Damage Plasticity Model Research Articles

Behavior and design of multi-sided composite sections

ABSTRACT Composite construction is advantageous due to the combination of steel and concrete materials in structural members. Composite column’s cross-section types such as hexagonal, octagonal, and decagonal and high diameter-to-thickness (D/t) ratios are highly desirable in transmission towers, yet not covered in the applicable codes. Therefore, the objective of this study is to investigate the behavior of composite columns with various characteristics including cross-section types, and height and propose a design procedure based on Force – Moment (P-M) Interaction diagrams and related equations. Three-dimensional non-linear finite element models were developed using a nonlinear finite element software to simulate and verify the behavior of the composite towers against prior experimental work. Concrete Damage Plasticity and Steel Bilinear Elasto-Plastic Model were calibrated and used in capturing the realistic nonlinear behavior of the materials and their interaction. Based on the computational models, a concrete reduction factor, needed for the development of design equations, was derived. Conclusively, typical normalized P-M Interaction diagrams were constructed for various polygonal shapes with high D/t ratios beyond code limitations. The corresponding derived design equations play a significant role in the applicability of the composite columns in transmission towers.

Simulation of Test Arch Based on Concrete Damage Plasticity Model and Damage Evolution Analysis

In light of the limited research on latent damages during the construction of large-span suspension arches, this study introduced a method to simulate structural damage utilizing random porosity. Initially, based on data from real-world engineering projects, the most susceptible areas within the arch structure were pinpointed. Subsequently, multiple test arch simulation models were constructed. Employing Python, commands for random porosity were implemented within ABAQUS and distinct mesh modules were devised to depict structures under varying degrees of damage. The current investigation delved into the structural responses of these susceptible areas under different damage rates, shedding light on damage progression patterns. Notably, our findings demonstrated that concealed damages on the top plate of the arch foot profoundly influenced structural integrity, whereas damages at the arch hance were comparatively minimal and predominantly manifest at the arch base. The pronounced localized damage at both the arch base and hance initiated and intensified at sectional corners, necessitating enhanced anti-crack measures in these regions. Moreover, depending on the stresses of the arch structure, diverse reinforcement strategies could be employed, optimizing the balance between load-bearing efficiency and cost considerations.

Performance Analysis of an Improved Gravity Anchor Bolt Expanded Foundation

With the continuous utilization of renewable energy, the number of onshore wind turbines is increasing. Small design improvements can save costs and facilitate the maintenance and repair of the wind turbine foundation. In this paper, an existing gravity expansion foundation with an anchor cage is improved. Our improvements further expand the space inside the foundation and reduce the length of the anchor bolt, which could reduce the costs and facilitate construction. To study the performance of the new foundation, a three-dimensional finite element model of the foundation–soil–anchor bolt was established via a finite element simulation. The damage evolution of the foundation was simulated with the concrete damage plasticity model (CDP). The separation ratio, foundation settlement, inclination ratio, reinforcement stress, foundation stress, and foundation damage of the new foundation under ultimate load conditions were analyzed. The influence of parameters h1 and b3 on the performance of the foundation was further studied. The finite element analysis results show that the tensile stress of concrete can be effectively reduced by appropriately increasing the corbel height and ring beam width of the foundation. The results also show that the improved wind turbine foundation force is reasonable and can meet the use of the actual project requirements on the level of finite element analysis.

Statistical approach of performance-based uncertainty quantification of prestressed concrete containment structures for internal pressure capacity

With several experiences on economic losses and environmental impacts caused by serious accidents, the ultimate internal pressure and failure modes of Prestressed Concrete Containment Structures (PCCSs) during severe accidents have gained greater attention. Regulatory Guide allows the use of a 3D Finite Element (FE) model to determine the containment internal pressure capacity, because the experiments of PCCSs are a very cost and time-consuming process. In this study, an FE model of PCCS tested at Sandia National Laboratories is developed to identify an effect of parameters in the Concrete Damage Plasticity (CDP) model on the response of the PCCS and is validated from the experimental data. In addition, a closed-form equation is developed to predict the responses of the PCCS through a regression analysis in conjunction with the validated FE model and performance-based uncertainty quantification of the PCCS is estimated by numerical analysis and the closed-form equation. The developed closed-form equation achieves high accuracy of 98% and the probabilistic characteristic of the PCCS obtained from the equation well represents the one obtained from the validated FE model. The closed-form equation rarely requires computational cost to investigate the probabilistic responses of the PCCS.

