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Journal articles on the topic 'Gradient damage'

Author: Grafiati

Published: 25 November 2022

Last updated: 27 December 2022

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1

Le, Duc Trung, Jean-Jacques Marigo, Corrado Maurini, and Stefano Vidoli. "Strain-gradient vs damage-gradient regularizations of softening damage models." Computer Methods in Applied Mechanics and Engineering 340 (October 2018): 424–50. http://dx.doi.org/10.1016/j.cma.2018.06.013.

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2

Saczuk, J., K. Hackl, and H. Stumpf. "Rate theory of nonlocal gradient damage-gradient viscoinelasticity." International Journal of Plasticity 19, no. 5 (May 2003): 675–706. http://dx.doi.org/10.1016/s0749-6419(02)00004-9.

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3

da Silva, L. R., and H. J. Herrmann. "Damage spreading in a gradient." Journal of Statistical Physics 52, no. 1-2 (July 1988): 463–70. http://dx.doi.org/10.1007/bf01016427.

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4

Zhao, Bing, Ying-ren Zheng, Ming-hua Zeng, Xue-song Tang, and Xiao-gang Li. "First-order gradient damage theory." Applied Mathematics and Mechanics 31, no. 8 (July 24, 2010): 987–94. http://dx.doi.org/10.1007/s10483-010-1334-9.

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5

Bui, Q. V. "Initiation of damage with implicit gradient-enhanced damage models." International Journal of Solids and Structures 47, no. 18-19 (September 2010): 2425–35. http://dx.doi.org/10.1016/j.ijsolstr.2010.05.003.

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6

Frémond, Michel, and Boumediene Nedjar. "Damage, gradient of damage and principle of virtual power." International Journal of Solids and Structures 33, no. 8 (March 1996): 1083–103. http://dx.doi.org/10.1016/0020-7683(95)00074-7.

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7

Kiefer, Bjoern, Tobias Waffenschmidt, Leon Sprave, and Andreas Menzel. "A gradient-enhanced damage model coupled to plasticity—multi-surface formulation and algorithmic concepts." International Journal of Damage Mechanics 27, no. 2 (January 5, 2017): 253–95. http://dx.doi.org/10.1177/1056789516676306.

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A non-local gradient-enhanced damage-plasticity formulation is proposed, which prevents the loss of well-posedness of the governing field equations in the post-critical damage regime. The non-locality of the formulation then manifests itself in terms of a non-local free energy contribution that penalizes the occurrence of damage gradients. A second penalty term is introduced to force the global damage field to coincide with the internal damage state variable at the Gauss point level. An enforcement of Karush–Kuhn–Tucker conditions on the global level can thus be avoided and classical local damage models may directly be incorporated and equipped with a non-local gradient enhancement. An important part of the present work is to investigate the efficiency and robustness of different algorithmic schemes to locally enforce the Karush–Kuhn–Tucker conditions in the multi-surface damage-plasticity setting. Response simulations for representative inhomogeneous boundary value problems are studied to assess the effectiveness of the gradient enhancement regarding stability and mesh objectivity.

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8

Lorentz, E., and A. Benallal. "Gradient constitutive relations: numerical aspects and application to gradient damage." Computer Methods in Applied Mechanics and Engineering 194, no. 50-52 (December 2005): 5191–220. http://dx.doi.org/10.1016/j.cma.2004.12.016.

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9

Lacy, Thomas E., David L. McDowell, and Ramesh Talreja. "Gradient concepts for evolution of damage." Mechanics of Materials 31, no. 12 (December 1999): 831–60. http://dx.doi.org/10.1016/s0167-6636(99)00029-0.

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10

Placidi, Luca, Emilio Barchiesi, and Anil Misra. "A strain gradient variational approach to damage: a comparison with damage gradient models and numerical results." Mathematics and Mechanics of Complex Systems 6, no. 2 (May 29, 2018): 77–100. http://dx.doi.org/10.2140/memocs.2018.6.77.

