Elastoplastic Damage Model Research Articles

Cyclic behaviour of 3D-woven composites in tension: Experimental testing and macroscale modelling

Composites with 3D-textile reinforcement present several engineering advantages. However, their intricate yarn architecture also creates a material with a number of nonlinear behaviours and features, which need to be understood in order to enable their efficient use. To demonstrate the anisotropic development of such non-linear behaviours, and how they depend on loading mode, tensile samples of a 3D-woven layer-to-layer angle interlock carbon-fibre reinforced epoxy composite are tested experimentally (data shared publicly). More specifically, specimens are cut and tested at orientations of 0°, 15°, 30°, 45° and 90° relative to the direction of the warp yarns. The samples are tested cyclically by loading and unloading them at progressively higher displacement values. By monitoring the reduction in stiffness and the development of permanent strains it is possible to identify material parameter values used to calibrate an anisotropic macroscale elasto-plastic damage model. The model shows promising agreement with the experimental results.

A microcrack-based anisotropic damage model for concrete under mechanical loading and calcium leaching

In underground construction, concrete is always subjected to triaxial stress and calcium ion leaching, which results in anisotropic damage to concrete and reduce the durability of the structure. To capture the anisotropic damage properties of concrete subjected to mechanical-chemical coupling effects and predict the durability of underground concrete structure accurately, a microcrack-based anisotropic damage model is proposed. The mechanical damage, reflecting the density and direction of the microcracks caused by mechanical loading, is defined by a second-order tensor. The degree of chemical damage is defined by the amount of solid calcium phase lost in the concrete. Considering oriented microcrack and the influence of chemical damage on fracture toughness, the anisotropic mechanical damage evolution law of microcrack was established by linear fracture mechanics. A phenomenological chemical model governed by a diffusion law considering the variation of diffusion coefficient with stress induced microcracks is defined to describe the calcium dissolution process. The simulation results are in good agreement with the experimental results. Compared with the traditional elastoplastic damage model, the maximum creep error is only 0.114 ‰.

A simple, fast, and robust criterion for predicting fracture load and crack growth path in notched elastoplastic plates under mixed-mode loading

This study assesses the combined in-plane tensile/shear failure of aluminum plates containing notches. With this aim, a numerical method, i.e., the so-called equivalent material concept (EMC) in association with the extended finite element method (XFEM), is introduced to simulate the fracture phenomenon. The predicted failure load, initiation angle, and growth path are compared to experimental results reported for aluminum alloys in the literature to evaluate the functionality of the proposed method. Also, the accuracy of the EMC-XFEM model was compared to the conventional Ductile Damage method. The EMC-XFEM combined model is found to be fast and robust with appropriate accuracy in fracture predictions of ductile samples in comparison with the elastoplastic damage model and experimental data.

An elastoplastic damage ice material model based on modified Tsai-Wu yield criterion: Experiment, theory and numerical application

Ice, as a novel green and sustainable building material, has attracted more and more attention in building engineering. Appropriate ice material models are crucial for the performance analysis of the increasing ice structures. There is still challenging in modelling ice responses due to the complexity of ice. This study aims to present a nonlinear elastoplastic damage model for ice material. First, a triaxial compression test of artificial ice is conducted. Based on the test results, the modified Tsai-Wu failure criterion with better performance in the tensile zone and physical meaning for hydraulic strength is established. Then, combining plasticity theory with damage mechanics, an elastoplastic damage constitutive law considering the difference between tensile and compressive properties is proposed. The piecewise damage model and the Weibull exponential damage model are employed for compression and tension damage, respectively. Moreover, the numerical iterative algorithm is developed and a user-defined material subroutine (UMAT) is embedded in the finite element software ABAQUS to simulate the mechanical properties of ice. Furthermore, the constitutive model is verified by comparing the FEM results with the results of uniaxial compression, triaxial compression, and three-point bending tests. The results show that the constitutive model can well describe the stress-strain nonlinear behavior and capture the basic failure mode of ice materials. Finally, considering temperature affecting on the failure surface, a temperature dependent ice material model is developed. The current study would help in the design, operation and maintenance of ice structures.