A 3D objective material model for elastic–plastic damage behavior of fiber reinforced polymer composites

To simulate the plastic deformation and the progressive failure process of fiber reinforced polymer composites under 3D stress conditions, a new elastic–plastic damage model is proposed to satisfy the objectivity of 3D stress conditions. A new two-parameter 3D plasticity criterion and a simple non-associated flow potential, expressed by stress invariants of a transversely isotropic unidirectional (UD) lamina, are developed to characterize plastic deformation in an objective way. Moreover, the material degradation model and damage evolution laws are constructed on a matrix fracture angle-dependent coordinate system to ensure the objectivity of the continuum damage mechanics (CDM) approach. In addition, a new linear law alleviating mesh dependence is derived to govern the damage variable evolution in the elastic–plastic damage process. ​The effectiveness and objectivity of the proposed material model are demonstrated by a series of test cases.

Auxetic cementitious cellular composite (ACCC) PVDF-based energy harvester

The high deformation capacity of auxetic cementitious cellular composites (ACCCs) makes them promising for strain-based energy harvesting applications in infrastructure. In this study, a novel piezoelectric energy harvester (PEH) with ACCCs and surface-mounted PVDF film based on strain-induced piezoelectric mechanisms has been designed, fabricated, and experimentally tested. Furthermore, a numerical model for simulating the energy harvesting of ACCC-PVDF system undergoing repeated mechanical loading has been established and validated against the experimental data. The mechanical behavior of ACCCs was simulated by the concrete damage plasticity model during the preloading stage, which was converted to the second-elasticity model during cyclic loading stage. Based on the mechanical responses, analytical formulas for piezoelectric effects were developed to calculate the output voltage of the PVDF film. The output voltages of the ACCCs-PVDF system under different loading amplitudes and loading frequencies were assessed. The experimental results and models of the ACCCs-PVDF energy harvester lay a solid foundation for utilizing architected cementitious composites in energy harvesting applications to supply self-power electronics in infrastructure.

Damage performance and failure analysis of reinforced concrete doubly curved shells under seismic excitations considering curvature and thickness variation

Most of the past investigations on the structural response of the doubly curved shell (DCS) roofs under seismic excitation were limited to linear dynamic analysis, whereas nonlinear dynamic analysis was rarely introduced, making it difficult to understand their dynamic behavior and draw general conclusions. Therefore, in the current study, linear dynamic analysis (LDA) and nonlinear dynamic analysis (NLDA) are conducted in tandem to fill the gap in the literature and give a complete perception of how these roofs respond to earthquakes. To this end, an innovative automatic finite element-based design algorithm is developed to obtain the steel reinforcement in preparation for the NLDA. Accordingly, the current study exploits the multi-layered shell element incorporated with the multi-axial concrete damage plasticity model (implemented via VUMAT subroutine) and the developed design algorithm (via Python script) to perform the NLDA and accurately capture the structural response and damage performance of these roofs. Unlike most common structures, the results demonstrated that DCS is highly affected by the vertical component of the earthquake rather than the horizontal component. The NLDA revealed that the shell exhibits severe damage and a high displacement response under strong seismic excitations, which could not be captured via the LDA. Additionally, the failure analysis is performed for the studied roof, considering the variation in shell curvature and thickness. This analysis shows a notable decrease in the demand-capacity ratio and steel rebar’s stress with increasing the shell curvature. Consequently, according to the proposed performance levels, the shell’s state changed from the initial failure to the elastic state. In contrast, slight changes in the overall behavior are observed due to the variation in the shell thickness. Finally, a new formula is proposed to predict the damage induced in the DCS under seismic excitations.

From ductile damage to unilateral contact via a point-wise implicit discontinuity

