Coupled Constitutive Model Research Articles

A photo-chemo-mechanical coupling constitutive model for photopolymerization-based 3D printing hydrogels

Photopolymerization-based 3D printing has emerged as a key technology in hydrogel manufacturing, broadening the attributes of hydrogels and extending their applications into diverse engineering fields. However, the mechanical properties of hydrogels dramatically impact the functionality and quality in practice. It is necessary to develop an appropriate theoretical model to predict the evolution of the mechanical properties of hydrogels during the photopolymerization process. In this work, systematical experiments were performed to investigate mechanical properties of PAAm hydrogel under different photopolymerization condition. The results reveal a noticeable increasement in both elastic and viscous behavior of hydrogel with the advancement of polymerization. To fully capture the experimental observations, we developed a coupled photo-chemo-mechanical theoretical framework that integrates reaction kinetics with a physically-based viscoelastic constitutive model. Within this model, the degree of conversion serves as an internal variable, which related to microscopic structures such as correlation length, and tube diameter. The developed model exhibits remarkable prediction ability for hydrogels with various degree of polymerization. The current work paves a potentially new avenue for understanding the evolution of mechanical properties in photopolymerized hydrogels, providing theoretical guidance for the manufacturing of hydrogels through photopolymerization-based 3D printing.

Damage Analysis and Startup Schedule Optimization of Steam Turbine Rotors With an Anisotropic Damage Coupled Viscoplastic Constitutive Model

Abstract The optimization of the operation scheme is of great significance for improving the flexibility of thermal power plants in energy systems dominated by renewable energy. However, thermal stress and corresponding thermomechanical fatigue damage are the main limitations. A unified viscoplastic constitutive model coupled with anisotropic damage is introduced and validated by comparing the experimental and simulated hysteresis loops and cyclic softening curves. The model is implemented into the ansys software by using the USERMAT subroutine to numerically investigate the high-temperature fatigue behavior of a 1000 MW steam turbine rotor on different startup schedules. The critical areas of the rotor are studied in terms of temperature, stress, accumulated inelastic strain, and damage. Based on the damage analysis, the hot start schedule is optimized and validated. The startup time can be significantly shortened within permitted fatigue damage. Moreover, the life expenditure under different loading-up rates is calculated and the extra startup costs can be evaluated accordingly for wider application.

Rock fracture propagation in a damage zone by a constitutive model coupling volume and cohesive elements

AbstractThis paper presents a method to simulate fracture propagation in a damage zone in 2D, whereby Cohesive Zone (CZ) elements are assigned the same Continuum Damage Mechanics (CDM) model as their adjacent finite elements. Material hardening is a result of damage‐induced stiffness reduction in the finite and cohesive elements, while softening is modeled by cohesive debonding only. The damage components calculated at the numerical integration points of each finite element are averaged and that average is assigned to the nodes of the adjacent CZ elements. CZ element debonding triggers when a critical damage threshold is reached, beyond which, a linear softening law is used in both mode I and mode II. The proposed model is calibrated against published triaxial compression tests conducted on shale. Single‐CZ element simulations confirm that, below the critical damage threshold, elastic deformation energy is stored and energy is dissipated by damage propagation and irreversible deformation. Passed the critical damage threshold, stored elastic energy is released in the form of cohesive debonding energy. Borehole breakout simulations indicate that the proposed CDM‐based CZ model can predict the formation of spiral‐shaped fractures around a free circular cavity under biaxial stress. Simulations of fracture propagation in textured materials suggest that cohesive debonding within and between grains is triggered by the coalescence of localized zones of continuum damage, and that the grain size distribution affects both the fracture pattern and the softening behavior of the specimen considered.