Elastoplastic damage model and numerical implementation of nano‐silica incorporated concrete

AbstractAn energy‐based isotropic elastoplastic damage model is developed for investigating the elastoplastic damage responses and stress–strain relationships of nano‐silica incorporated concrete. The formulation employs a multiscale micromechanical framework to determine the effective elastic properties of composites at different scales. The stress–strain constitutive relation is derived by splitting the strain tensor into “elastic‐damage” and “plastic‐damage” parts while introducing the homogenized free potential energy function and the undamaged potential energy function. The elastoplastic damage response of the material is further characterized by elastic–plastic‐damage coupling. To construct realistic 3D three‐phase concrete mesostructures in numerical simulations, this paper introduces an encapsulation placement method that avoids particle overlap checking when placing aggregates. This methodology allows adjustments for the aggregate compactness as needed and enhances computational efficiency in concrete mesostructure construction. The numerical results of the modeling show good agreement with the experimental values in the open literature. Further, the influence of nano‐silica addition contents and ITZ (interfacial transition zone) thicknesses on the elastoplastic damage response of nano‐silica incorporated concrete are quantitatively and qualitatively investigated for the optimization of nano‐silica incorporated cementitious composites. The proposed model facilitates simulating and optimizing the mechanical characteristics of nano‐silica incorporated concrete and enhances the computational efficiency of 3D concrete modeling with the introduced encapsulation placement method.

Investigation of soil damping for offshore wind turbine monopile-soil system in stiff clay on elastoplastic-damage model

Damping plays a crucial role in the design of offshore wind turbine (OWT) monopile foundations. The soil damping of the monopile-soil system (MSS) represents the energy dissipation mechanism arising from the interaction between the pile and the soil. It is typically derived by back-calculating from the overall damping measured in the entire OWT structure. However, few studies have independently examined the soil damping in MSS, and the impact of key parameters such as pile diameter, pile embedded depth, cyclic load amplitude, and load eccentricity on the variation of soil damping in MSS remains unclear. This paper introduces an elastoplastic-damage constitutive model for the numerical simulation of the damping ratio variation in seabed soil and MSS. The model is implemented in ABAQUS software and validated against cyclic triaxial tests on stiff clay soil. On this basis, a three-dimensional finite element sensitivity study was conducted to elucidate the effect of these key parameters on the MSS damping ratio. The results of the study reveal that the MSS damping ratio exhibits a nonlinear and asymmetric trend as the loading cycles increase. The MSS damping ratio decreases with increasing pile diameter and embedded depth but increases with increasing lateral cyclic load amplitude and load eccentricity from the mudline.

A damage constitutive model for consistent description of static and fatigue behaviors of ultra-high performance concrete containing coarse aggregate

A suitable constitutive model for describing the mechanical behaviors of ultra-high performance concrete (UHPC) under various loading histories plays a vital role in analyzing its structural performance. In this work, a consistent elastoplastic damage model is developed for UHPC containing coarse aggregate (UHPC-CA) subjected to static and fatigue loads, in which the driving and alleviating effects induced by the inclusions of coarse aggregate and steel fiber are considered. For damage evolution, based on the acting mechanism of the non-uniformity of stress wave propagation determined by the loading rate on the mechanical responses of UHPC-CA, the loading rate is skillfully integrated into the damage evolution rule to achieve the consistent description of mechanical behaviors of UHPC-CA under static and fatigue loading conditions. Regarding plasticity growth, an empirical plastic deformation model is adopted to improve the computational efficiency of structural nonlinear analysis. To verify the applicability of the proposed model, a user-defined UMAT subroutine is further developed for the subsequent numerical implementation. The comprehensive comparisons between the numerical predictions and independent experimental results at both the material level and structural level solidly demonstrate the capacity of the consistent model to capture the main features concerning the mechanical performance of UHPC-CA subjected to different loading paths.

