Damage Mechanics Model Research Articles

An adaptive mesh refinement algorithm for crack propagation with an enhanced thermal–mechanical local damage model

This paper presents a computationally effective approach for crack propagation under mechanical and thermal loads based on an adaptive mesh refinement (AMR) approach tailored for our recently developed enhanced local damage model. The mesh-dependent issue encountered in the classical local theories is effectively mitigated by incorporation of fracture energy and element characteristic length into the damage evolution function. Our previous research has demonstrated that being equipped by a novel equivalent strain derived from the bi-energy norm concept and a new damage criterion recently proposed by Mazars et al., the model provides results comparable to the reference experimental data as well as other numerical models based on non-local/gradient damage and phase field method. In the framework of computational efficiency using finite elements, we significantly enhance the performance of our enhanced local model by considering adaptive mesh refinement (AMR). The finite element mesh is locally refined in the damaged zone, and the mesh refinement is conducted on-the-fly during the analysis. For that purpose, the damage parameter whose information is stored at integration points is selected as an indicator to mark whether an element should be refined or not after every loading step. For quadrilateral element mesh, a quad-tree technique is utilized, meaning that each marked element is further divided into four smaller quadrilateral elements. The so-called hanging nodes appear during the process, and the elements are thus treated as n-gons and are constructed by the Laplace shape functions, instead of the usual Lagranges shape functions. To show the accuracy and effectiveness of the proposed scheme, several numerical examples involving homogeneous and heterogeneous materials are studied. In these examples, the damage is induced either by only mechanical loads or by both mechanical and thermal loads.

Simulation and Experimental Analysis of Surface Crack Propagation in Oscillating Bearings

: This study investigates the propagation of surface cracks in bearings under oscillating conditions. Voronoi elements are employed to simulate the microstructure of bearings, and combined with a cohesive zone model of continuum damage mechanics to simulate the propagation of cracks. A new type of oscillating contact fatigue test machine was designed to conduct experiments on contact crack propagation under oscillating conditions, and the experimental results were analyzed. By comparing the simulation results with experimental data, the validity of the theoretical analysis was confirmed.

Predicting the fatigue life of additively manufactured AlSi10Mg alloy using a physics-informed neural network incorporating continuous damage mechanics

The material characteristics of additively manufactured AlSi10Mg alloy, including the random distribution of process-induced micro defects, microstructual anisotropy, and grain morphologies with complex diversity, poses a significant challenge in accurately predicting its fatigue life, limiting its application in the aircraft field. This work herein introduces a novel approach incorporating a physics-informed neural network (PINN), in which an artificial neural network (ANN) is embedded with a damage mechanics model (CDM) and the critical process parameters of laser powder bed fusion (L-PBF) additive manufacturing. The partial differential equations of the updated CDM model are introduced into the training procedures of the PINN to building a loss function, effectively “teaching” the PINN to learn the physical knowledge. A comparison of the fatigue life prediction results of ANN and the proposed PINN models shows that the PINN model outperforms its counterparts with a 38.71% higher prediction accuracy. The effects of L-PBF process parameters on the fatigue life of as-built AlSi10Mg is examined using both ANN and PINN, proving the better predictive performance and data-physics consistency of the PINN model. The scheme of this work can inform the efficient prediction of fatigue life of additively manufactured alloys and also reverse prediction or fast finding of optimized process parameters for additive manufacturing.

Investigation of the failure mechanisms of Zr alloy with Cr2AlC coatings using in-situ bending tests: Experiments and simulations

The failure mechanisms of Cr2AlC-coated zirconium samples under different mechanical loading conditions have been investigated by combining in-situ bending tests and finite element simulations. The results of interrupted in-situ bending tests reveal that new critical cracks are mainly initiated in the Cr2AlC coating layer, followed by subsequent propagation into the Zr substrate with increasing plastic deformation. The formation of new critical cracks in Cr2AlC material is described using the maximum principal stress criterion. A stress state-dependent damage mechanics model combined with an advanced plasticity model is used to capture the ductile fracture behavior of the Zr substrate. Finite element simulations have been performed to identify the failure properties of coating and substrate materials, leading to the accurate reproduction of experimental fracture behavior.