CEM–DSR-based explicit solution of limit expansion pressure in unsaturated soils and its application

In this study, an explicit solution for the limit expansion pressure of cavity expansion in unsaturated soil, which follows a hydraulic coupling constitutive model, was proposed based on the cavity expansion method (CEM) and deep symbolic regression (DSR). In detail, a semi-analytical elastic–plastic solution for cavity expansion in unsaturated soils was obtained based on the unsaturated critical state model; hence, a database was created. To obtain an explicit solution for the limit expansion pressure, DSR, which is a gradient-based approach to symbolic regression based on reinforcement learning, was applied. Subsequently, 13- and 4-parameter regression analyses were conducted, with satisfactory results being obtained. Finally, based on the proposed explicit expression, a theoretical calculation model for the jacked-pile penetration resistance in unsaturated soils was established. The study presented in this paper opens up possibilities for obtaining theoretical solutions to issues such as predicting pile driving performance in unsaturated soils.

A hydraulic-mechanical (HM) coupling constitutive model for unsaturated soil-continuum interfaces considering bonding effect

Unsaturated soil-continuum interfaces determine the behavior of structures such as friction piles embedded in unsaturated soil and retaining walls with unsaturated backfill. Developing accurate constitutive models for these interfaces is essential for innovative computational design and analysis in geotechnical engineering. This study presents a rigorous mathematical derivation to quantify the bonding effect at interparticle and pore space contact zones, introducing a bonding variable and a state parameter based on the ratio between current and critical void ratios. The novelty lies in introduction of a hydraulic-mechanical (HM) coupling constitutive model for unsaturated soil-continuum interfaces, incorporating the bonding effect and critical-state concept. Despite the 16 parameters in proposed model, all are methodically calibrated using suction-controlled interface shear tests. Effectiveness of the model is demonstrated through predictions in interface shear tests involving unsaturated Toyoura sand, smooth/rough steel, and published tests with unsaturated Minco silt and steel. The model's applicability is extended to diverse conditions, including structural stiffness, interface thickness, counterface roughness, and drying- wetting (D-W) cycles. This model provides a unified framework for analyzing volume changes and stress-displacement responses in unsaturated soil-continuum interfaces, providing valuable insights for design of pile foundations in unsaturated soils.

Study on Experimental and Constitutive Model of Granite Gneiss under Hydro-Mechanical Properties

Permeability, as a critical element in making sure the underground facilities are secure, is a vital consideration in analyzing the rock material seepage. Selecting granite gneiss from underground oil storage as the research sample in this study. Triaxial mechanical property tests under different hydro-mechanical properties were carried out under the rock full-automatic triaxial servo system that controls the application of axial pressure, confining pressure, and seepage pressure. Through experiments carried out, we obtained the rock samples’ mechanical properties and permeability in three stages of the stress–strain process. The study shows that the seepage pressure considerably affects granite gneiss strength and deformation parameters under hydro-mechanical properties. On the basis of the same confining pressure, in pace with the growth in seepage pressure, elastic modulus, the deformation modulus, and the peak strength present a prominent decreasing inclination. The derived mechanical parameters are bound up with the stages we divided. This study analyzes and discusses the relationship among the strains and permeability, establishing the granite gneiss hydro-mechanical coupling constitutive model. Verification shows the results in numerical and experimental matches well, indicating that the rock hydro-mechanical properties could be effectively represented by the constitutive model.

Modeling on magnetization behavior of ferromagnetic material during cyclic deformation

In this paper, a nonlinear magneto-mechanical coupling constitutive model is established to describe the magnetization behavior of ferromagnetic materials under cyclic elastoplastic deformation. The critical state is introduced into the hysteretic magneto-mechanical model. In the critical state, the magnetization rates of loading and unloading are different. A new nonlinear plastic effective magnetic field is proposed by considering the effect of pinning sites caused by cross slip dislocation to describe the magnetization behavior under asymmetric cyclic loading. The softening factor and activation condition of plastic modulus parameter are introduced based on the cyclic plastic constitutive model to describe the decrease of plastic modulus. A new magnetization model for ferromagnetic materials under cyclic plastic deformation is established by combining the magneto-mechanical coupling model with the cyclic plastic constitutive model. Compared with the experiments and existing models, it is shown that the proposed model can capture the deformation and magnetization behavior well under cyclic loading.