An Elastoplastic Damage Model for Sandstone Considering the Compaction Effect and Freeze–Thaw Action

An Elastoplastic Damage Model for Sandstone Considering the Compaction Effect and Freeze–Thaw Action

Experimental and model investigation on hydro-mechanical behaviour of sandy mudstone

The hydro-mechanical behaviour and the constitutive model of sandy mudstone were investigated in this article. Two groups of hydro-mechanical triaxial compression tests were conducted. The results indicated that the inelastic deformation, damage, permeability and failure of the sandy mudstone were affected by the pore pressure and confining pressure. The hydro-mechanical behaviour was characterised by the coupled elastoplastic damage model. This model was based on the effective stress principle and numerical return mapping algorithms. Sensitivity analysis was also performed to examine the effects of four key parameters on the modelling of elastoplastic and damage behaviour. This study can provide a foundation for physical understanding and mathematical modelling of sandy mudstone under coupled loads.

A fully coupled thermo-hydro-mechanical elastoplastic damage model for fractured rock

A detailed and fully coupled thermo-hydro-mechanical (THM) model for fractured rock is presented. This model distinguishes itself by harmoniously integrating elastoplastic material behaviour with a continuum damage mechanics framework. Solid matrix displacement, pore and fissure water pressures and temperature of the solid are introduced as the primary nodal variables. The ingenuity of this research is embedded in the intricate coupling of THM processes with plastic deformation and damage mechanics in a double porous medium, a venture that significantly broadens the remit of existing methodologies. The model is implemented using finite element method (FEM) and validation is achieved by comparing the FEM results against existing literature numerical outcomes describing linear and elastoplastic continuum damage behaviour of fractured rock. The model also exhibits an extraordinary proficiency in reproducing experimental triaxial test results, using THM components conjoined with elastoplastic bounding surface aspects and inherent hardening effects. It is imperative, nonetheless, to underscore the model's sensitivity to certain material properties, inclusive of strength parameters, leakage coefficients, and permeability attributes. This fully coupled THM model provides a comprehensive and sophisticated tool for investigating the behaviour of fractured rock under various loading conditions. It can help us better understand the physics of fractured rock behaviour and contribute to the development of more accurate and reliable models for engineering applications, such as CO2 injection.

Elastoplastic damage behavior of quasi-brittle rocks considering crack closure evolution

Crack closure evolution in compaction stage of quasi-brittle rocks is a very common phenomenon. A distinct feature of quasi-brittle rocks is that, under compression, presence of microcracks can increase nonlinear mechanical response of rock under low confining pressure, while gradually decrease nonlinear behavior of rock under high confining pressure. Previous studies have mainly focused on modelling the damage evolution caused by plastic strain, with few attempts to describe nonlinear behavior of compaction stage and reveal elastic damage dissipation mechanism triggered by the crack closure evolution. This paper presents a coupled elastoplastic damage model, which incorporates crack closure to describe the distinct behavior of rock based on the framework of continuum thermodynamics. Comparison between the model predictions and test results of three rock specimens shows that the model can capture whole process mechanical behavior of quasi-brittle rocks over a wide range of confining pressure using a set of model parameters. Parametric studies are carried out to quantify the effects of crack closure evolution and dissipation mechanism of elastic damage and plastic flow of the rock. The proposed model based on an implicit return mapping algorithm has been used to simulate the plastic damage response of rock specimen under displacement control.

Experimental investigation and micromechanics-based constitutive modeling of the transition from brittle to ductile behavior in saturated low-porosity rocks

This paper presents a unified experimental and numerical investigation on the transition from brittle to ductile behavior in a low-porosity sandstone under drained conditions. The experimental results demonstrate a transition in the mechanical behavior from brittle faulting to dilatant ductile flow at room temperature with an increase in effective confining pressure, suggesting that microcracking-controlled local friction is the underlying plastic deformation mechanism. For constitutive modeling, the sandstone is considered as a heterogeneous medium composed of a pores-weakened elastic solid matrix and distributed microcracks. By following a two-step homogenization procedure and irreversible thermodynamics framework, a micromechanics-based elastoplastic damage model incorporating a non-associated local plastic flow rule is formulated, in which the coupling between plasticity, damage and pore pressure is taken into account. In this context, a non-associated macroscopic effective strength criterion as an inherent part of the corresponding model is derived. Originally, a theoretical linear relation between critical state of damage at peak strength and effective confining pressure is established, which is efficient in describing post-peak softening behavior. Comparisons of numerical simulations with experimental data demonstrate that the proposed model effectively reproduces the main features of the sandstone with a brittle-ductile transition.