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11

Zhang, Siqian, Jing Liu, Haoyu Zhang, Jie Sun, and Lijia Chen. "Damage Adaptive Titanium Alloy by In-Situ Elastic Gradual Mechanism." Materials 13, no. 2 (January 15, 2020): 406. http://dx.doi.org/10.3390/ma13020406.

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Natural materials are generally damage adaptive through their multilevel architectures, with the characteristics of compositional and mechanical gradients. This study demonstrated that the desired elastic gradient can be in-situ stress-induced in a titanium alloy, and that the alloy showed extreme fatigue-damage tolerance through the crack deflection and branch due to the formation of a three-dimensional elastically graded zone surrounding the crack tip. This looks like a perceptive and adaptive mechanism to retard the crack: the higher stress concentrated at the tip and the larger elastic gradient to be induced. The retardation is so strong that a gradient nano-grained layer with a thickness of less than 2 μm formed at the crack tip due to the highly localized and accumulated plasticity. Furthermore, the ultrafine-grained alloy with the nano-sized precipitation also exhibited good damage tolerance.

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12

Simone, Angelo. "Explicit and implicit gradient-enhanced damage models." Revue Européenne de Génie Civil 11, no. 7-8 (August 2007): 1023–44. http://dx.doi.org/10.1080/17747120.2007.9692975.

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13

Liebe, Tina, Paul Steinmann, and Ahmed Benallal. "Some aspects of a gradient damage formulation." Revue Européenne des Éléments Finis 10, no. 2-4 (January 2001): 157–72. http://dx.doi.org/10.1080/12506559.2001.11869245.

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14

de Borst, R., A. Benallal, and O. M. Heeres. "A Gradient-Enhanced Damage Approach to Fracture." Le Journal de Physique IV 06, no. C6 (October 1996): C6–491—C6–502. http://dx.doi.org/10.1051/jp4:1996649.

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15

Simone, Angelo. "Explicit and implicit gradient-enhanced damage models." Revue européenne de génie civil 11, no. 7-8 (October 1, 2007): 1023–44. http://dx.doi.org/10.3166/regc.11.1023-1044.

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16

Lorentz, E., and V. Godard. "Gradient damage models: Toward full-scale computations." Computer Methods in Applied Mechanics and Engineering 200, no. 21-22 (May 2011): 1927–44. http://dx.doi.org/10.1016/j.cma.2010.06.025.

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17

Peerlings, R. H. J., R. de Borst, W. A. M. Brekelmans, and M. G. D. Geers. "Gradient-enhanced damage modelling of concrete fracture." Mechanics of Cohesive-frictional Materials 3, no. 4 (October 1998): 323–42. http://dx.doi.org/10.1002/(sici)1099-1484(1998100)3:4<323::aid-cfm51>3.0.co;2-z.

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18

Putar, Filip, Jurica Sorić, Tomislav Lesičar, and Zdenko Tonković. "Damage modeling employing strain gradient continuum theory." International Journal of Solids and Structures 120 (August 2017): 171–85. http://dx.doi.org/10.1016/j.ijsolstr.2017.04.039.

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19

PEERLINGS, R. H. J., R. DE BORST, W. A. M. BREKELMANS, and J. H. P. DE VREE. "GRADIENT ENHANCED DAMAGE FOR QUASI-BRITTLE MATERIALS." International Journal for Numerical Methods in Engineering 39, no. 19 (October 15, 1996): 3391–403. http://dx.doi.org/10.1002/(sici)1097-0207(19961015)39:19<3391::aid-nme7>3.0.co;2-d.

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20

Poh, Leong Hien, and Gang Sun. "Localizing gradient damage model with decreasing interactions." International Journal for Numerical Methods in Engineering 110, no. 6 (September 22, 2016): 503–22. http://dx.doi.org/10.1002/nme.5364.

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21

Mao, Wenlong, Tianwen Wang, and Yiming Shu. "Model and Experimental Studies of the Seepage Failure of Damaged Geotextile at the Joint between Tubes in a Geotextile Tube Dam." Water 14, no. 23 (December 2, 2022): 3934. http://dx.doi.org/10.3390/w14233934.