Fracture Resistance of Chemo-Mechanically Coupled Solid Solutions

Abstract Fracture in solid solutions, such as electrodes for lithium-ion batteries and fuel cells, is mediated by intricate interactions between solid-state diffusion and crack propagation. In this work, we developed a composition-dependent cohesive zone model and integrated it with a chemo-mechanical coupling constitutive model to study the fracture mechanisms of solid solutions. The computational framework was used to investigate the effective fracture properties of chemo-mechanically coupled solid solutions over a wide range of crack growth velocities and compositional dependence of intrinsic fracture energy. The results revealed an important characteristic crack velocity, which is set by the ratio of the diffusivity to the intrinsic fracture energy and dictates the effective fracture resistance of the material. We also applied the model to study the fracture behavior of two-phase lithiated silicon (Si) and germanium (Ge) nanostructures as candidate high-capacity anodes for next-generation lithium-ion batteries, and showed that Ge nanostructures are more fracture resistant than their Si counterparts. The computational study presented here provides important insights for the rational design, operation, and mechanical testing of chemo-mechanically active material systems for their use in energy storage and conversion.

A new hydro-mechanical coupling constitutive model for brittle rocks considering initial compaction, hardening and softening behaviors under complex stress states

After the excavation of underground engineering, the failure and instability of surrounding rock under hydro-mechanical coupling conditions is a common type of engineering disaster. However, the hydro-mechanical coupling mechanical characteristics of rock have not been fully revealed, and suitable models for the stability analysis of surrounding rock under hydro-mechanical coupling conditions are very scarce. Therefore, a series of triaxial compression and cyclic loading and unloading hydro-mechanical coupling tests were carried out to study the mechanical characteristics, deformation and mechanical parameters of rock under different confining pressures and pore pressures. Then, based on Biot’s effective stress principle, a hydro-mechanical coupling damage constitutive model within the framework of irreversible thermodynamics was proposed to describe the initial compaction effect, pre-peak hardening and post-peak softening behaviors. The functional relationships between the proposed model key parameters (η and ζ) and the effective stress were established to characterize the pre- and post-peak nonlinear behaviors of rock. A compaction function Ck for the evolution of the undamaged Young’s modulus in initial compaction stage was introduced to characterize the pre-peak compaction effect. A user-defined material subroutine (UMAT) was compiled in ABAQUS to numerically implemented the proposed model. The numerical simulation results are highly consistent with the test results, the proposed model can also predict the hydro-mechanical coupling characteristics of rock under untested stress levels. In addition, the yield function of the proposed model considers the influence of intermediate principal stress, which is also suitable for the simulation of hydro-mechanical coupling characteristics under true triaxial stress states.Graphical abstract

Durability and Performance Analysis of Polymer Electrolyte Membranes for Hydrogen Fuel Cells by a Coupled Chemo-mechanical Constitutive Model and Experimental Validation.

In this paper, a chemo-mechanically coupled behavior of Nafion 212 is investigated through predictive multiphysics modeling and experimental validation. Fuel cell performance and durability are critically determined by the mechanical and chemical degradation of a perfluorosulfonic acid (PFSA) membrane. However, how the degree of chemical decomposition affects the material constitutive behavior has not been clearly defined. To estimate the degradation level quantitatively, fluoride release is measured. The PFSA membrane in tensile testing shows nonlinear behavior, which is modeled by J2 plasticity-based material modeling. The material parameters, which contain hardening parameters and Young's modulus, are characterized in terms of fluoride release levels by inverse analysis. In the sequel, membrane modeling is performed to investigate the life prediction due to humidity cycling. A continuum-based pinhole growth model is adopted in response to mechanical stress. As a result, validation is conducted in comparison with the accelerated stress test (AST) by correlating the size of the pinhole with the gas crossover generated in the membrane. This work provides a dataset of degraded membranes for performance and suggests the quantitative understanding and prediction of fuel cell durability with computational simulation.

