Continuum Damage Model Research Articles

Coupling of discrete crack and continuous damage model to describe the complete process of concrete fracture

Coupling of discrete crack and continuous damage model to describe the complete process of concrete fracture

Numerical modeling and experimental validation of low velocity impact of woven GFRP/CFRP composites

Low-velocity impact of 2D woven glass fiber reinforced polymer (GFRP) and carbon fiber reinforced polymer (CFRP) composite laminates was studied experimentally and numerically. Hybrid laminates containing blocked layers of GFRP/CFRP/GFRP with all plies oriented at 0° were investigated. Relatively high impact energies were used to obtain full perforation of the laminate in a low-velocity impact setup. Numerical simulations were carried out using the in-house transient dynamics finite element code, Sierra/SM, developed at Sandia National Laboratories. A three-dimensional continuum damage model was used to describe the response of a woven composite ply. Two methods for handling delamination were considered and compared: (1) cohesive zone modeling and (2) continuum damage mechanics. The reduced model size achieved by omission of the cohesive zone elements produced acceptable results at reduced computational cost. The comparison between different modeling techniques can be used to inform modeling decisions relevant to low velocity impact scenarios. The modeling was validated by comparing with the experimental results and showed good agreement in terms of predicted damage mechanisms and impactor velocity and force histories.

Three-dimensional anisotropic unified continuum model for simulating the healing of damaged soft biological tissues.

The soft biological tissues have the ability to heal and self-repair after damage or injury. During the healing process, damaged tissues are replaced by newly produced undamaged tissue to restore homeostasis. Computational modeling serves as an effective tool for simulating the healing process and understanding the underlying mechanisms. In previous work, we developed the first unified continuum damage model for the healing of soft biological tissues. However, the initial theory lacked generalizability to more realistic scenarios and applicability to biomechanical problems due to the simplicity of the isotropic constitutive model and two-dimensional simulations. Therefore, we further improve our approach by developing a three-dimensional anisotropic unified healing model to address more realistic challenges. By using the Holzapfel-Gasser-Ogden model as the hyperelastic term, the influence of the collagen fibers is considered and the reorientation of fibers in healing is simulated. Three numerical examples related to hypertension, aneurysm, and restenosis of the atherosclerotic artery after balloon angioplasty are presented to demonstrate the effectiveness of the proposed model. By comparing numerical solutions and reference solutions, we demonstrate the ability of the proposed model in simulating long-term tissue healing process and analyze the impact of anisotropic terms.

A nonlocal kernel-based continuum damage model for compaction band formation in porous sedimentary rock

A nonlocal kernel-based continuum damage model for compaction band formation in porous sedimentary rock

Proposal for a New Method for Evaluating Polymer-Modified Bitumen Fatigue and Self-Restoration Performances Considering the Whole Damage Characteristic Curve

Fatigue performance and self-repairing activity of asphalt binders are two properties that highly influence the fatigue cracking response of asphalt pavement. There are still numerous gaps in knowledge to fill linked with these two characteristics. For instance, current parameters fail to accommodate these two bitumen phenomena fully. This study aims to propose a new procedure to address this issue utilizing the linear amplitude sweep (LAS) test, LAS with rest period (RP) (LASH) test, and simplified viscoelastic continuum damage (S-VECD) model. This research work used four different types of asphalt binders: neat asphalt (NA), self-healing thermoplastic polyurethane (STPU)-modified bitumen (STPB), self-healing poly (dimethyl siloxane) crosslinked with urea bond (IPA1w)-modified bitumen (IPAB), and styrene–butadiene–styrene (SBS)-modified bitumen (SBSB). Before the testing process, all the materials were subjected to short-term and long-term aging. The new procedure showed a superior capacity to analyze and accommodate all bitumen fatigue performances and self-repairing activities compared to the current method. Another finding proved that asphalt binders with a higher self-restoration behavior failed to show a better fatigue performance. Moreover, the higher fatigue performance increments produced by STPU and IPA1w in NA concerning the control bitumen were 123.7% and 143.7%, respectively. Those values were obtained with 1.0% STPU and 0.5% IPA1w in NA. A breakthrough finding demonstrated that asphalt binder fatigue response is augmented when the RP was applied at a higher damage intensity (S) value. STPB and IPAB reached their highest increments of fatigue response, containing 1.0% of STPU and 0.5% of IPA1w, respectively. Those augmentations were 207.54% and 232.64%, respectively.