Regulatory Peptide Pro-Gly-Pro Accelerates Neuroregeneration of Primary Neuroglial Culture after Mechanical Injury in Scratch Test

The scratch test is used as an experimental in vitro model of mechanical damage to primary neuronal cultures to study the mechanisms of cell death in damaged areas. The involvement of NMDA receptors in processes leading to delayed neuronal death, due to calcium dysregulation and synchronous mitochondrial depolarization, has been previously demonstrated. In this study, we explored the neuroregenerative potential of Pro-Gly-Pro (PGP)—an endogenous regulatory peptide with neuroprotective and anti-inflammatory properties and a mild chemoattractant effect. Mechanical injury to the primary neuroglial culture in the form of a scratch caused acute disruption of calcium homeostasis and mitochondrial functions. This was accompanied by neuronal death alongside changes in the profile of neuronal markers (BDNF, NSE and GFAP). In another series of experiments, under subtoxic doses of glutamate (Glu, 33 μM), delayed changes in [Ca2+]i and ΔΨm, i.e., several days after scratch application, were more pronounced in cells in damaged neuroglial cultures. The percentage of cells that restored the initial level of [Ca2+]i (p < 0.05) and the rate of recovery of ΔΨm (p < 0.01) were decreased compared with undamaged cells. Prophylactic application of PGP (100 μM, once) prevented the increase in [Ca2+]i and the sharp drop in mitochondrial potential [ΔΨm] at the time of scratching. Treatment with PGP (30 μM, three or six days) reduced the delayed Glu-induced disturbances in calcium homeostasis and cell death. In the post-glutamate period, the surviving neurons more effectively restored the initial levels of [Ca2+]i (p < 0.001) and Ψm (p < 0.0001). PGP also increased intracellular levels of BDNF and reduced extracellular NSE. In the context of the peptide’s therapeutic effect, the recovery of the damaged neuronal network occurred faster due to reduced astrogliosis and increased migration of neurons to the scratch area. Thus, the peptide PGP has a neuroprotective effect, increasing the survival of neuroglial cells after mechanical trauma in vitro by reducing cellular calcium overload and preventing mitochondrial dysfunction. Additionally, the tripeptide limits the post-traumatic consequences of mechanical damage: it reduces astrogliosis and promotes neuronal regeneration.

Damage characterization and modelling of FRP laminated composites subjected to external edge-on impact

This paper presents both experimental and numerical investigations into the edge-on impact behavior of T700/YPH307 composite laminates with varying lay-up designs and impact energy levels. Various non-destructive testing techniques, including visual inspection, ultrasonic C-scanning and X-ray computed tomography (CT), were used to detect the post-impact damage status and further reveal its 3D spatial distribution. A continuum damage mechanics (CDM) model, incorporating in-plane shear nonlinearity, fracture plane angle within anisotropic materials, as well as fiber kinking failure in longitudinal compression, was established using an explicit solver. Detailed comparison of the experimental and numerical results was conducted in mechanical response curves and failure mechanisms, where a good agreement was observed. Parameter analyses on the in-situ strengths and the friction coefficient were also performed, offering guidelines for the edge-on impact modelling. Failure mechanisms induced by edge-on impact typically exhibit two distinct features: a highly localized debris wedge, which can be regarded as a trigger in the subsequent occurrence of damage, and the bending fracture of the outer plies resulting from the wedge effect during the oscillating stage of an impact force plateau. Besides, higher impact energy exacerbated internal damage, while the influence of the lay-ups was relatively limited.

Laser powder bed fusion manufactured TPMS cellular structures: Failure modeling by using initial damage concept and continuum damage mechanics model

The present study examined the compressive mechanical properties and failure modes of Schwarz P and Schwarz G Triple Periodic Minimal Surface (TPMS) cellular structures using Finite Element (FE) simulations and experimental tests. A novel approach based on the initial damage parameter, which accounts for the initial defects induced by the Laser Powder Bed Fusion (LPBF) manufacturing process, was employed to model the compression behavior of the cellular structures. Compression tests were conducted on 3 Schwarz P and 3 Schwarz G specimens. A digital camera captured the deformation patterns of the specimens, revealing that shear bands formed in the Schwarz P specimens, while the Schwarz G specimens deformed uniformly. The FE simulations utilized modified material parameters according to the Continuum Damage Mechanics (CDM) framework. Moreover, an isotropic CDM model with micro-defect closure effect was implemented to investigate the failure mechanisms of the specimens. The FE simulation results indicated that the CDM model accurately predicted the mechanical behavior of the cellular structures fabricated by the LPBF process. The Scanning Electron Microscopy (SEM) images confirmed that the specimens had manufacturing defects such as micro-voids, pores, and surface roughness and that the crack initiation locations corresponded to the maximum damage locations of the FE simulations.