Temperature-Moisture-Mechanical coupling fatigue behaviours of screwed Composite-Steel joints

This paper seeks to probe temperature-moisture-mechanical coupling fatigue behaviours of screwed composite-steel joints by using experimental and numerical methods. Novel temperature-moisture-mechanical (TMM) coupling constitutive model, fatigue failure criterion and progressive fatigue damage algorithm (PFDA) are first devised for simulating fatigue failure mechanisms and modes and for predicting fatigue lives of single-lap screwed composite-metal joints (CMJs) in arbitrary temperature-moisture environment. In order to validate the presented model and algorithm, tension–tension fatigue tests are then conducted on the CMJs in four representative environments: low temperature of −40 °C and dry (LTD), room temperature of + 23 °C and dry (RTD), room temperature of + 23 °C and wet (RTW) and elevated temperature of + 55 °C and wet (ETW), respectively. Finally, the TMM coupling fatigue behaviors of the CMJs are analyzed and discussed from the experiments and progressive fatigue damage modelling, and predicted results agree well with experimental findings, demonstrating the feasible and practical usage of the proposed model.

Damage constitutive model and mechanical properties of jointed rock mass under hydro-mechanical coupling

The damage evolution law and mechanical property weakening mechanism of jointed rock mass under hydro-mechanical coupling are important scientific problems in deep rock mass excavation. In this paper, the mineral composition of rock specimens was analyzed, and the distribution law of nuclear magnetic resonance T2 spectrum of granite under different axial stress was studied. Then the mechanical properties of jointed rock samples under triaxial stress and seepage pressure were studied. Based on the analysis of the stress field at the joint tip, the damage model of the jointed rock mass was obtained. Furthermore, the tensor of damage variables was analyzed, and the stress intensity factor under seepage pressure was calculated. The seepage pressure promotes the damage evolution process of jointed rock mass specimens and accelerates the strength failure of jointed rock mass specimens. The damage constitutive model of jointed rock mass under seepage pressure was established and verified. Based on the weakening law of seepage pressure, the developed hydro-mechanical coupling constitutive model was customized and imported into FLAC3D with the calculation function of the Mohr-Coulomb constitutive model as the compilation template. A three-dimensional numerical simulation model of underground rock mass engineering was established to analyze the stability of rock mass with different joint dip angles. For the surrounding rock with the dominant angle of 85° in the mine, its stability is poor, and the support needs to be strengthened.

Thermomechanical coupling effect on the phase transition wave propagation in an SMA TiNi bar subjected to shock loading

Phase transition can strongly affect the stress wave propagation features. In this paper, the influence of temperature on the phase transformation wave (PTW) propagation was investigated theoretically and numerically with a thermo-mechanical coupling constitutive model and kinetic relation of the phase transition. The results showed that the temperature interface is also the phase transition threshold stress discontinuity. For shock wave propagating in the rod with fixed temperature interfaces, the transformation from shock wave to phase transition wave, then to an elastic wave was predicted due to the temperature interface effect, and an unloading elastic wave during loading was discovered induced by the boundary effect, which has barely been studied before. Moreover, for the adiabatic shock loading, phase transition wave front is not only a material interface, but also a temperature discontinuity. A loading shock wave with phase transition was predicted due to the second phase strengthening and an unloading shock wave with reverse transformation was generated arising from unloading path changing effect induced by adiabatic temperature rise across the transformation shock front. The theoretical analysis and simulation discloses the evolution of phase transition waves affected by temperature interfaces and reflect the intrinsic characteristic of phase transition materials with strong nonlinear behavior due to the dynamic thermo-mechanical coupling.