Study on the Damage Characteristics of Wheat Kernels under Continuous Compression Conditions.

Peeling wheat yields higher-quality flour. During processing in a flaking machine, wheat kernels undergo continuous compression within the machine's chamber. As this compression persists, damage to the kernels intensifies and accumulates, eventually leading to kernel breakage. To study the damage characteristics of wheat kernels during peeling, this study established a continuous damage model based on Hertzian contact theory and continuous damage theory. The model's accuracy was validated through experiments, culminating in the calculation of critical parameters for wheat peeling. This study focused on different wheat varieties (Ningmai 22 and Jichun 1) and kernel sizes (the thicknesses of the small, medium, and large kernels were standardized as follows: Ningmai 22-2.67 ± 0.07 mm, 2.81 ± 0.07 mm, and 2.95 ± 0.07 mm; Jichun 1-2.98 ± 0.11 mm, 3.20 ± 0.11 mm, and 3.42 ± 0.11 mm). Continuous compression tests were conducted using a mass spectrometer, and critical damage parameters were analyzed and calculated by integrating the theoretical model with experimental data. The test results showed that the average maximum crushing force (Fc) for small, medium, and large-sized kernels of Ningmai 22 was 96.71 ± 2.27 N, 110.17 ± 2.68 N, and 128.41 ± 2.85 N, respectively. The average maximum crushing deformation (αc) was 0.65 ± 0.08 mm, 0.68 ± 0.13 mm, and 0.77 ± 0.17 mm, respectively. The average elastic-plastic critical pressure (Fs) was 50.21 N, 60.13 N, and 59.08 N, respectively, and the average critical values of elastic-plastic deformation (αs) were 0.37 mm, 0.38 mm, and 0.39 mm, respectively. For Jichun 1, the average maximum crushing force (Fc) for small-, medium-, and large-sized kernels was 113.34 ± 3.15 N, 125.28 ± 3.64 N, and 136.15 ± 3.29 N, respectively. The average maximum crushing deformation (αc) was 0.75 ± 0.11 mm, 0.83 ± 0.15 mm, and 0.88 ± 0.18 mm, respectively. The average elastic-plastic critical pressure (Fs) was 58.11 N, 64.17 N, and 85.05 N, respectively, and the average critical values of elastic-plastic deformation (αs) were 0.45 mm, 0.47 mm, and 0.52 mm, respectively. The test results indicated that during mechanical compression, if the deformation is less than αs, the continued application of the compression load will not result in kernel crushing. However, if the deformation exceeds αs, continued compression will lead to kernel crushing, with the required number of compressions decreasing as the deformation increases. If the deformation surpasses αc, a single compression load is sufficient to cause kernel crushing. Since smaller wheat kernels are more susceptible to breakage during processing, the peeling pressure (F) within the chamber should be controlled to remain below the average elastic-plastic critical pressure (Fs) of small-sized wheat kernels. Additionally, the kernel deformation (α) induced by the flow rate and loading in the chamber should be kept below the average elastic-plastic critical deformation (αs) of small-sized wheat kernels. This paper provides a theoretical foundation for the structural design and optimization of processing parameters for wheat peeling machines.

Summary of Rock Damage Mechanics Classification

As an important means to study the mechanical properties and failure mechanism of rock materials and engineering mechanics, damage mechanics is often used to assist in the analysis of the failure process and mechanism of rock, metal, and other materials in the current research. In the use of damage mechanics to study the properties of rock materials and explore the deformation and failure law of rock, important research results have been achieved. The research methods of damage mechanics can be roughly divided into three types: statistical damage model, mesoscopic damage model, and continuous damage model. Based on the existing literature in hand, according to the division of damage mechanics research methods in the academic community, this paper collates and considers that the existing damage model construction can be summarized from the mechanical point of view. The pure theory is derived or fitted from the mathematical point of view. One of them is derived from the mechanism point of view, and the other is derived from the phenomenon point of view. The stress, strain, acoustic emission, and other data are analyzed and reconstructed, and both have advantages and disadvantages.