Determination of equivalent crack length for voids in metallic alloys based on continuum damage mechanics modeling

Metals contain different kinds of spatial defects significantly reducing the fatigue performance. Accurate defect-based life prediction methods are required to improve structural integrity analysis and life design reliability. The present work developed a method to determine the equivalent crack length for defects based on continuum damage mechanics. The spatial effects of defects in the calculation of the equivalent crack were quantified and verified by fatigue tests. It is confirmed that the equivalent crack length of both slit and elliptic defects is affected not only by the defect geometry but also by the applied load. Based on the equivalent crack and combined with Paris’ law, the predicted fatigue lives of various slit holes under different loading orientations are within the double scatter band and are much more accurate than the conventional projection method.

Comparative study of multiple statistical damage mechanics models for rock behaviors under high temperature

Under the influence of external factors such as high temperature, chemical corrosion, and loading-unloading cycles, micro-cracks and pores may develop within rock structures. Continuum damage mechanics (CDM) characterizes these micro-defects arising within rocks, investigating the physico-mechanical behaviors of rocks in damaged states. This study, grounded in the theoretical framework of CDM and utilizing the Mohr-Coulomb failure criterion, integrates different probability distributions and damage coupling methods to develop three statistical damage models. The investigation primarily explores the effects of strength criteria, probability functions, and damage coupling mechanisms on the statistical damage models. In addressing the complex interplay between rock micro-defects and external stressors such as high temperatures and chemical corrosion, this study leverages the principles of CDM within the Mohr-Coulomb criterion framework. It advances the field by developing three innovative statistical damage models, enriched by diverse probability distributions and damage coupling methods. The research delineates the substantial impact of strength criteria, probability functions, and damage coupling mechanisms on the behavior of these models. Notably, it achieves a synthesis of theoretical constructs and experimental validation, demonstrating the models' capacity to reflect the nuanced behaviors of damaged rock accurately. Furthermore, this investigation contributes a methodological blueprint for statistical damage model construction, underscoring the critical selection of strength criteria and probability distributions. These efforts fortify the theoretical underpinnings necessary for the enhanced engineering application of statistics-driven damage analysis.

Regularized Density-Driven Damage Mechanics Model for Failure Analysis of Cementitious Composites

Regularized Density-Driven Damage Mechanics Model for Failure Analysis of Cementitious Composites

Study of Damage Mechanism and Evolution Model of Concrete under Freeze–Thaw Cycles

Researching the mechanical characteristics of concrete subjected to the freeze–thaw cycle is crucial for building engineering in cold climates. As a result, uniaxial compression tests were performed on concrete samples exposed to various freeze–thaw (F–T) cycles, and the measurements of the pore size distribution, porosity, and P-wave velocity of the saturated concrete samples were obtained, both before and after being exposed to the F–T cycles. Concrete’s F–T damage mechanism and damage evolution model were thoroughly examined. Using rock structure and moisture analysis test equipment to observe the T2 spectrum, the results showed that the F–T cycles can cause the internal structure of the samples to deteriorate. Porosity and F–T cycles have a positive correlation, although P-wave velocity has a negative correlation with the F–T cycles. As the F–T cycles increased, the specimens’ peak strength and elastic modulus steadily declined, while the peak strain clearly exhibited an increasing trend. A microscopic F–T damage model that takes into account the pore size distribution was developed, based on the relative changes in the pore structure distribution (PSD), before and after the F–T cycles. The concrete sample damage evolution law under various F–T cycles was examined using the following metrics: total energy, pore size distribution, static and dynamic elastic moduli, porosity, and P-wave velocity. Uniaxial compressive strength (UCS) and peak strain tests were used to evaluate the accuracy of the pore size distribution damage model, as well as that of five other widely used damage models.

Microscale modeling of damage mechanisms in dual‐phase steel DP800

Microscale modeling of damage mechanisms in dual‐phase steel DP800

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.

A Multiscale Inelastic Internal State Variable Corrosion Model.