Ductile damage models and cohesive laws incorporate the material plasticity entailing the growth of irrecoverable deformations even after complete failure. This unrealistic growth remains concealed until the unilateral effects arising from the crack closure emerge. We address this issue by proposing a new strategy to cope with the entire process of failure, from the very inception in the form of diffuse damage to the final stage, i.e. the emergence of sharp cracks. To this end, we introduce a new strain field, termed discontinuity strain, to the conventional additive strain decomposition to account for discontinuities in a continuous sense so that the standard principle of virtual work applies. We treat this strain field similar to a strong discontinuity, yet without introducing new kinematic variables and nonlinear boundary conditions. In this paper, we demonstrate the effectiveness of this new strategy at a simple ductile damage constitutive model. The model uses a scalar damage index to control the degradation process. The discontinuity strain field is injected into the strain decomposition if this damage index exceeds a certain threshold. The threshold corresponds to the limit at which the induced imperfections merge and form a discrete crack. With three-point bending tests under pure mode I and mixed-mode conditions, we demonstrate that this augmentation does not show the early crack closure artifact which is wrongly predicted by plastic damage formulations at load reversal. We also use the concrete damaged plasticity model provided in Abaqus commercial finite element program for our comparison. Lastly, a high-intensity low-cycle fatigue test demonstrates the unilateral effects resulting from the complete closure of the induced crack.

Cracking in Reinforced Concrete Cross-Sections Due to Non-Uniformly Distributed Corrosion.

Corrosion affecting reinforced concrete (RC) structures generates safety and economical problems. This paper is focused on the simulation of corrosion-induced fractures in concrete, whereby non-uniform corrosion growth is taken into account. In particular, the volumetric expansion of rust accumulated around reinforcement bars causes cracking of the surrounding concrete. This phenomenon is simulated using the finite element (FE) method. In the analyses, concrete is described as a fracturing material by using a damage-plasticity model, steel is assumed to be elastic-plastic and rust is modeled as an interface between concrete and steel. The behavior of corrosion products is simulated as interface opening. Two-dimensional FE models of RC cross-sections with 2, 4 or 6 reinforcing bars are considered. Crack formation and propagation is examined. Moreover, interactions between cracks and patterns of possible failure are predicted. The most developed and complex crack pattern occurs around the side reinforcing bar. Conclusions concerning the comparison of results for uniform and non-uniform corrosion distribution as well as the prediction of concrete spalling are formulated.

Finite element analysis of RC moment-resisting frames to assess effective slab width; a parametric study

In reinforced concrete (RC) moment-resisting frames (MRFs) with cast-in-situ slabs, the slab action as tension flange during lateral loading enhances the flexural capacity of beams in negative moments. This enhancement may lead to strong beam-weak column unfavorable failure mode in these structures. Field observations of RC MRFs during strong ground motion indicated that the effective slab width values considered by the seismic provisions of the design codes are not adequate to guarantee the achievement of the design method of weak beam-strong column. An accurate estimation of effective slab width needs to assess factors such as geometrical characteristics of connection, continuity of models, and imposed story drift level. A 3D spatial two-story RC MRF was developed using finite element analysis (FEA) to explore the effect of mentioned factors on effective slab width. For finite element (FE) modeling of RC MRF, the concrete damaged plasticity (CDP) model is applied. The CDP model parameters are defined using a mesh-independent methodology introduced in the literature. Comparing the FEA results and results obtained from three half-scale RC MRFs, tested under reversed cyclic loading conditions showed an excellent correlation. The results predicted by the FE model in terms of lateral load–displacement response, reinforcement yielding sequence, crack patterns, and failure modes had a considerable agreement with test observations. The validated FE model was used to develop the other models to conduct a parametric study in the next step. Geometric parameters studied in this paper through numerical modeling were longitudinal and transverse beam length and height, and cross-sectional column dimension. Results of the parametric study showed that the effect of the ratio of transverse beam length to height is significantly more than the ratio of longitudinal beam length to height. The trend of effective slab width versus story drift depends on connection geometry, especially the ratio of transverse beam length to transverse beam height. Finally, an equation was driven to predict the effective slab width using linear regression analysis.

Numerical analysis on the mechanical response of grouted connection for pile-bucket foundation

As a new foundation type for offshore wind turbine (OWT), pile-bucket foundation, which consists of a monopile and a bucket foundation, has good prospect in engineering application and has received wide attention. However, most of the current research ignored the function of grouted connection (GC) and assumed that the pile and bucket were rigidly connected, which may lead to unrealistic estimation of the loading response of pile-bucket foundation. In this study, Finite Element Analysis (FEA) is conducted to study the influence of grout connection on the bearing characteristics of pile-bucket foundation, with a special focus on the mechanical response of the grout connection itself. The concrete damage plasticity (CDP) model is used to simulate the mechanical response of the grout material. After validation of the numerical model, twelve simulations are conducted by changing the grout thickness, grout length and stiffener arrangements. Though the variance of grout thickness and grout length has little impact on the load-displacement curves of the pile-bucket foundation, the optimal grout thickness and grout length could be determined according to the development of contact pressure, stress and damage of the grout connection. On the other hand, the employment of stiffener leads to notable stress concentration and fluctuation, however, it also improves the overall capacity of the pile-bucket foundation and effectively controls the damage of the grouted connection. The numerical result is expected to provide some reference value for the structural design of grouted connection for pile-bucket foundation.

