Macroscopic Stress-strain Relations Research Articles

Study on the mechanical behavior of millennium-ancient bricks based on microscopic characteristics

The wide performance variation and inability for destructive testing make accurately determining ancient brick mechanical properties crucial for assessing structural safety in ancient masonry. This paper uses multiscale modeling with microscopic finite element analysis to quantitatively assess ancient brick macroscopic stress–strain relationship and compressive strength based on microstructural characteristics. The basic parameters such as porosity, pore size distribution, mineral composition and volume ratio, and microstructure characteristics of ancient bricks were obtained by corresponding methods. The Mori-Tanaka homogenization theory was applied to derive a three-phase equivalent brick matrix using elastic moduli and Poisson’s ratios of quartz, kaolinite, and montmorillonite at the microscale. The Representative Volume Element model with pores was created based on this matrix and pores, integrating Drucker-Prager plastic damage for finite element analysis of ancient brick mechanical behavior. The results indicate that stress–strain curves from the multi-scale micromechanics model resemble macroscopic experimental curves and maintain consistent peak strength. This shows that combining microscopic testing with finite element simulation for analyzing the mechanical properties of ancient bricks is feasible, providing a new non-destructive means of obtaining these properties.

Micromechanical properties and deformation behavior of the constituent phases in 3rd generation complex phase AHSS: In-situ neutron experiment and crystal plasticity simulation

This paper investigated the micromechanical properties and deformation behavior of the constituent phases in 3rd generation (GEN) complex phase advanced high-strength steel (AHSS). The hybrid method was a comprehensive combination of uniaxial tensile test with digital image correlation (DIC), electron backscatter diffraction (EBSD), in-situ neutron diffraction (NED) and crystal plasticity finite element method (CPFEM). Results reveal that the microstructure of 3rd GEN AHSS exhibits a complex phase of ferrite (46.2 %), bainite (36.1 %), martensite (9.4 %) and austenite (8.3 %), which would be promising microstructure in the development of new-generation complex phase AHSS. The significant findings are: (1) excellent ductility is obtained while high strength is preserved despite small martensite volume fraction, which can reduce the tendency of martensite cracking; (2) macroscopic stress-strain relationships and microscopic hardening properties of constituent phases are successfully determined, which are very important for predicting the overall performance of complex phase AHSS; (3) presence of bainite with high volume fraction plays a critical role in inducing plastic strain localization in ferrite, resulting in the heterogeneous stress/strain distribution. It is disclosed that pronounced strain localization is mostly initiated in ferrite grains while the deformation bands are mainly located in ferrite/bainite grain boundaries. Furthermore, strain partitioning between ferrite and bainite results in the high-stress concentration in bainite grains. As a result, these “hot zones”, i.e., ferrite grains, ferrite/bainite grain boundaries and bainite grains, experience high strain, strain gradient and stress, respectively, which can be a primary origin of ductile fracture initiation in the 3rd GEN complex phase AHSS. The findings reported in the present investigation would be of great interest in the development of new-generation complex phase automotive steels.

A hybrid algorithm of particle swarm optimization and finite element method to identify local mesoscopic damage of concrete-like materials

Meso-scale material modeling and parameter identification are still unsettled issues in the current multi-scale methods for the field of computational mechanics. In this investigation, a hybrid algorithm of particle swarm optimization and finite element method coupled with continuum damage mechanics is proposed to forecast local mesoscopic elasticity modulus and damage of concrete-like materials based on the macroscopic stress-strain relationship data curve. The algorithm establishes a bridge between mesoscopic mechanical analysis and macroscopic mechanical analysis, which can also guarantee the consistency of analysis in different scales. A representative numerical case is conducted to support the algorithm. Additionally, the effect of different divisions of representative volume element is analyzed based on the algorithm, and the recommended size of representative volume element is 5 mm. The prediction results match well with the corresponding macroscopic experimental results and mesoscopic experimental results based on the chosen recommended size of representative volume element. The effectiveness of the algorithm is verified, which can support an effective numerical tool to optimize and identify mesoscopic mechanical parameters and damage for multi-scale material modeling and analysis.