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This paper focuses on the impact of geotextile tube damage at the joints between tubes on dam structures subjected to seepage. First, a seepage-induced failure critical gradient model for damaged geotextile tubes was developed. Tests were conducted using geotextile specimens with precut O-shaped holes to simulate the seepage erosion process. Various overburden loads (0, 5, 10, 20, and 30 kPa) and hole radii (0.5, 1.0, 1.5, and 2 cm) were examined. Based on the test phenomena and the changes in pore-water pressure and seepage flow, four progression stages (seepage stability, sand particle wash-out, preferential flow formation and development, and complete failure) were identified. The experimental critical gradients obtained under different conditions agreed well with the model results. The critical gradient is positively correlated with the overburden load and negatively correlated with the hole radius. Critical gradient growth gradually slows with increasing overburden load. The critical gradient difference caused by the hole size decreases rapidly. When the overburden load increases to 20 kPa, this difference is essentially unchanged. These findings can provide a better understanding of the performance of damaged geotextile tubes.

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22

Xing, Hai Yan, Ya Tong Han, Ping Qin, and Chang Hai Liu. "MMM Identifying Damage for Recycled Pumping Rod Base on SVM." Applied Mechanics and Materials 401-403 (September 2013): 1251–54. http://dx.doi.org/10.4028/www.scientific.net/amm.401-403.1251.

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Remanufacturing is an important way to develop recycling economy. However, the quality reliability testing is a bottleneck for the recycled product. Metal Magnetic Memory (MMM) technology is a valid method for early damage testing based on the magneto-mechanical effect. This paper aims at quantitative identifying damage for the recycled pumping rod（RPR）. The MMM rules of RPR damage are found through fatigue experiments. By using four-dimensional MMM parameter vectors, that is, peek-peek value，differential gradient，integral gradient and energy, are marked the damages. Furthermore，a multi-level damage classification model has been established base on optimal multi-classification algorithm of support vector machine (SVM) for RPR. The relationship is given between the damage degrees and MMM signals, which provides a theoretical basis and engineering tool of RPR reliability evaluation.

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23

Wood, Bruce W., and Charles C. Reilly. "Atypical Symptoms of Cold Damage to Pecan." HortScience 36, no. 2 (April 2001): 298–301. http://dx.doi.org/10.21273/hortsci.36.2.298.

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Bearing pecan [Carya illinoinensis (Wangenh.) K. Koch] trees overly stressed by crop load and premature autumn defoliation either died or were severely damaged by -3°C in mid-November. Orchard damage was associated with death of tree roots during the dormant season. Exposure of stressed trees to -5°C in mid-March produced an atypical, but distinct, bottom-to-top-of-canopy gradient in bud death and reduced growth of shoots and foliage that was consistent with the pattern of reduced carbohydrate reserves of associated support shoots. Additionally, the foliage of damaged trees contained higher concentrations of N, P, K, Ca, Mg, Mn, Fe, and B. Trees did not exhibit traditional symptoms of cold damage, thus these findings extend cold injury diagnostic criteria to include both root and tree death during the dormant season and also a distinct gradient in shoot death during early spring. Damage by cold appears to be preventable by avoiding excessive tree stress due to overcropping and premature defoliation.

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24

Wosatko, Adam. "Comparison of evolving gradient damage formulations with different activity functions." Archive of Applied Mechanics 91, no. 2 (February 2021): 597–627. http://dx.doi.org/10.1007/s00419-021-01889-2.

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AbstractIn the paper, two existing upgrades of the gradient damage model for the simulations of cracking in concrete are compared. The damage theory is made nonlocal via a gradient enhancement to overcome the mesh dependence of simulation results. The implicit gradient model with an averaging equation, where the internal length parameter is assumed as constant during the strain softening analysis, gives unrealistically broadened damage zones. The gradient enhancement of the scalar damage model can be improved via a function of an internal length scale, so an evolution of the gradient activity is postulated during the localization process. Two different modifications of the averaging equation and respective evolving gradient damage formulations are presented. Different activity functions are tested to see whether the formation of a too wide damage zone still occurs. Activating or localizing character of the gradient influence can be introduced and the impact of both approaches on the numerical results is shown in the paper. The aforementioned variants are implemented and examined using the benchmarks of tension in a bar and bending of a cantilever beam.