Numerical implementation of tension–compression asymmetry in a gradient‐extended two‐surface damage–plasticity model

AbstractBased on the spectral decomposition of the strain tensor, the tension‐compression asymmetry (TCA) in a gradient‐extended two‐surface damage‐plasticity model is considered in this study. More specifically, the gradient extension is applied in the current model as a suitable damage regularization technique to prevent pathological mesh dependence issues. Furthermore, plasticity and damage are treated as distinct but strongly coupled dissipative mechanisms by using two different types of damage and yield criteria as well as the related loading/unloading conditions, respectively. Finally, a specific material parameter is adopted to control the degree of TCA which results in a unique damage evolution in compression.

Numerical seismic analysis of high-piled wharf strengthened with CFRP

High-piled wharves are widely employed in coastal areas, but their vulnerability to earthquake damage necessitates effective strengthening measures. This research focuses on investigating the effectiveness of carbon fiber reinforced polymer (CFRP) laminates in enhancing the seismic resistance of high-piled wharves. Full-scale 3D numerical high-piled wharves, divided into As-built groups and Retrofit groups, were established herein. During modeling, the concrete damage plasticity model (CDP) and the finite-infinite coupling element were contemplated. Two representative ground motions, i.e., the EI Centro wave and the Northridge wave, with peak accelerations of 0.2g and 0.4g, respectively, were utilized to simulate different earthquake scenarios. The responses of the resulting earthquake-induced deck displacement, pile distortion, and pile bending moment profile were explored. The computational analysis revealed significant improvements in the seismic performance of the retrofitted wharves compared to the as-built structures, proving that the externally bonded CFRP method was of great significance in improving overall structural seismic performance. Notably, the retrofitted wharf exhibited reduced deck displacement and remarkable decreases in pile deformation and bending moment. The modeling and analysis techniques can be applied to general wharves or other buildings strengthened with CFRP.

Constitutive modeling of orthotropic nonlinear mechanical behavior of hardened 3D printed concrete

3D printing of concrete is a promising construction technology, offering the potential to build geometrically complex structures without the use of cost-intensive formwork. The layer-wise deposit of filaments during the 3D printing process results in an intrinsic orthotropic mechanical behavior in the hardened state. Beyond that, the material behavior of 3D printed concrete (3DPC) is governed by a highly nonlinear behavior, characterized by irreversible deformations, strain hardening, strain softening and a degradation of the material stiffness. In this contribution, a new constitutive model for describing the orthotropic and highly nonlinear material behavior of 3DPC will be presented. It is formulated by the extension of a well-established isotropic damage plasticity model for concrete to orthotropic material behavior by linear mapping of the stress tensor into a fictitious isotropic configuration. The performance of the new model will be evaluated by finite element simulations of three-point bending tests of 3DPC samples, performed for different orientations of the loading direction relative to the printing direction and comparison with experimental results. In addition, the applicability of the model to replicate the mechanical behavior of 3DPC, manufactured by the alternative 3D printing process of binder jetting of cementitious powders, will be demonstrated by 3D finite element simulations of an arch structure with varying orientations of the loading direction relative to the layering. Overall, the proposed model provides a computationally efficient modeling approach for large-scale finite element simulations of 3DPC structures, being a promising alternative to complex and computationally expensive finite element models considering distinct interfacial planes.