We present a corrosion internal state variable (ISV) damage model based upon the integrated computational materials engineering (ICME) hierarchical multiscale paradigm. Structure-property experiments for magnesium alloys were used where the only inputs were the volume fractions of each element of the periodic table. This macroscale ISV corrosion model finds its basis in Horstemeyer's mechanical damage model, which includes three separate ISVs for damage nucleation, growth, and coalescence, as well as Walton's inclusion of corrosion, which introduces five new ISVs for pit nucleation, growth, and coalescence, along with general corrosion and intergranular corrosion. While Walton's corrosion ISVs are phenomenological in nature, herein we develop a multiscale physical basis for the corrosion ISVs. The parameters for the macroscale corrosion ISVs were garnered from the mesoscale Butler-Volmer equations. Pure magnesium with differing amounts of aluminum were used in corrosion tests to exemplify the different pitting, general corrosion, and intergranular corrosion rates, and the macroscale ISV model was calibrated with said data, in which the only inputs to the model are the volume percentages of the elements magnesium and aluminum. Although magnesium alloys were used to motivate and calibrate the model, the model is abstract enough to possibly capture other material systems as well.

(Invited) Lifetime Predictive Model of Capacity Loss, Resistance Increase, and Irreversible Thickness Growth

We present a battery lifetime model that predicts Irreversible battery thickness change under constant pressure operation as the battery ages, along with capacity loss and resistance growth. These metrics are very important for predicting lithium-ion battery state of health (SOH) and remaining useful life due to their interdependence with battery packaging and safety. To design and operate battery storage systems safely, we must be able to predict and detect changes in all three SOH metrics over life accurately and simultaneously. Traditionally, these three SOH metrics have been modeled separately. However, we developed a single model that simultaneously predicts battery capacity, resistance, and expansion over its lifetime.In this work, battery degradation is modeled using the single particle model (SPM) framework, including mechanical damage in the electrodes, which results in loss of active material (LAM), and the side reactions for SEI growth and Li plating, which result in loss of lithium inventory (LLI). We introduce an equivalent stress and concentration dependence of stress to the mechanical damage model. Commonly used fatigue models assume symmetric cycles (zero-mean stress) [1]. To account for cycling conditions with different currents on charge and discharge, an equivalent stress that adjusts for non-zero mean stress is needed. The concentration dependency of strain and the resulting stress allows us to capture different degradation rates for cells cycled at different depths of discharge (DOD). Lithium plating at the separator interface is often described as a spatially non-uniform process using the pseudo-2D (P2D) model. This phenomenon can be captured in the SPM framework using a current-dependent dynamic term to account for spatial-nonuniformity of electrolyte dynamics at higher currents.Experimental data from cells cycling with periodic reference performance tests were used to tune the degradation model. In addition to the standard I, V, and T measurements, continuous measurements of the thickness change of the battery pouch cells were recorded. From this data, we extracted the capacity, electrode state of health (eSOH), resistance, and reversible and irreversible expansion. The test conditions were designed to excite different dominant degradation mechanisms (e.g. mechanical damage) by cycling the cells at different conditions (C-rate, temperature, preload pressure, and DOD). The tuning, which uses accelerated aging simulations [2] (to speed up the tuning process), results in a single set of parameters that predicts capacity loss, resistance growth, and irreversible thickness change as the battery ages, even for conditions that were not used for parameter tuning.The tuning is performed in two sequential steps. First, the parameters related to the electrochemical and mechanical degradation rates, which result in LLI and LAM, are tuned to match the extracted eSOH variables at each Reference Performance Test (RPT). The first tuning gives us the amount of plated Li, SEI growth, and mechanical damage in the particles. We then relate these quantities to irreversible expansion using a linear relationship in the case of SEI and mechanical damage and quadratic in the case of Li plating [3]. The same relationship is used for all cells, and this represents the 2nd tuning step. Our data set and calibration are unique in that the dominant degradation mode is the loss of lithium inventory due to the loss of active anode material. Most prior work on lifetime predictive models relied on SEI growth as the dominant degradation mode. Figure 2 shows the tuned model prediction of the three performance metrics over the cycle life of cells for various cycling conditions. The markers represent the measurement at each reference performance test, and the lines correspond to the model.

Modeling of Concrete Deterioration under External Sulfate Attack and Drying-Wetting Cycles: A Review.