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25

Walter, Christopher A., Mark B. Burnham, Mary Beth Adams, Brenden E. McNeil, Lindsay N. Deel, and William T. Peterjohn. "Nitrogen Availability Decreases the Severity of Snow Storm Damage in a Temperate Forest." Forest Science 66, no. 1 (November 7, 2019): 58–65. http://dx.doi.org/10.1093/forsci/fxz064.

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Abstract Storms are among the greatest natural disturbances in temperate forests, and increased nitrogen (N) availability is thought to increase storm damage. However, the extent to which N availability increases damage from snowfall is less clear. To test how N availability might affect the susceptibility of trees to snow damage in a temperate forest, we took advantage of an opportunistic storm and surveyed damage in fertilized and unfertilized stands, and across a native N availability gradient. In response to a severe, early season snow storm—a consequence of Superstorm Sandy—the percentages of both basal area and stems damaged were lower in a fertilized watershed than in an unfertilized watershed. Across the native N availability gradient, the percentage of basal area damaged by snow decreased with higher soil N. The effects of N availability on damage were also affected by tree species. Our results suggest that N availability decreases damage from snow storms, contrary to our hypotheses drawn from broader studies. Understanding the relation between storm damage and N availability is important, considering the global increase in N deposition, and since severe storms are likely to become more prevalent with climate change.

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26

Nedjar, B. "Elastoplastic-damage modelling including the gradient of damage: formulation and computational aspects." International Journal of Solids and Structures 38, no. 30-31 (July 2001): 5421–51. http://dx.doi.org/10.1016/s0020-7683(00)00358-9.

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27

Graham, John. "Rapid Purification of Nuclei from Animal and Plant Tissues and Cultured Cells." Scientific World JOURNAL 2 (2002): 1551–54. http://dx.doi.org/10.1100/tsw.2002.832.

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Nuclei are isolated by buoyant density banding in a discontinuous iodixanol gradient, under isoosmotic conditions. The low viscosity of the gradient allows the purification to be carried out at 10,000g in only 20 min. The method avoids possible damage to nucleoprotein complexes caused by hyperosmotic sucrose gradients. Although developed for mammalian liver the method can be applied (with or without minor modifications) to any tissue or cell type.

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28

Soo Lon Wah, William, and Yung-Tsang Chen. "A new approach toward damage localization and quantification of structures under changing temperature condition." Journal of Low Frequency Noise, Vibration and Active Control 39, no. 3 (August 27, 2018): 572–87. http://dx.doi.org/10.1177/1461348418793079.

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Most damage detection methods developed in the literature cannot give the locations and extent of damages under the presence of varying temperature condition. This is because temperature condition changes the vibration properties of a structure, which are commonly analyzed for damage detection, and temperature gradient throughout the structure makes it difficult to create a baseline for the undamaged structure, as the baseline is generally constructed using features obtained under a wide range of temperature conditions. In this paper, a new insight on how to approach damage detection using only a single temperature condition to create the baseline is proposed. This approach solves the damage detection under changing temperature problem in two stages by first quantifying the change of stiffness of all the elements in a structure due to temperature and damage effects, followed by removing the temperature effect, a global effect, to give the actual damage locations and extent. Using single temperature condition allows new measurements to be compared to a benchmark so that local deviation can be obtained, thus making the damaged elements identifiable. The proposed approach is tested using a beam structure model and a shear building under different gradient temperature conditions, and the results demonstrate that the method successfully eliminates the change in elemental stiffness due to temperature effect and gives correct damage locations and extent. The approach can be implemented with other existing damage detection methods that did not consider the effect of temperature so that structures under varying temperature condition can be analyzed.