PFC–FLAC coupling-based numerical simulation of triaxial test on soybean granular material

A discrete-continuous (PFC–FLAC) coupling method was used in this study to simulate laboratory triaxial tests with soybean granular material. The mesoscopic mechanical parameters of the soybean granular material were calibrated by comparing them with actual laboratory test results, and the validity of the modeling method was verified. Subsequently, the particle motion law and mechanical mechanism of the soybean granular materials were analyzed based on the particle displacement field, velocity field, and force chain network. The results showed that the coupled PFC–FLAC method could better describe the macroscopic stress–strain relationship, deformation damage characteristics, and shear strength mechanical indexes of soybean granular materials. With increasing confining pressure (50–200 kPa), the bulging deformation of the specimens changed from uniform to concentrated but uneven. The particle contact number and maximum particle contact stress increased by 19.3 and 48%, respectively. Additionally, variations of the macroscopic properties of the specimens with microscopic parameters were revealed. Under the same conditions, the change in the peak stress of the specimen was proportional to the interparticle friction coefficient. Moreover, the slope of the stress–strain curve increased gradually with an increase in the effective modulus.

General theory for plane extensible elastica with arbitrary undeformed shape

A general expression for the strain energy of a homogeneous, isotropic, plane extensible elastica with an arbitrary undeformed configuration is derived. This expression appears to be suitable for one-dimensional models of polymers or vesicles, the natural configuration of which is characterized by locally changing curvature. In a linear setting, we derive the macroscopic stress–strain relations, providing an universal criterion for the neutral curve location. In this respect, we further demonstrate that the neutral curve existence constitutes the fundamental requirement for the conformational dynamics of any inextensbile biological filament.

Micro and Macroscopic Stress-Strain Relations in Disordered Tessellated Networks.

We demonstrate that for a rigid and incompressible network in mechanical equilibrium, the microscopic stress and strain follows a simple relation, σ=pE, where σ is the deviatoric stress, E is a mean-field strain tensor, and p is the hydrostatic pressure. This relationship arises as the natural consequence of energy minimization or equivalently, mechanical equilibration. The result suggests not only that the microscopic stress and strain are aligned in the principal directions, but also microscopic deformations are predominantly affine. The relationship holds true regardless of the different (foam or tissue) energy model considered, and directly leads to a simple prediction for the shear modulus, μ=⟨p⟩/2, where ⟨p⟩ is the mean pressure of the tessellation, for general randomized lattices.

Multiscale simulation of elastic response and residual stress for ceramic particle reinforced composites

In this study, the elastic response and residual stress of the ceramic matrix composites were simulated in multiscale view for exploring the elastic modulus of the two-phase composites reinforced with ceramic particles by diffraction method. Combined with the macroscopic stress-strain relationship of two-phase composites, the effective elastic response model under uniaxial loading was theoretically predicted by introducing the effective representative volume element (RVE). Subsequently, the effective elastic properties of the material and its constituents were calculated, along with comparison with the experimental values reported in the literature. On the basis of Eshelby's inclusion theory, a micromechanical elastic response model for the two-phase composites was established, and a series of micromechanical field equations related to the crystal planes diffraction elastic constants were derived. A comparison with the different micromechanical models for predicting the crystal planes diffraction elastic constants of the ceramic matrix and particle reinforcement was carried out, so as to qualitatively and quantitatively analyze the residual stress. It was revealed that the effective elastic parameters of the ZrB2 matrix and SiC particle reinforcement were very close to the experimental values reported in literature, and the calculated values of the elastic modulus in seven crystallographic diffraction directions were similar to the experimental values. In addition, the average residual stress of the SiC reinforcement and the ZrB2 ceramic matrix predicted by the developed model were consistent with the measured, which proved the reliability and accuracy of the theoretical model for multiscale simulation of the residual stress of two-phase composites.

Friction-damage coupled models and macroscopic strength criteria for ice-saturated frozen silt with crack asperity variation by a micromechanical approach

This paper aims to present physical friction-damage coupled models and derive macroscopic nonlinear strength criteria for ice-saturated frozen silt. Two material scales are considered here. The material at the mesoscale is composed of a frozen silt matrix and embedded mesocracks. At the microscale, the frozen silt matrix is composed of elastic mineral grains and elastic ice crystals. Considering this microstructure, for the ice-saturated frozen silt, the plastic deformation is related to frictional sliding along the mesocracks, and damage is due to the propagation of mesocracks. We obtain the effective elastic properties with a two-step linear Mori-Tanaka homogenization procedure. For the second homogenization step, we deduce the macroscopic stress-strain relations and local thermodynamic forces associated with damage and plasticity. Then, an energy release-based damage criterion is developed to capture the evolution of damage, and a friction sliding criterion with an associated/nonassociated local plastic flow rule is introduced to describe the rate of plasticity. The friction sliding criterion considers the variation of surface asperities of mesocracks as a result of pressure melting and damage evolution. In this context, associated/nonassociated multiscale friction-damage models are established. Furthermore, associated/nonassociated macroscopic nonlinear strength criteria as inherent parts of the corresponding multiscale models are derived under a large range of compressive stresses. For application, a semi-implicit local numerical algorithm of the multiscale models is developed. The accuracy of associated/nonassociated multiscale models is assessed by comparing their numerical simulations with conventional triaxial compression (CTC) tests. Although the associated multiscale model correctly predicts the nonlinear strength behavior and axial deformation of the Lanzhou frozen silt under CTC tests with different temperatures, it fails to quantitatively reproduce volumetric deformation. Nonassociated multiscale model predictions with experimental data of volumetric deformation are significantly improved compared to the associated multiscale model.