Damage of CRTS III type ballastless track-32 m simply supported girder structural system under long-term deformation effects

Until now, the CRTS (China’s Railway Track System) III type ballastless track-girder system has been gradually used in high-speed railway engineering. However, the effect of long-term deformation of prestressed box girders on the upper track structure is often overlooked. Given the strict requirements for track smoothness in high-speed railways, an in-depth study of the long-term deformation of the CRTS III type ballastless track-32 m simply supported girder system (girder-track system) is particularly important. In this study, a refined finite element model was established for a three-span CRTS III type ballastless track- simply supported box girder system. Based on the aid of the CEB-FIP 90 creep model and the UMAT (User-Material) subroutine, the long-term deformation calculations were investigated. Furthermore, an in-depth analysis of stress and damage of the CRTS III type ballastless track under the long-term deformation of the box girder was conducted by combining concrete damaged plasticity (CDP) and cohesive zone model (CZM) constitutive models. The numerical simulated results indicated that after four years of operation, the creep camber of the box girder in the girder-track system would reach to 3.41 mm. The maximum tensile and compressive longitudinal stresses of the base plate would reach to 0.537 MPa and 11.983 MPa, respectively. Meanwhile, the maximum tensile and compressive longitudinal stresses of the self-compacting concrete layer would reach to 0.958 MPa and 2.701 MPa, respectively. In the box girder mid-span, significant damage could be observed in the edge of the two base plates near the mid-span, with a maximum compressive damage rate of 0.164 and the maximum tensile damage rate of 0.304. The research of this study has achieved the prediction of long-term deformation in the girder-track system, providing an important basis for the reliability assessment and life prediction of the girder-track system.

Tensile Behavior of Anchored Stainless Steel T‐Head Blind Bolts within Concrete‐Filled Steel Square Tubes

AbstractBased on a recent review on blind bolted connections to concrete‐filled steel tubes, there is a need to improve the performance of anchored blind bolts in such composite connections. This paper presents a study on the pull‐out behavior of anchored blind bolts under applied tensile load in terms of stiffness, yield strength, ultimate strength and load‐displacement response. A finite element (FE) model with concrete damage plasticity model was developed for parametric study. Effects of key parameters, such as concrete strength, bolt grade, embedment length, tube thickness and tube grade, on the tensile behavior of the connection were studied to identify the key parameters influencing the behavior. Finally, a predictive model based on component method was proposed to estimate the structural behavior of the blind‐bolted connections.

A quantitative investigation on the fragmentation performance of SCDA in cracking steel fiber reinforced concrete

A better application of Soundless Chemical Demolition Agents (SCDAs) in fragmentation is based on our knowledge on their expansive characteristics. In this study, an integration of experimental and modeling approaches was developed to investigate SCDA expansion and corresponding cracking processes of Steel Fiber Reinforced Concrete (SFRC). The expansive properties of the selected SCDA were first estimated by free volume expansion (FVE) tests and expansion pressure (EP) tests. Then, cracking experiments were performed on 150 mm cubic SFRC blocks with a predrilled hole, and the cracking process was monitored by using Acoustic Emission (AE) and Digital Image Correlation (DIC) techniques. Generally, the cracking process can be divided into three phases, termed micro-cracking phase, macro-cracking phase, and failure phase. It was observed the hole diameter and fiber content exert significant influences on the cracking process. The crack initiation time was shortened as the hole diameter increases, while it was prolonged with increasing fiber content. The cracked area ratio was further proposed and measured to assess the cracking performance of SCDA. The ratio increases from 2.73% to 8.293% as the hole diameter increases from 16 mm to 26 mm, while it decays from 9.75% to 1.823% as the fiber content increases from 0 to 2.4%. After verified with the experimental data, a modified Concrete Damaged Plasticity (CDP) model was adopted to extend the fragmentation of SFRC from the centimeter scale to the meter scale. The simulations were conducted on SFRC models with various hole diameters, spacings, and fiber contents. The simulated results show the fragmentation performance is related to both hole parameters (e.g., hole diameter, spacing, etc.) and SFRC properties (including elastic modulus, fiber content, etc.). In particular, the cracked area (DamageT > 0.9) varies directly with hole spacing, diameter, and fiber content. Built on the simulated results, an empirical equation was formulated to quantitatively evaluate the fragmentation ability of individual holes. In addition, extra simulations were conducted to assess the efficiency of SCDA in cracking PC/SFRC beams of various sizes. The obtained cracked area tends to decrease first and then approach a constant value with increasing beam sizes, indicating the existence of a size effect, which is primarily due to variations in concrete restraints provided by beams of different sizes. This work quantitatively evaluates expansive properties of SCDA and SCDA-induced cracks, and thus provides a reference for optimizing the field application parameters.