Enhanced LaRC05 failure criteria for investigating low-velocity impact on fiber-reinforced composites: An experimental and computational study

A finite element model was developed using both continuum and discrete damage modeling techniques to provide detailed predictions for ply-by-ply damage progression in composite laminates during low-velocity impact (LVI) events. A new fiber failure model was incorporated into the LaRC05 failure criteria to predict fiber pull-out and fiber crushing during the fiber damage evolution. In addition, the selective range golden section search (SRGSS) algorithm was implemented to efficiently predict fiber breakage, pull-out, splitting, kinking and crushing, and matrix cracking. The delamination was captured by cohesive element layers embedded between every adjacent composite ply. The interactions of intralaminar matrix cracking and delamination were modeled by deploying cohesive elements within each composite ply. The prediction results were validated by 30 J and 75 J drop-weight tests with different-sized impactors, as well as X-Ray CT inspections on 254 mm by 304.8 mm [0/45/90/-45]4s IM7/977–3 laminates. The model predicted the maximum deflection and contact duration with <2 % error, and the peak load, damaged areas, and absorbed energy with <8 % error. The matrix fracture plane and the fiber kink band angle were found with 1° precision 48 % faster via the SRGSS algorithm. The detailed sequences of damage occurrence were predicted by analyzing the energy dissipation histories through various damage modes. Although this modeling methodology was developed for LVI scenarios, it has broad applications for predicting failures in composites.

Nonlinear viscoelastic effect on the fatigue performance of wood tar-based rejuvenated asphalt

The nonlinear viscoelasticity (NLVE) effects of rejuvenated asphalt are often neglected during fatigue degradation, potentially leading to misjudgment of its true fatigue performance. To more accurately quantify the fatigue life of rejuvenated asphalt under NLVE effects, frequency sweep (FS), incremental stress sweep (ISS), and linear amplitude sweep (LAS) tests were used to study two types of rejuvenated asphalt. FS and ISS tests respectively obtained the dynamic modulus |G*|LVE and |G*|NLVE representing the linear viscoelasticity (LVE) and NLVE of rejuvenated asphalt, and incorporated them into the simplified viscoelastic continuum damage (S-VECD) model to establish the fatigue failure criterion and predict the fatigue life of rejuvenated asphalt under high strain levels in LAS tests. The findings indicate that the NLVE-based-S-VECD model quantifies fatigue damage in rejuvenated asphalt lower than the LVE model, and the fatigue life of rejuvenated asphalt increases significantly after considering the NLVE effect. Besides, the failure difference (∆GR) and failure area difference (∆A) defined during the modeling process explain the impact of NLVE on the fatigue failure criterion average pseudo strain energy release rate (GR) of rejuvenated asphalt, validating the necessity of incorporating NLVE into the fatigue performance analysis of rejuvenated asphalt. Therefore, it's necessary to account for the impact of NLVE effect on the fatigue performance of rejuvenated asphalt in engineering practice, which will contribute to the development and application of rejuvenator.

Hierarchical rank-one sequence convexification for the relaxation of variational problems with microstructures

This paper presents an efficient algorithm for the approximation of the rank-one convex hull in the context of nonlinear solid mechanics. It is based on hierarchical rank-one sequences and simultaneously provides first and second derivative information essential for the calculation of mechanical stresses and the computational minimisation of discretised energies. For materials, whose microstructure can be well approximated in terms of laminates and where each laminate stage achieves energetic optimality with respect to the current stage, the approximate envelope coincides with the rank-one convex envelope. Although the proposed method provides only an upper bound for the rank-one convex hull, a careful examination of the resulting constraints shows a decent applicability in mechanical problems. Various aspects of the algorithm are discussed, including the restoration of rotational invariance, microstructure reconstruction, comparisons with other semi-convexification algorithms, and mesh independency. Overall, this paper demonstrates the efficiency of the algorithm for both, well-established mathematical benchmark problems as well as nonconvex isotropic finite-strain continuum damage models in two and three dimensions. Thereby, for the first time, a feasible concurrent numerical relaxation is established for an incremental, dissipative large-strain model with relevant applications in engineering problems.