A Regularised Anisotropic Elastoplastic Damage and Viscoplastic Model and Its Hydromechanical Application to a Meuse/Haute-Marne URL Drift

A Regularised Anisotropic Elastoplastic Damage and Viscoplastic Model and Its Hydromechanical Application to a Meuse/Haute-Marne URL Drift

A multiscale elastoplastic tensive behavior of quasi-continuous network structured (Ti3AlC2-Al3Ti)/2024Al composite

A multiscale elastoplastic damage model to predict mechanical response and fracture behavior of quasi-continuous network structured (Ti3AlC2-Al3Ti)/2024Al composites under uniaxial tension, along with the flexible program for structure reconstruction is proposed. Microscale constituents consist of dispersed in-situ Al3Ti and matrix, while the mesoscale constituents include Ti3AlC2, the matrix, and the interface. The brittle damage model is employed to degrade the stiffness of Ti3AlC2, and a modified Johnson-Cook model is applied to the matrix to accommodate the effect of grain size on the yield strength of the material. The period boundary condition is adopted to the bilinear constitutive relation in microscale analysis, and the output is calculated and transferred to mesoscale as the interface property of Ti3AlC2 and matrix. The numerical simulation results agree well with that of the corresponding quasi-static tension experiment and the deformation response of quasi-continuous network structured (Ti3AlC2-Al3Ti)/2024Al composites is discussed.

An elastoplastic damage model for concrete considering the influence of mesostructure on transverse deformation

The deformation of mesostructures such as micropore collapse or microcrack expansion within concrete can hugely influence its macro transverse deformation. This deformation characteristic is not effectively characterized in existing elastoplastic damage constitutive models based on micromechanics. This discrepancy can result in substantial disparities between the calculated results and the actual situation when carrying out the stress and deformation analysis of concrete structures. Through an in-depth examination of how micropore collapse and microcrack shear expansion affect transverse measurable strain, a new calculating method for concrete transverse deformation is established according to its actual evolution characteristics. The reliability of the proposed method is verified based on the triaxial compression test results. Research results indicate that the transverse deformation of concrete increases slightly before the peak deviatoric stress, and significantly in the post-peak stage. If deformation is restricted, changes in transverse deformation can profoundly affect the stress state of concrete. Micropore collapse reduces the macroscopic transverse deformation of concrete, while microcrack expansion has the opposite effect. The strain caused by micropore collapse and microcrack expansion can be deemed as derivative strain of plastic strain, and an influence coefficient can be used to characterize the impact of these two factors on macroscopic transverse deformation. It is proposed that the total transverse strain consists of elastic strain and the product of plastic strain and plastic strain influence coefficients. The development characteristics of concrete transverse deformation can be effectively captured when describing the plastic strain influence coefficient using an arctangent function.

Constitutive modeling of clay shales in undrained conditions and its experimental verification for Opalinus Clay

Clay shales are low-permeable sedimentary rocks that exhibit inherent cross-anisotropic stiffness, strength, and permeability. Accurate design of tunnels excavated in clay shales requires appropriate constitutive models that account for the anisotropic properties of the host rock, especially under undrained conditions. This paper presents a transversely isotropic elastoplastic-damage model for fully-saturated clay shales in undrained conditions. The model describes four deformation regimes observed during consolidated undrained experiments, i.e. (1) transversely isotropic elastic deformation, (2) anisotropic plastic deformation with cross-anisotropic peak strength, (3) semi-brittle post-peak softening due to both strength and stiffness degradation, and (4) residual strength state. The performance of the model was evaluated using available laboratory tests for Opalinus Clay, the selected host rock for underground disposal of radioactive waste in Switzerland. A large experimental data set, consisting of 18 undrained triaxial compression tests, was used to back-calculate the required model parameters. The adopted experimental data include the effective stress path and the stress–strain curves of specimens with bedding orientations between 0° and 90° with respect to the loading and effective consolidation stresses between 0.76 and 16 MPa. It is shown that the proposed model adequately captures the key material features of Opalinus Clay observed in the undrained experiments.