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29

Lu, Ling Ling, Chen Guang Huang, and Xi Wang. "A Damage Identification Method Based on Differential Gradient of Normalized Strain." Applied Mechanics and Materials 330 (June 2013): 321–30. http://dx.doi.org/10.4028/www.scientific.net/amm.330.321.

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A damage identification method based on differential gradient of normalized strain (DGNS) is presented to overcome the disadvantages of traditional static damage identification, such as the complicacy of measurement system and the limited measurement points etc. Two numerical simulations were conducted on a dog-bone specimen to verify the feasibility of the method. In the experiment, differential of strain contour density (DSCD), which has the same physical meaning with DGNS，significantly improves the smoothness and visualization of field information. Both the simulation and experiment results show that, DGNS (DSCD) is capable of describing the structural damage property meanwhile effectively isolates the damaged areas from regions with inhomogeneous deformation due to geometric inhomogeneity. Moreover, DGNS (DSCD) is a structural intrinsic parameter, and independent on external loads.

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30

Solyaev, Yury, Sergey Lurie, Emilio Barchiesi, and Luca Placidi. "On the dependence of standard and gradient elastic material constants on a field of defects." Mathematics and Mechanics of Solids 25, no. 1 (July 30, 2019): 35–45. http://dx.doi.org/10.1177/1081286519861827.

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In this work, we consider a strain gradient elasticity theory with an extended number of field variables: the displacement vector and an additional scalar field defining the internal micro-deformation. The total internal energy of the model depends on the strain, the micro-deformation function, their gradients, and the coupling. The considered model can be treated as gradient/micromorphic. Moreover, the micro-deformation field can be treated as a field of scalar defects distributed along the medium. Based on analytic (one-dimensional) solutions of uniform/non-uniform deformation of the rod, we introduce (i) an apparent stiffness and (ii) an apparent length scale parameter. Subsequently, we provide a variant of continuum-on-continuum homogenization by equating tip displacements for the gradient/micromorphic medium and an equivalent strain gradient one. Elongation of the gradient/micromorphic rod is therefore equated with the corresponding elongation of the equivalent strain gradient rod, whose behavior is characterized by the apparent material constants. Subsequently, the non-dimensional coupling number is identified with a damage parameter. It is shown that, on the one hand, the apparent stiffness of the rod is reduced when such parameter increases. On the other hand, the apparent length scale parameter (i.e. the apparent second gradient elastic coefficient) increases when the damage parameter increases. Therefore, it is shown that the presence of defects in a second gradient linear elastic material may increase its apparent strain gradient behavior.

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31

Xiao, Li, Jialiang Zhang, Wei Huang, Juli Carrillo, Evan Siemann, and Jianqing Ding. "Tallow tree allocates contrasting secondary chemicals in response to varying environments along elevational gradients." Journal of Plant Ecology 13, no. 3 (April 3, 2020): 295–303. http://dx.doi.org/10.1093/jpe/rtaa014.

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Abstract Aims Understanding how tree species regulate multiple types of secondary chemicals along elevational gradients is critical for elucidating the physiological and ecological strategies of plants in response to varying biotic and/or abiotic environments. This study aims to examine how Chinese tallow tree (Triadica sebifera) allocates resources to the production of different secondary chemicals in response to varying environments across elevational gradients. Methods We conducted field surveys of different herbivore feeding guilds and their damage rates on Chinese tallow trees along an elevational gradient in China and measured secondary chemicals (tannins and flavonoids) in damaged and undamaged leaves. Important Findings The odds of a leaf being damaged (chewing or scarring) decreased with elevation. Flavonoid concentrations increased with elevation in undamaged leaves but decreased with elevation in damaged leaves, with quercitrin contributing most strongly to this pattern, likely as results of plant responding to changing biotic or abiotic stresses along elevational gradients. Tannin concentrations did not vary with elevation, so undamaged leaves had relatively lower tannin to flavonoid ratios at high elevation than at low elevation. Our study reveals variation in herbivory and contrasting trends in plant secondary metabolism along an elevation gradient and highlights the importance of simultaneously considering multiple types of secondary chemicals in plant physiological and ecological strategies.

