian processes together with Bayesian calibration effectively combines the information coming from experiments and numerical simulations. The framework described is applied to the calibration of three widely employed material constitutive relations for metals under high strain rates and temperatures, namely, the Johnson–Cook, Zerilli–Armstrong, and Arrhenius models.

Higher-Order Peridynamic Material Correspondence Models for Elasticity

Higher-order peridynamic material correspondence model can be developed based on the formulation of higher-order deformation gradient and constitutive correspondence with generalized continuum theories. In this paper, we present formulations of higher-order peridynamic material correspondence models adopting the material constitutive relations from the strain gradient theories. Similar to the formulation of the first-order deformation gradient, the weighted least squares technique is employed to construct the second-order and the third-order deformation gradients. Force density states are then derived as the Frechet derivatives of the free energy density with respect to the deformation states. Connections to the second-order and the third-order strain gradient elasticity theories are established by realizing the relationships between the energy conjugate stresses of the higher-order deformation gradients in peridynamics and the stress measures in strain gradient theories. In addition to the horizon, length-scale parameters from strain gradient theories are explicitly incorporated into the higher-order peridynamic material correspondence models, which enables application of peridynamics theory to materials at micron and sub-micron scales where length-scale effects are significant.

Validation of a stochastically homogenized peridynamic model for quasi-static fracture in concrete

Concrete is the most widely used man-made composite material. Its damage and fracture behavior determines reliability of many engineering structures. The quasi-static fracture behavior in concrete structures is investigated here using an intermediately homogenized peridynamic (IH-PD) model. The case of anchor pull-out from a concrete plate is used to validate the IH-PD in terms of the load–displacement behavior (peak load and softening behavior), crack path asymmetry and path tortuosity. While the simplest material constitutive relationship (linear elastic with brittle failure) is used for the peridynamic bonds, the IH-PD model is shown to be superior in modeling concrete failure than a corresponding homogenous PD model with a material model (bond force-strain relationship) with softening. The model is successfully tested for additional cases pertaining to mode I, mode II dominated, and mixed mode fracture. The model’s success comes from the preservation of some micro-scale heterogeneity, stochastically generated in the IH-PD model to match concrete’s phases volume fractions, while its computational cost is equivalent to that of a homogenized peridynamic model.

Development of a supramolecular polymer based self-healing multilayer system for inflatable structures

Self-healing materials have become more and more interesting for the space industry, since they can lead to the creation of space systems and structures able to repair autonomously after accidental damages caused by collision with micrometeoroids and orbital debris during the entire operational life. The implementation of these novel materials results in higher protection and safety for astronauts, and longer missions in the perspective of lunar bases establishment and manned exploration of Mars.The present study aims to experimentally and numerically characterize an intrinsic self-healing supramolecular polymer that is potentially applicable to space suits, habitats and inflatable structures in general. A dedicated test device has been developed to evaluate the sealing performance of the material through flow rate measurements after a puncture event. The experimental part is followed by the study of the material's constitutive relations including hyperelastic and viscoelastic responses. The related model parameters are computed and calibrated through optimization and data matching tools in order to simulate damage and healing events.Results show that the selected supramolecular polymer possesses effective self-healing abilities also under pressurized conditions, demonstrating its applicability to the considered specific fields in the space sector. Furthermore, for what concerns the analyzed puncture experiments and field of solicitation, the developed model can follow the relaxation process related to the self-healing behavior, since it can predict whether the material is effectively able or not to flow and repair.

Out-of-plane stability of concrete-filled steel tubular arches at elevated temperatures

This paper investigates the flexural-torsional buckling behaviour of concrete-filled steel tubular circular arches under mechanical and thermal loading. A thermo-elastic pre-buckling analysis is first conducted by employing the principle of virtual work to derive the non-linear equations of equilibrium. The governing geometrical, equilibrium and constitutive material relations are numerically solved as a system of first-order differential equations with boundary conditions of pinned or fixed ends. The prebuckling analysis is then generalised to consider basic creep strain which is found to have a negligible impact on the prebuckling response under short-term heating. Subsequently, an elastic out-of-plane buckling analysis is performed using energy methods and the influence of thermal loading on buckling loads is examined. The results show that stability boundaries decrease with an increase in thermal loading, and that the rate of reduction is independent of the type of end-supports. Additionally, a Finite Element (FE) model is developed to analyse the inelastic lateral buckling strength of CFST arches under both uniform thermal and fire loading. The FE analysis is validated by comparison to the numerical method derived herein for the elastic buckling analysis.

Study on Mechanical Properties of Weakened Steel Frame Joints at Beam Ends

In order to study the hysteretic properties of steel frame T-shaped weakened joints, 12 groups of steel frame weakened joints and 1 group of common joints are designed with the weakened form, the weakened diameter and the distance from the weakened center to the column end as the parameters. Based on simplified mechanical model and material constitutive relationship, the finite element model is established by ABAQUS software to analyze the hysteretic properties of the joint specimen. By comparing with the existing test results of the weakened joint, both have a good agreement, and the rationality of the finite element model is verified. The simulation analysis of the weakened joints of the beam webs is carried out in the further and the load-displacement hysteretic curves are extracted as well as skeleton curves and stress cloud diagram of the joints. The influence rules of the weakened form, weakened diameter and weakened distance from the center to the column end on the seismic performance of the joints are obtained, and the design suggestions for the weakened joints are put forward. These can lay a foundation for time-history analysis of the frame structure with this kind of joints.