Experimental investigation and micromechanics-based damage modeling of the stress relaxation mechanical properties in gray sandstone

The geomechanical behaviors of the gray sandstones under dry and fully saturated conditions are investigated by both of experimental and numerical studies in this paper. Conventional triaxial compression tests and single-stage stress relaxation tests are performed on cylindrical specimens under these two different states. The experimental results show that both peak strength and elastic modulus are reduced due to the presentence of the pore water which is contributed the weakening. While the typical incomplete attenuation characteristics of the two states are only having slight difference, the final stress relaxation extent under the statured condition is larger than the dry condition when the strain ratio is the same. Based on the pioneering work, a new micromechanical damage–friction coupling constitutive model with containing fewer parameters and each being physically meaningful for the stress relaxation is proposed here. Its chief novelty lies in considering both the instantaneous plastic internal variables and relaxation load to build the relationship between model’s parameter and experimental data. The single-stage relaxation tests of the sandstones are well-benchmarked with this model, which indicates that the proposed new model can capture the incomplete attenuation features of stress relaxation behavior of gray sandstones.

Size-dependent and nonlinear magneto-mechanical coupling characteristics analysis for extensional vibration of composite multiferroic piezoelectric semiconductor nanoharvester with surface effect

We study the extensional vibration of composite multiferroic piezoelectric semiconductor (PS) nanoharvester driven via a time-harmonic magnetic field. A theoretical analysis about working performances of device is performed based on zero-order plate equations with surface and nonlocal effects, consisting of a nonlinear magneto-mechanical coupling constitutive model for giant magnetostrictive material Terfenol-D and a linear phenomenological theory of PS material ZnO. Numerical results indicate that the basic bahaviors (including resonant frequency, bandwidth characteristic, magneto-electric (ME) coupling effect, output power and energy conversion efficiency) of the nanoharvester, can be dramatically improved through circuit types, semiconduction, external magnetic field, pre-stress and surface effect. This work is essential and crucial for understanding the size-dependent and nonlinear mechanical behaviors of multiferroic PS nanodevices under the extremely complex magnetic field and pre-stress field environments.

Mechanical behavior and constitutive model of NEPE solid propellant in finite deformation

Nitrate ester plasticized polyether (NEPE) solid propellant was widely used in carrier rocket and guided missiles, owing to its excellent mechanical properties, high specific impulse and good performance of low temperature storage. The material of NEPE suffered from thermal cycle, high pressure impulse and vibration during service life. Thus, the mechanical properties of NEPE had important implications for the safety of structure and service life. Experimental results indicated that the material presents significant time-dependence and nonlinear characteristics. In order to clarify the damage mechanism of NEPE solid propellant, the mesostructure evolution was investigated with the 3D in-situ observations by using synchrotron radiation computed tomography (SR-CT). The voids initiated at the interface between matrix and particles and propagated along the loading direction. With the increasing of loading, matrix breaking, particles breaking and debonded particles were observed in the near-surface regions. Furthermore, a visco-hyperelastic constitutive model coupling damage was proposed to describe the mechanical behavior of NEPE under finite deformation. The constitutive model provides a good simulation with experimental results, which is meaningful to the structure integrity assessment of NEPE solid propellant.

Unloading and reloading stress-strain relationship of recycled aggregate concrete reinforced with steel/polypropylene fibers under uniaxial low-cycle loadings