Hybrid fire collapse simulation of reinforced concrete structures under localized fires

The safety of extensive reinforced concrete (RC) buildings under sudden fire scenarios is of particular concern nowadays. Localized fires may bring serious damage and even collapse to the RC bearing structures, causing huge casualties and economic losses. However, due to the limitations of test facilities, technology, and high costs, etc., full-scale and even reduced-scale structural fire tests have been very limited. The recent development of numerical techniques instead of challenging physical tests has provided exciting prospects for refinement of structural fire behavior prediction. This paper is therefore focused on a hybrid fire collapse simulation method through performing damage analysis of the locally fire-heated components and collapse simulation of the remaining major structure. The damage and failure behavior of the fire-exposed substructure is simulated based on an energy-based elastoplastic damage model for concrete at elevated temperatures. While the resulting deformation and collapse of the rest main structure is modeled by conventional collapse analysis. The key to the hybrid simulation is the coordination of internal forces and deformations between the substructure and the main structure. The developed method allows for an integrated simulation of the whole process from high temperature damage of materials to fire destruction of local components and to the collapse of the entire RC structure.

Elastoplastic Damage Modeling of Rock Spalling/Failure Induced by a Filled Flaw Using the Material Point Method (MPM)

Elastoplastic Damage Modeling of Rock Spalling/Failure Induced by a Filled Flaw Using the Material Point Method (MPM)

A Novel Elastoplastic Damage Model for Hard Rocks under True Triaxial Compression: Analytical Solutions and Numerical Implementation

In this work, a novel elastoplastic damage model is proposed to capture the mechanical and deformation behaviors of hard rocks subjected to true triaxial compression (TTC). A yield function based on the Mogi–Coulomb strength criterion is constructed in the stress space. Generalized plastic shear strain as a function of a continuous and smooth hardening or softening variable is adopted in the yield function; this guarantees that the yield function at the peak stress level has the same form as the strength criterion. Moreover, a proper damage criterion is derived, considering the development of microcrack-induced damage. The novelty of the proposed model consists in the ability to derive its analytical solutions under a novel TTC loading with a constant load angle; this is helpful for calibrating the model parameters. For application, an efficient and convergent semi-implicit return mapping (SIRM) algorithm involving a plasticity-damage decoupling correction procedure is then developed for the numerical implementation of the proposed model under general loading cases. The robustness of the SIRM algorithm is examined through comparisons between numerical results and the derived analytical solutions. An interesting observation is that, for the SIRM algorithm, plasticity and damage evolution are insensitive to the size of the load step. The verification of the model is finally shown through applications to Westerly and Linghai granite under a typical TTC loading path.

A temperature-dependent elastoplastic damage model for frozen sandstone

Subzero temperature has a significant effect on mechanical behaviors of rocks. When a sandstone is in subzero temperature environments, the sandstone exhibits temperature-dependent mechanical characteristics due to the freezing of pore water and the shrinkage of mineral particles. To disclose the influence of subzero temperature on the mechanical behaviors of the frozen sandstone, triaxial compressive tests were carried out at four confining pressures (0 MPa, 1 MPa, 3 MPa, 5 MPa) and four subzero temperatures (0 °C, −5 °C, −10 °C, −15 °C). The laboratory tests show that the frozen sandstone undergoes four typical deformation stages from initial loading to failure: compaction, elasticity, yield and postpeak failure stage. With the temperature decreasing, the compaction stage gradually shortens, and the nonlinear behavior of yield stage weakens. The peak strength and initial yield stress of the frozen sandstone increase, and the initial and ultimate yield surfaces expand gradually with decreasing temperature. Based on the deformation features of the frozen sandstone, an elastoplastic damage model is established by considering the effect of subzero temperature on the yield process and deformation. The elastoplastic damage model was calibrated by the experimental data, and the comparisons demonstrate that the proposed constitutive model well agrees with the stress–strain curves at the four subzero temperatures. An exponential evolution law of the macroscopic damage is found in the elastoplastic model, which is totally consistent with the microscopic damage variation monitored by the acoustic emission (AE) technology. Therefore, the temperature-dependent elastoplastic model can well predict the whole deformation behaviors of the sandstone under different subzero temperatures and gives a quantitative description on the damage evolution, and may serve as theoretical references for the construction and safety operation of frozen rock masses in cold regions.