A B-spline based gradient-enhanced micropolar implicit material point method for large localized inelastic deformations

The quasi-brittle response of cohesive-frictional materials in numerical simulations is commonly represented by softening plasticity or continuum damage models, either individually or in combination. However, classical models, particularly when coupled with non-associated plasticity, often suffer from ill-posedness and a lack of objectivity in numerical simulations. Moreover, the performance of the finite element method significantly degrades in simulations involving finite strains when mesh distortion reaches excessive levels. This represents a challenge for modeling cohesive-frictional materials, given their tendency to experience strongly localized deformations, such as those occurring during shear band dominated failure. Hence, accurate modeling of the response of cohesive-frictional solids is a demanding task. To address these challenges, we present an extension of the material point method (MPM) for the unified gradient-enhanced micropolar continuum, aiming at the analysis of finite localized inelastic deformations in cohesive-frictional materials. The generalized gradient-enhanced micropolar continuum formulation is employed to tackle challenges related to localization and softening material behavior, while the MPM addresses issues arising from excessive deformations. The method utilizes a B-spline formulation for the rigid background mesh to mitigate the well-known cell crossing errors of the MPM. To demonstrate the performance of the method, 2D and 3D numerical studies on localized failure in sandstone in plane strain compression and triaxial extension tests are presented. A comparison with finite element results confirms the suitability of the formulation. Moreover, an efficient numerical implementation of the formulation is presented, and it is demonstrated that the additional MPM specific overhead is negligible.

A fibre direction informed continuum damage model with enriched kinematics for modelling matrix cracking in composites

Continuum Damage Mechanics models are widely used for simulation of ply-level damage such as matrix cracking in composites. Although their ease of implementation within the finite element framework is appealing, several limitations exist such as a smeared representation of sharp cracks, mesh orientation bias of crack growth, inaccurate energy dissipation due to approximate definition of characteristic length etc. In this work, a new ‘semi-discrete’ continuum damage model is proposed for matrix cracking, that includes sharp crack kinematics. The mesh orientation bias is eliminated by a fibre-directed growth driving criterion. The crack characteristic length is exactly computed due to an accurate geometric representation of the crack surface. The model also addresses a well-known problem of spurious stress transfer across crack faces when deformation becomes large. Through several challenging benchmark problems, the model is shown to perform nearly as good as discrete crack models while being simpler and more robust.

Crystal plasticity analysis of tensile plastic behavior and damage mechanisms of additive manufactured TiAl alloy under elevated temperatures

A crystal plasticity model based on Electron Backscatter Diffraction (EBSD) experimental data has been developed to simulate the tensile behavior of additively manufactured TiAl alloys at various temperatures. To accurately capture the activity of different slip systems and their contribution to the material's plasticity, multiple slip systems across different phases are considered. The validity of the model is verified by comparing the simulation results, such as microscopic properties, with experimental and test data. Additionally, a continuous damage model is incorporated to analyze the damage behavior of additively manufactured TiAl alloys at different temperatures. Compared to experimental data, the crystal plasticity model incorporating damage effectively simulates the tensile failure behavior of TiAl alloys across a range of temperatures.

Topology optimization for fatigue reserve factors

This paper describes a topology optimization approach that applies the common fatigue analysis practices of rainflow cycle counting and critical plane searches to cover both proportional and non-proportional fatigue loading conditions of metals. The existing literature on topology optimization has so far mainly considered fatigue damage under proportional loading conditions and typically uses continuous damage models to avoid the discontinuous nature of fatigue rainflow cycle counting and critical plane searches. Furthermore, previous publications often introduced heuristic schemes to scale the fatigue damage and set the move limits for the design variables rather low to avoid oscillations in the design variables and damage responses during the optimization iterations, because fatigue damage is typically highly localized. Therefore, these approaches cause many optimization iterations. Contrarily, our present approach applies the fatigue reserve factor (FRF) directly in the optimization formulation instead of the fatigue damage where FRF is a fatigue reserve factor for infinite fatigue life. The inverse FRF scales nearly linearly with the stresses. Therefore, the present approach needs no heuristic scaling for the fatigue topology optimization. The numerical implementation applies the semi-analytic adjoint sensitivity method for multiple load cases. Numerically, FRF shows more stable optimization convergence using less optimization iterations. Different FRF topology-optimized designs for a variety of fatigue damage types are validated and compared. Additionally, the optimized FRF designs are compared to both strictly stiffness optimized designs and stress strength optimized designs.