3‐D base force element method on meso‐damage analysis for recycled concrete

AbstractThe 3‐D base force element method (BFEM) for damage problems is proposed, which is applied to analyze the damage mechanism of recycled aggregate concrete (RAC). A piecewise curve damage constitutive model is given to simulate the constitutive relationships of RAC phases. A spatial random aggregate model of RAC is proposed. 3‐D numerical simulations of RAC under uniaxial mechanical stress are carried out. The macroscopic stress–strain relationship and failure process of RAC under uniaxial stress based on the 3‐D BFEM are obtained. The numerical results show a good consistency with the experimental results. This illustrates that the numerical simulation can reflect the nonlinearity deformation, stress redistribution, and crack propagation process of RAC. In addition, the influence of recycled aggregate replacement percentage on strength and elastic modulus is investigated. The results show that the content proportion of recycled aggregate has a great effect on RAC, which have to be considered in the analysis and the application of RAC.

Comparison of progressive damage simulation of 3D woven composites between voxel and conformal discretization models

This paper comprehensively compares the progressive damage simulation of 3D woven composites between the voxel and conformal mesh models. A progressive damage model for capturing the damage mechanisms of 3D woven composites is proposed, in which the longitudinal fiber fracture, transverse inter-fiber crack and matrix failure are detected by the Puck criterion, 3D hashin criteria and modified von Mises criterion, respectively. Benefiting from the periodicity of the woven architecture, a mesoscopic representative volume cell with high fidelity is constructed based on the microscope observations. The voxel and conformal meshing techniques are employed to discretize the periodic RVC model, and a mesh convergence analysis is performed to estimate the influence of element size. The comparison of the two discretization models is conducted in terms of fiber volume fraction, macroscopic stress-strain relations, damage developments and local stress fields. The results indicate that the damage initiations and developments obtained from voxel models are highly influenced by the spurious stress concentrations and artificial connections induced by the steplike elements.

A novel technique for dynamic shear testing of bulk metals with application to 304 austenitic stainless steel

This paper describes a new single-shear specimen (SSS) and method to characterize the dynamic shear behavior of bulk metals using a traditional Split Hopkinson Pressure Bar (SHPB). By this method, the shear behavior of materials can be tested conveniently over a wide range of strain rates within 105 s−1. This technique was applied to a 304 austenitic stainless steel (ASS) under shear strain rates from 0.001 s−1 to 38700 s−1 at room temperature. Based on finite element (FE) simulations, it was found that the deformation of the specimen shear zone was dominated by shear stress/strain components. Stress state parameters represented by stress triaxiality η and Lode angle parameter θ- were found very close to zero, indicating a deformation mode of simple shear. Besides, an obvious gap existed between the local deformation behavior in the specimen shear zone and the macroscopic stress-strain relations measured by the strain gauges on the SHPB bars. A correction coefficient method was adopted to extract the real shear behavior from the experimentally obtained force-displacement data. Through comparisons between the tested and simulated stress-strain curves, a good agreement was obtained.

Tensile Fracture Behavior of Corroded Pipeline: Part 1—Experimental Characterization

The understanding of the axial tensile behavior of environmentally corroded pipelines is of great significance for the design, maintenance, and evaluation of such structures. This article presents some experimental data recorded from 210 tensile tests on pipe, which were corroded from grade of 10% to 70% by electrochemical accelerated corrosion method. The fracture modes show that, for the uncorroded pipe, the fracture frequently occurs in the middle of the specimen and then propagates perpendicular to the loading direction. However, for the corroded pipe, the crack’s position, evolution angle, and path have strong randomness. The comparative analysis based on the macroscopic stress‐strain relationship shows that the rapid decrease of the yield stress, ultimate strength, and strain at the fracture for corroded pipe are correlated with the fracture patterns; i.e., the fracture patterns of pipe are changed from uniform to scattered with the continuous increase of the corrosion rate. The reduction factor based on experimental data is recommended for the consideration of the corrosion effect on the tensile strength of the steel pipe. Discussion on the tensile capacity during the service time is also presented.