To solve the key scientific problems such as low toughness and easy cracking of recycled aggregate concrete (RAC), A new sustainable material (fiber-reinforced recycled aggregate concrete - FRAC) was obtained by adding steel fiber (SF) and polypropylene fiber (PPF) into RAC matrix. Few experimental results were reported for the material under uniaxial low-cycle loading, and consequently, there is a gap in constitutive propositions to predict its behavior. Thus, one purpose of this research is to provide experimental results for FRAC characterizing damage growth and residual strain during cyclic compression in low-cycle tests with increasing strain amplitudes. Another purpose is to present a constitutive model to predict this behavior of FRAC accounting for fiber content. It is worth noting that the present results are relevant to displacement-controlled tests. The development law of residual strain (permanent strain) is explored, and the relationships between residual strain and unloading strain/reloading strain are proposed. The unloading stress-strain/reloading stress-strain equations are given. The damage evolution law of FRAC is revealed. Also, a new damage model represented by residual strain is suggested accounting for the fiber content. Furthermore, a stress-strain constitutive model coupling damage for FRAC is proposed. The model predicted with accuracy the unloading path, reloading path, residual strain development, and damage evolution for the composite accounting for fiber content.

Tunability of resonator with pre-compressed springs on thermo-magneto-mechanical coupling band gaps of locally resonant phononic crystal nanobeam with surface effects

A locally resonant (LR) thermo-magneto-mechanical phononic crystal (PC) nanobeam by periodically attaching “vertical spring-precompressed spring-mass” resonators onto the surface of base nanobeam is proposed, which the corresponding band structure is calculated by extending surface elasticity theory and thermo-magneto-mechanical coupling constitutive model to plane wave expansion (PWE) method. In addition, the influencing rules of resonator, thermo-magneto-mechanical fields, surface effects and geometric parameters are discussed. Numerical results and further analysis demonstrate that more band gaps with lower starting frequency and wider frequency range can be opened by periodically adding resonators onto the surface of nanobeam. The horizontal springs with larger degree of pre-compression can obtain lower starting frequency of first band gap. The effect of operating temperature on band gaps can be regarded as the relation between operating temperature and Young’s modulus of epoxy. Moreover, a singular pre-stress is existed that makes the band gaps not easily opened, which keeps increasing by increasing operating temperature, magnetic field, the ratio between width and thickness or decreasing the ratio between lengths of Terfenol-D and epoxy. All the researches are expected to be applied to the active control of vibration propagation in the field of nano thermo-magneto-mechanical system.

Constitutive behavior and microstructural evolution of 2060 Al–Li alloy under high strain rate: Experiment and simulation

Being impacted at higher strain rates, the dislocation density in the metal material increases, which leads to the phenomenon of grain refinement. The refined grains demonstrate the hardening effect of the material processed by high-velocity impacts well. However, the mechanical response and the microstructure evolution of the new material, 2060 Al–Li alloy, under high-velocity impact remain to be unclear. In this study, the mechanical behavior of 2060 Al–Li alloy at high strain rates was investigated by split Hopkinson pressure bar (SHPB), and the influence of higher strain rates on the microstructure evolution of 2060 Al–Li alloy was further revealed by X-ray diffraction (XRD) and electron backscatter diffraction (EBSD) experiments. Meanwhile, a coupling constitutive model was proposed to correlate the macro and micro properties of the material and was applied to characterize the mechanical behavior and microstructure evolution of 2060 Al–Li alloy. The experimental results showed that when the strain rate increased from 3189 s−1 to 9053s−1, a significant strain rate hardening phenomenon was exhibited in 2060 Al–Li alloy, which could be ascribed to the significant increase in the dislocation density. Meanwhile, as the strain rate increases, the proportion of low-angle grain boundaries (LAGB) in the material increases, along with the augmented sub-grains. After the impact, the Goss texture {110}<001> became conspicuous, while the Cube texture {100}<001> in the material became gradually eclipsed. When the strain rate is up to 9053s−1, the Goss texture took on orientational dominance. Finally, based on the coupling constitutive model, the dislocation density and grain size of the specimen after impact were predicted, and the calculated results were in good agreement with the experiments.

Multiple Solutions of Nonlinear Coupled Constitutive Relation Model and its Rectification in Non-Equilibrium Flow Computation

Multiple Solutions of Nonlinear Coupled Constitutive Relation Model and its Rectification in Non-Equilibrium Flow Computation