Experimental and simulative investigations of burr formation in planing of AISI 1045

The clearance flow in dry-running vacuum pumps is the main loss mechanism. To reduce the clearance mass flow rate in rarefied gas flows, sawtooth structures transversing to the direction of flow can be utilized. However, due to the sawtooth’s structure size, micro-machining is necessary, whereby burr formation is a central challenge. First, the effectiveness of non-idealized sawtooth structures is investigated, demonstrating a high sensibility of the performance regarding the geometry of the tip. Therefore, burr formation in the cutting process must be minimized. For this reason, a 3D finite element (FE) chip formation model capable of predicting the burr formation is developed. An analysis of the burr formation zone showed positive triaxialities; thus, the triaxiality-dependent Johnson–Cook damage model is utilized. To minimize the mesh-induced error, a convergence analysis is conducted, showing no convergence of the maximum burr height. This is caused by the pathological mesh size dependence of local continuum damage models. A comparison of the cutting experiments and simulations revealed a reasonable prediction of cutting forces. In contrast, the passive force is predicted poorly, which is attributed to the underestimation of the ploughing force for non-elastic simulations. The prediction quality regarding the maximum burr height differs for the investigated cutting speeds, which can be explained by a built-up edge and a change in the machine tool compliance. Thereby, an analysis of the burr formation revealed that the burr height is captured by a non-physical remeshing algorithm and that the burr volume might be a more appropriate characteristic.

Material Parameter Identification for a Stress-State-Dependent Ductile Damage and Failure Model Applied to Clinch Joining

Similar to bulk metal forming, clinch joining is characterised by large plastic deformations and a variety of different 3D stress states, including severe compression. However, inherent to plastic forming is the nucleation and growth of defects, whose detrimental effects on the material behaviour can be described by continuum damage models and eventually lead to material failure. As the damage evolution strongly depends on the stress state, a stress-state-dependent model is utilised to correctly track the accumulation. To formulate and parameterise this model, besides classical experiments, so-called modified punch tests are also integrated herein to enhance the calibration of the failure model by capturing a larger range of stress states and metal-forming-specific loading conditions. Moreover, when highly ductile materials are considered, such as the dual-phase steel HCT590X and the aluminium alloy EN AW-6014 T4 investigated here, strong necking and localisation might occur prior to fracture. This can alter the stress state and affect the actual strain at failure. This influence is captured by coupling plasticity and damage to incorporate the damage-induced softening effect. Its relative importance is shown by conducting inverse parameter identifications to determine damage and failure parameters for both mentioned ductile metals based on up to 12 different experiments.

Mechanistic Pavement Modeling of Typical Brazilian Pavements: Cohesive Zone Fracture Modeling and Continuum Damage Modeling

Pavement performance evaluation with respect to fatigue cracking has seen a major shift toward more rigorous mechanistic models that can capture the complex damage response of the mixtures more accurately. This study utilized two mechanistic methods (cohesive zone [CZ]-based fracture modeling and continuum damage [CD] modeling) to study the cracking behavior of asphalt mixtures and subsequently predict the damage-associated performance of pavements. A Superpave mixture designed for Brazilian highway conditions was selected to evaluate the two modeling approaches for the performance of the mixture when utilized as a surface course within typical Brazilian highway pavements. The mixture was first evaluated for its linear viscoelastic properties, and then the damage characteristics of the mixture were obtained through two different experiments: the semi-circular bending (SCB) beam test and the cyclic fatigue (CF) test. The SCB tests performed at different loading rates were used to obtain the model parameters of the nonlinear viscoelastic CZ model with a Gaussian damage evolution criterion, while the CF tests were performed at different strain amplitudes, and the mixture-specific damage characteristic curve and the fatigue failure criterion were obtained using the simplified-viscoelastic continuum damage model. From a design perspective, three pavement structures that varied in geometry (pavement layer thickness) and underlying layer properties were selected while retaining the same asphalt mixture. The three pavement scenarios were evaluated for the fatigue cracking performance from each of the mechanistic modeling methods. The results indicate that both methods rank the performance of the pavement structures in a similar manner, while the damage initiation and progression were seen to be different because of the different mechanics in modeling cracks.