Study on Voxel Finite Element Analysis of Open-Cell Polyurethane Foam

Establishment of a design method for the macroscopic stress-strain relationship of open-cell foam has been investigated because of the foam’s complicated microstructures. In this study, a material design method for the mechanical behavior of open-cell polyurethane foam using voxel finite element analysis is proposed to consider the microscopic structure and matrix properties. A finite-strain hyperelastic model was applied to a matrix of polyurethane foam. The Mooney-Rivlin model was adopted for the potential energy function of the hyperelastic model. To determine the mechanical properties of the matrix, original, solid specimens of polyurethane were prepared. The material parameters of the matrix were identified based on the tensile loading test results of the solid specimens. Microstructures of the open-cell polyurethane foam were determined using a CT-scanning system. Finite element models constrained by the original microstructural configurations were applied to numerical simulations. Periodic finite element models based on the modified microstructural configurations, the relative density of which was the same as that of the original models, were applied to the simulation. Based on the numerical results, verification of the design performance of the simulation code for open-cell polyurethane foam was performed. The simulation results were reasonably consistent with compression loading test results up to the plateau region.

A novel DEM approach for modeling brittle elastic media based on distinct lattice spring model

The Discrete Element Method (DEM), also known as Distinct Element Method (DEM), is extensively used to study divided media such as granular materials. When brittle failure occurs in continuum such as concrete or ceramics, the considered media can be viewed as divided. In such cases, DEM offers an interesting way to study and simulate complex fracture phenomena such as crack branching, crack extension, crack deviation under coupled mode or crack lip closure with friction.The fundamental difficulty with DEM is the inability of the method to deal directly with the constitutive equations of continuum mechanics. DEM uses force–displacement interaction laws between particles instead of stress–strain relationships. Generally, this difficulty is bypassed by using inverse methods, also known as calibration processes, able to translate macroscopic stress–strain relationships into local force–displacement interaction laws compatible within DEM frameworks. However, this calibration process may be fastidious and really hard to manage.The presented work proposes to improve the Distinct Lattice Spring Model in order to deal with non-regular domains, by using Voronoi cells, which allow to completely fill the volume space of discrete domains. With this approach, the rotational effects must be included in the contact formulation, which enables the management of large rigid body rotations. This work also introduces a simple method to manage brittle fracture. Using non-regular domains avoids the cracks paths conditioning, and allows to reproduce quantitatively the Brazilian test, very popular in the rock mechanics community.

Rock Failure Analysis under Dynamic Loading Based on a Micromechanical Damage Model

A micromechanical constitutive damage model accounting for micro-crack interactions was developed for brittle failure of rock materials under compressive dynamic loading. The proposed model incorporates pre-existing flaws and micro-cracks that have same size with specific orientation. Frictional sliding on micro-cracks leading to inelastic deformation is very influential mechanism resulting in damage occurrence due to nucleation of wing-crack from both sides of pre-existing micro-cracks. Several homogenization schemes including dilute, Mori-Tanaka, self-consistence, Ponte-Castandea & Willis are usually implemented for up-scaling of micro-cracks interactions. In this study the Self-Consistent homogenization Scheme (SCS) was used in the developed damage model in which each micro-crack inside the elliptical inclusion surrounded by homogenized matrix experiences a stress field different from that acts on isolated cracks. Therefore, the difference between global stresses acting on rock material and local stresses experienced by micro-crack inside inclusion yields stress intensity factor (SIF) at the cracks tips which are utilized in the formulation of the dynamic crack growth criterion. Also the damage parameter was defined in term of crack density parameter. The developed model was programmed and used as a separate and new constitutive model in the commercial finite difference software (FLAC). The dynamic uniaxial compressive strength test of a brittle rock was simulated numerically and the simulated stress-strain curves under different imposed strain rates were compared each other. The analysis results show a very good strain rate dependency especially in peak and post-elastic region. The proposed model predicts a macroscopic stress-strain relation and a peak stress (compressive strength) with an associated transition strain rate beyond which the compressive strength of the material becomes highly strain rate sensitive. Also the damage growth process was studied by using the proposed micromechanical damage model and scale law was plotted to distinguish the dynamic and quasi-dynamic loading boundary. Results also show that as the applied strain rate increases, the simulated peak strength increases and the damage evolution becomes slower with strain increment.