On the ductile damage progression in surface-damaged metallic strands: Towards a damage tolerance analysis

This paper reports a novel and straightforward numerical approach to perform a damage tolerance analysis for metallic strands. This methodology relies on the ductile damage evolution laws experienced by metallic wires and strands under tensile monotonic load. Regarding the wires, this new approach integrates both micromechanics–based and continuum damage mechanics-based approaches. Tensile capacity tests of high strength steel and aluminium alloy wires are simulated using 3-D nonlinear finite element models along with the Gurson-Tvegaard-Needleman constitutive plasticity-damage model (micromechanics–based approach) whose parameters are calibrated iteratively using the disturbed state concept. Numerical simulations reproduce the different phases of the ductile damage process which are then related to an isotropic damage index (continuum damage mechanics-based approach). Results show that the wires develop nonlinear ductile damage evolution laws well captured by the Bonorás model with critical damages ranging from 0.12 to 0.25. The existing gap between wires and strand damage evolutions is then filled by using proper kinematic assumptions for both intact and damaged strands along with a homogenization procedure. The latter have a prescribed number of surface wires, symmetrically and asymmetrically distributed, fully cut to simulate service damage. For validation purposes, strands with 1 × 7 construction typology are analyzed whose diameters range between [9.5–14.3] mm. One approach to assess strands structural integrity and safety conditions is to analyze the stability of damage states as the degradation process occurs. Using this metric for the 1 × 7 strands, reveals that two surface wires cut is the maximum acceptable surface damage which meets the criterion established in different international standards for this strand construction typology. Otherwise, the damage state progresses to either an unstable or inflection state that accelerates the reduction of the capacity of a damaged strand to withstand more damage.

Application of bridge information modelling using laser scanning for static and dynamic analysis with concrete damage plasticity

A new proposal has been applied using Bridge Information Modeling associated to Terrestrial Laser Scanning TLS and photogrammetry to obtain the digital model of an existing bridge. For the laser scanning process. Thus, it was also possible to identify the pathologies and damages in the concrete of the bridge. Furthermore, it was shown how geo-information with remote sensing using the station Trimble SX 10 can be applied in area of bridge projects with less time and lower cost, in relationship to a conventional survey Asbuilt with manual survey in field. One of the innovations of this paper was to obtain the digital model of the bridge by integration of TLS and photogrammetry to obtain the 3D digital model. The new methodology consisted of acquisition of the bridge scenes through points previously implanted, making the polygonal contour of the entire bridge. Furthermore, the execution of the field survey from georeferenced points to capture the scenes during the sweep with TLS facilitated the refinement and, consequently, it was possible to obtain the digital model with the concrete damage. It was also possible to perform a complex nonlinear analysis with Finite Element with the digital model of the bridge. Therefore, it was applied a reverse analysis of the strength of the structure using the Concrete Damage Plasticity Model using ABAQUS software. Two numerical analyses were performed on the bridge; one considering only the static behavior of the bridge and another considering the dynamic behavior. In the static analysis, the behavior of the dapped-end beam of the bridge, was investigated. On the other hand, in the dynamic evaluation, the natural frequency and damping ratio for bridges with Dapped-end beams was obtained in ABAQUS through Rayleigh damping and compared with the technical literature, which presented satisfactory results.

Physically Based Constitutive Modeling of Dynamic Strain Aging in C45 Steel

Abstract Dynamic strain aging (DSA) is a sudden increase in the strength of a material under certain combinations of temperatures and strain rates. Despite the phenomenon being reported in several other studies, the literature still lacks a specific constitutive model that can physically interpret its effect. Therefore, this work proposes a modification based on physical parameters to the Voyiadjis and Abed (VA) model to account for the effect of DSA in C45 steel. The resulting modified model is then coupled with an energy-based damage model to further capture the effect of material softening. Previously, in VA model, it was assumed that the total activation energy for overcoming the obstacles without external work remains the same which works well in the absence of DSA. However, during DSA, the mobile dislocations are pinned by the diffusing solute atoms. This results in an increase in the total activation free energy needed by the dislocations to overcome the obstacle. Thus, an increase in strength is observed. It is shown in the current work that utilizing the concept of increased solute concentrations at local obstacles, in conjunction with the physical description that the VA model is based upon, successfully captures the phenomenon of DSA in C45 steel. In addition, the metal experiencing softening after reaching its ultimate strength is due to the significant growth of voids and cracks within the microstructure. To capture this behavior, an energy-based damage parameter is incorporated into the proposed model. The coupled plasticity-damage model shows a good comparison with the experimental results.