This paper comprehensively summarizes moisture transport, ion transport, and mechanical damage models applied to concrete under sulfate attack and drying-wetting cycles. It highlights the essential aspects and principles of each model, emphasizing their significance in understanding the movement of moisture and ions, as well as the resulting mechanical damage within the concrete during these degradation processes. The paper critically analyzes the assumptions made in each model, shedding light on their limitations and implications for prediction accuracy. Two primary challenges faced by current models under sulfate attack and drying-wetting cycles are identified: the limited consideration of the coupled effects of chemical and physical attacks from sulfate, and the unclear mechanism of the sulfate attacks. Future research directions are proposed, focusing on exploring the transport mechanism of sulfate ions under various driving forces and further clarifying the crystallization process and expansion damage mechanism in concrete pores. Addressing these research directions will advance our understanding of sulfate attack under drying-wetting cycles, leading to improved models and mitigation strategies for enhancing the durability and performance of concrete structures.

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.

Research on dynamic mechanical properties and damage model of ceramic materials under multi‐axial stress

AbstractDue to their exceptional impact resistance, ceramics are extensively used in various fields. However, unavoidable pores, microcracks, and inherent defects can degrade the performance of ceramic materials. A damage model of SiC ceramics under passive confining pressure was constructed based on the Lemaitre strain equivalence principle and the Weibull distribution function. This paper presented a dynamic damage model for SiC ceramics subjected to passive confinement pressure based on the principles of damage mechanics. Additionally, the split Hopkinson pressure bar device was employed to investigate the compressive strength and damage evolution of SiC ceramics at various shock pressures and confinement degrees. The experimental results indicate that constraints can reduce the damage to ceramics. The metal sleeve increased stiffness when compressing the ceramic material, allowing the specimen to convert from brittle–plastic–brittle. When sufficient constraints can be provided, the peak strain decreases gradually with the increase of the impact air pressure. Experimental data showing good agreement with the proposed model validated and analyzed the established model. Thinner boundary constraints cannot maintain the stability of ceramic structures, thicker boundaries do not significantly improve performance, and thicker boundaries can cause more weak areas. This paper provides guidance for the design of encapsulated ceramic composite armor by quantitatively studying the constraint thickness.

Mechanical characteristics and damage model for rock-like specimen with two parallel grout-filled cracks

To investigate the mechanical properties of rock-like specimens with two parallel cracks filled with grout, uniaxial compression tests in combination with digital image correlation (DIC) and acoustic emission (AE) techniques have been performed on grout-filled cracked specimens with different rock bridge dip angles β. Results indicated that with the increase of β, the uniaxial compression strength, cumulated AE count, AE energy, as well as shear crack proportion initially decreases and subsequently increases. The overall AE b-value and the DIC-based maximum principal strain initially increases and subsequently decreases as β increases. The failure mode also varies from tensile to mixed tensile-shear mode. Furthermore, a particle flow code (PFC) model, which considers the grout filling, grout-rock interface, and rock, has been proposed. Numerical results showed that the range of microcracks inclination angle first decrease from 70°−100° to 70°–90° and then increases to 70°–110°. Besides, existence of grout filling and changes of bridge angle leads to significant difference in PFC particle displacement, which can cause the changed of crack initiation positions and failure modes. Finally, a damage model considering stress intensity factor for the grout-filled specimen was established. Both of pre-crack damage and loading damage were considered in this model, and a damage repair factor was proposed to describe effect of grout filling. The results showed that grouting could can effectively suppress stress concentration caused by pre-existing crack, thereby changes the strength of cracked specimen.

Development of corrosion-fatigue analysis method of cable hangers in tied-arch bridges considering train-bridge interaction

This study proposes an integrated corrosion-fatigue analysis method for bridge hangers by combining the dynamic bridge-train interaction analysis for random train arrivals with various speeds and the linear elastic fracture mechanics (LEFM)-based crack propagation analysis considering the corrosion-fatigue effects. Accordingly, a three-stage process, namely, zinc coating corrosion, pit-crack transition, and corrosion-fatigue crack propagation for wires in hangers, was proposed to simulate the total service life. A train-bridge-interaction analysis was conducted on a tied-arch bridge with multiple cable hangers using the vector form intrinsic finite element method, where the stresses in the hangers were generated under high-speed train loads. The pit-crack transition was analyzed based on the pit growth and fatigue growth; whose rates compete to dominate the transition phenomenon. The fatigue crack growth rate was estimated using a LEFM approach considering the equivalent stress ranges and number of stress cycles. The effects of reducing the cable cross-section and updating the internal stress of the multi-layered wires were investigated. The present method was compared with the continuum damage mechanics model for validation. A relatively short remaining corrosion-fatigue life was found in the cables under the train loads, after corrosion of the zinc coating and pit-crack transition in the steel wires were developed.