Macro/micro simultaneous validation for multiscale analysis of semi-periodically perforated plate using full-field strain measurement

Multiscale analysis of a semi-periodically perforated plate based on a homogenization theory is experimentally validated both macroscopically and microscopically, using a full-field strain measurement. To do this, a plate-fin-type perforated plate with a misaligned microstructure is considered as a semi-periodically perforated plate. Then, a homogenization theory that can analyze macroscopic behavior and microscopic stress and strain distributions of the perforated plate is presented. To validate the theory, a tensile test of a plate-fin-type semi-periodically perforated plate made of epoxy resin is conducted. During the test, the microscopic deformation of the specimen is observed with a digital image correlation (DIC) full-field measurement system, from which microscopic strain distribution of the specimen is calculated. It is shown that the obtained strain distribution satisfies the unit-cell periodicity except at edges of the periodic structure, and that the strain distribution is in good agreement with the result of analysis using the homogenization theory. It is also shown that the macroscopic stress–strain relationships obtained by the experiment and analysis agree well, supporting the macroscopic and microscopic validity of the multiscale analysis using the homogenization theory.

Optimal design of a honeycomb core composite sandwich panel using evolutionary optimization algorithms

The present paper deals with the optimal design of a composite sandwich panel with honeycomb core structure using particle swarm optimization (PSO) technique. The face sheets of sandwich panel are considered to be thin and the sandwich panel is subjected to a uniformly distributed normal load. The Navier type solution and the closed-form expressions for the macroscopic in-plane elastic constants of the honeycombs are used to predict the deflection of the panel. Also, the maximum stress in the composite sandwich panel is determined using the macroscopic stress–strain relation of the honeycomb core and the plate. Niching Memetic PSO (NMPSO) and Locally Informed Particle Swarm (LIPS) variants of PSO are examined to minimize the weight of the panel. Numerical results showed that the optimal geometry of the honeycomb cell has this property that its radius and thickness converge to their lower bounds while its length converges to its upper bound. This means that to have an optimal panel, each cell should have the allowable minimum cross section (highest number of cells) and maximum allowable length. Moreover the effects of panel aspect ratio, cell width and applied load were examined. Also, the numerical results confirm the efficiency and effectiveness of the NMPSO in finding optimal solution on the constrained and unconstrained objective functions.

Micromechanical Analysis of SiC/Al Metal Matrix Composites: Finite Element Modeling and Damage Simulation

The influence of interface strengths and microstructures on the strength and damage of SiC particle reinforced aluminum Metal Matrix Composite (MMC) is investigated under uniaxial tensile, simple shear, biaxial tensile and combined tensile and shear loadings. An algorithm to generate automatically the microstructural models of MMCs with random distribution of particle shapes, dimensions, orientations and locations is proposed and implemented within Matlab. A damage model based on the stress triaxial indicator is developed to simulate the ductile failure of metal matrix, the other damage model based on the maximum principal stress criterion is developed to simulate the brittle failure of SiC particles, and 2D cohesive element is utilized to describe interface decohesion between matrix and particles. A series of numerical experiments are performed to study the macroscopic stress–strain relationships and microscale damage evolution in MMCs under different loading conditions.

Instability of a composite reinforced with coated inclusions due to interface debonding

A theoretical analysis of the instability arising from interface debonding in a composite containing coated inclusions subject to remote hydrostatic tensile traction is presented. The composite macroscopic stress–strain relation incorporating the influence of interfacial displacement jumps is discussed in detail for our proposed spherically symmetric model. Because of the model assumptions, this relation is limited to composites with small volume fractions of the inclusion and coating. The influences of the maximum traction and bonding characteristic length at the inclusion/coating and coating/matrix interfaces on the peak stress, corresponding strain, and strain interval are fully investigated. The various interfacial parameters are found to have significant influences on the instability of the composite arising from interface decohesion at both interfaces. In particular, the bonding characteristic length for the coating/matrix interface is the most critical parameter for improving the overall bearing capacity of the composite. These results can serve as guidelines for material selection to optimize composite performance.

Crystal Plasticity Analysis of Scale Effect on Tensile Properties of Ferrite/Cementite Fine Lamellar Structure under Lattice Strain

Tensile properties of ferrite lamella in pearlite under lattice strain are examined by a strain gradient crystal plasticity analysis. Tensile direction is made to be parallel to the lamella. Obtained results of macroscopic stress-strain relation of the lamella show significant increase of yield stress and strain hardening rate with the reduction of the lamella thickness and further increase of the yield stress with positive normal lattice strain parallel to the tensile direction in the ferrite layer. Whereas normal lattice strain perpendicular to the tensile direction contributes little to the tensile properties.