Upper bounds on absorption and scattering

A general framework for determining fundamental bounds in nanophotonics is introduced in this paper. The theory is based on convex optimization of dual problems constructed from operators generated by electromagnetic integral equations. The optimized variable is a contrast current defined within a prescribed region of a given material constitutive relations. Two power conservation constraints analogous to the optical theorem are utilized to tighten the bounds and to prescribe either losses or material properties. Thanks to the utilization of matrix rank-1 updates, modal decompositions, and model order reduction techniques, the optimization procedure is computationally efficient even for complicated scenarios. No dual gaps are observed. The method is well-suited to accommodate material anisotropy and inhomogeneity. To demonstrate the validity of the method, bounds on scattering, absorption, and extinction cross sections are derived first and evaluated for several canonical regions. The tightness of the bounds is verified by comparison to optimized spherical nanoparticles and shells. The next metric investigated is bi-directional scattering studied closely on a particular example of an electrically thin slab. Finally, the bounds are established for Purcell’s factor and local field enhancement where a dimer is used as a practical example.

A two dimensional VCFEM formulated with plastic, creep and thermal strain for simulate fatigue of porous material

In this paper, a two-dimensional Voronoi cell finite element model is developed for analyzing homogeneous materials containing dispersed voids in the matrix. The complementary energy functional, formulated with plastic, creep and thermal strain, is applied for the numerical simulation of fatigue behavior of porous materials under different conditions. The paper starts with a description of 2D porous material. To complete the computation of nonlinear strain, the constitutive relation of material in the complementary energy functional is changed. In order to verify the validity and accuracy of the model, the result of simulations is compared with the counterpart of the normal displacement finite element program ABAQUS. The comparison results suggest that the VCFEM, with the same accuracy, have the advantages of simple meshing, faster computation. In the numerical simulation, the model is applied for simulating low-cycle fatigue, variable temperature low cycle fatigue and thermo-mechanical fatigue, at the same time, the influence of porosity is also discussed.

Constant deceleration approaches for penetration analysis of rigid projectile into concrete: Revisited

A new approach of constant deceleration penetration into concrete targets has been presented recently. It is based on observations from two-dimensional numerical simulations of penetration into aluminum targets, showing a rather constant deceleration during the tunneling stage, which leads to conjecturing a general simple constant deceleration approach to represent constant resistance during penetration. This approach has been extended to concrete materials despite their entirely different behavior. This article reviews the one-stage constant deceleration approach and compares it with test data and with analytical and numerical models. This study clearly shows that concrete penetration cannot be presented by the proposed constant deceleration approach. The constant deceleration approach assigns constant deceleration to the projectile from its impact with the target and ignores the entrance stage. This study shows that a two-stage simplified approach shows superior results compared to the one-stage approach. Experimental studies with instrumented projectiles show that although at low-strength concrete the deceleration variation with time is moderate, its variation with time at higher strength concrete is significant. The variable deceleration–time records are confirmed by theoretical models using the material constitutive relationships. It has been found that the proposed constant deceleration is merely a calibration constant to the measured penetration depth and does not represent a physical deceleration of the penetrating projectile. It is concluded that there cannot exist a simplified approach with a constant deceleration or even an arbitrarily predefined another shape of the deceleration curve that may properly represent different penetration scenarios in concrete targets.

Mechanical Performance Evaluation of the Al-Mg-Si-(Cu) Aluminum Alloys after Transient Thermal Shock through an Novel Equivalent Structure Design and Finite Element Modeling

In this paper, the microstructure evolution and mechanical performance of the Al-Mg-Si-(Cu) aluminum alloy after transient thermal shock were investigated through experimental tests and finite element simulations. A novel equivalent structure was designed as a typical case in which one side of the plate was welded therefore the other side was thermally shocked with different temperature distribution and duration. The temperature gradient which influences most importantly the mechanical properties was simulated and experimentally verified. Through cutting layers and tensile testing, the mechanical response and material constitutive relation were obtained for each layer. Gurson-Tvergaard-Needlemen (GTN) damage parameters of these samples under large strains were then obtained by the Swift law inverse analysis approach. By sorting the whole welded joint into multi-material composed structure and introducing the obtained material constitutive relation and damage parameters, tensile properties were precisely predicted for typical types of weld joint such as butt, corner, and lap joints. The results show that precipitate coarsening, phase transformation from β″ phase to Q′ phase, and dissolving in the temperature range of 243.3–466.3 °C during the thermal shock induced a serious deterioration of the mechanical properties. The highest reduction of the ultimate tensile strength (UTS) and yield strength (YS) would be 38.6% and 57.4% respectively. By comparing the simulated and experimentally obtained force-displacement curves, the error for the above prediction method was evaluated to be less than 8.1%, indicating the proposed method being effective and reliable.