Crash analysis of glass mat thermoplastic (GF/PA6) tubes considering splaying failure mode and energy absorption

Glass mat thermoplastic tubes are potential materials for improving crashworthiness owing to their excellent crash energy absorption capability due to their splaying failure mode of glass mat thermoplastic tubes, which must be considered in the crash analysis to accurately predict their crash performance. This study investigates the crash analysis of glass-mat thermoplastic composite tubes to realize the splaying failure mode and crash energy absorption capability. We evaluated the mechanical properties and fracture toughness of advanced glass mat thermoplastics, termed multi-layered hybrid mats, and employed the result in a 3D Hashin-type continuum damage model implemented with a user material subroutine. For the crash analysis of glass mat thermoplastic tubes, a three-dimensional finite element (FE) model, including cohesive elements in the middle layer of the tube to simulate the splaying failure mode, was constructed. In addition, in the process of the efficient FE modeling of the crash tube, the fracture toughness correction factor was proposed and optimized to calibrate the energy absorption in conjunction with crash test results, as interlaminar fracture modeling causes a difference in energy absorption between the actual test and simulation. As a result, the proposed crash analysis predicted the energy absorption capacity and a splaying failure mode of glass-mat thermoplastic tubes, demonstrating strong concordance with experimental results.

Study on the damage mechanism and evolution model of preloaded sandstone subjected to freezing–thawing action based on the NMR technology

Abstract Investigating the damage degradation of rock during the freezing and thawing process is more consistent with the actual engineering environment, considering its internal initial damage. In this study, the effects of initial damage from preloading and subzero-temperature freezing–thawing on microscopic and macroscopic mechanical properties of sandstone were studied based on the nuclear magnetic resonance (NMR) technique. The results show that the P-wave velocity of the sample decreased, while the porosity increased as the initial damage level increased. The distribution of T2 signal intensity exposed to the low-temperature freezing–thawing–saturation treatment was rather larger than that under normal temperature conditions for samples with different levels of initial damage from preloading, indicating that the low-temperature freezing–thawing condition would promote the porosity and have an obvious increase in damage. A continuum damage model considering subzero-temperature freezing–thawing damage from different pore sizes was finally introduced to describe the damage evolution mechanism of sandstone. The research results can be used to quantitatively evaluate the damage evolution mechanism of sandstone treated by subzero-temperature freezing–thawing without mechanical tests. Furthermore, the analysis and research results show that the damage variables of sandstone obtained by the NMR theory were lower than those of classical rock mechanics theory.

Thermomechanical analysis of SiC-based duplex claddings with varying thickness ratio for accident-tolerant nuclear fuel systems

SiC-based duplex claddings, consisting of monolithic SiC and SiC/SiC fiber composite, are emerging as a promising candidate for accident-tolerant fuel (ATF) systems in nuclear reactors. To analyze the performance of ATFs with SiC-based duplex claddings, a comprehensive computational analysis framework is presented that captures the essential properties and behaviors of the UO2-SiC fuel system. Utilizing a previously developed continuum damage model, the pseudo-ductile behavior of SiC/SiC fiber composites is accurately modelled, connecting damage evolution parameters to instantaneous stiffness matrix degradation. This framework is used to investigate the performance of UO2-SiC fuel rods under normal operating conditions and a typical Loss of Coolant Accident (LOCA) scenario. We assess the effects of the thickness ratio of the monolithic SiC and SiC-based composite layers, as well as pellet-clad cold gap thickness on the failure and leakage probabilities of the cladding. These claddings, with a thickness ratio ranging from 0.25 to 0.75, demonstrated minimal failure and leakage probabilities for both the original and reduced pellet-clad gap thickness (82.5/70 µm). When the gap thickness was further reduced to 57.5 µm, pellet-cladding mechanical interaction was observed and this greatly elevated the failure probability of the MSiC layer, thus giving rise to a loss of hermeticity. This research underscores the significant role of varying individual layer thicknesses in shaping fuel rod safety and offers potential for optimization across diverse operational conditions.