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32

Molnár, Gergely, Aurélien Doitrand, Adrien Jaccon, Benoit Prabel, and Anthony Gravouil. "Thermodynamically consistent linear-gradient damage model in Abaqus." Engineering Fracture Mechanics 266 (May 2022): 108390. http://dx.doi.org/10.1016/j.engfracmech.2022.108390.

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33

Forest, Samuel. "Micromorphic Approach for Gradient Elasticity, Viscoplasticity, and Damage." Journal of Engineering Mechanics 135, no. 3 (March 2009): 117–31. http://dx.doi.org/10.1061/(asce)0733-9399(2009)135:3(117).

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34

Narayan, Sooraj, and Lallit Anand. "Fracture of amorphous polymers: A gradient-damage theory." Journal of the Mechanics and Physics of Solids 146 (January 2021): 104164. http://dx.doi.org/10.1016/j.jmps.2020.104164.

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35

Titscher, Thomas, Javier Oliver, and Jörg F. Unger. "Implicit–Explicit Integration of Gradient-Enhanced Damage Models." Journal of Engineering Mechanics 145, no. 7 (July 2019): 04019040. http://dx.doi.org/10.1061/(asce)em.1943-7889.0001608.

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36

Askes, H., and L. J. Sluys. "Explicit and implicit gradient series in damage mechanics." European Journal of Mechanics - A/Solids 21, no. 3 (January 2002): 379–90. http://dx.doi.org/10.1016/s0997-7538(02)01214-7.

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37

Martínez-Pañeda, E., and C. Betegón. "Modeling damage and fracture within strain-gradient plasticity." International Journal of Solids and Structures 59 (May 2015): 208–15. http://dx.doi.org/10.1016/j.ijsolstr.2015.02.010.

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38

Pamin, Jerzy. "Gradient plasticity and damage models: a short comparison." Computational Materials Science 32, no. 3-4 (March 2005): 472–79. http://dx.doi.org/10.1016/j.commatsci.2004.09.018.

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39

Li, Gang, and Fuh-Gwo Yuan. "Gradient enhanced damage sizing for structural health management." Smart Materials and Structures 24, no. 2 (January 23, 2015): 025036. http://dx.doi.org/10.1088/0964-1726/24/2/025036.

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40

Peerlings, R. H. J., W. A. M. Brekelmans, R. de Borst, and M. G. D. Geers. "Gradient-enhanced damage modelling of high-cycle fatigue." International Journal for Numerical Methods in Engineering 49, no. 12 (2000): 1547–69. http://dx.doi.org/10.1002/1097-0207(20001230)49:12<1547::aid-nme16>3.0.co;2-d.

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41

Zreid, Imadeddin, and Michael Kaliske. "On the gradient enhancement of microplane damage models." PAMM 14, no. 1 (December 2014): 155–56. http://dx.doi.org/10.1002/pamm.201410065.

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42

Wulfinghoff, Stephan, Atefeh Alipour, Shahed Rezaei, Julian Kochmann, and Stefanie Reese. "Generalized Interface Models With Damage in Gradient Plasticity." PAMM 16, no. 1 (October 2016): 411–12. http://dx.doi.org/10.1002/pamm.201610194.

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43

Verhoosel, Clemens V., Michael A. Scott, Thomas J. R. Hughes, and René de Borst. "An isogeometric analysis approach to gradient damage models." International Journal for Numerical Methods in Engineering 86, no. 1 (February 11, 2011): 115–34. http://dx.doi.org/10.1002/nme.3150.

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44

Thamburaj, Priya, Michael H. Santare, and George A. Gazonas. "The Effect of Graded Strength on Damage Propagation in Continuously Nonhomogeneous Materials." Journal of Engineering Materials and Technology 125, no. 4 (September 22, 2003): 412–17. http://dx.doi.org/10.1115/1.1605116.

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A damage model developed by Johnson and Holmquist is implemented into a dynamic finite element code. This is then used to study the effect of grading of the phenomenological damage parameters on the propagation of damage through the material. The numerical results for two one-dimensional example problems with different boundary conditions are presented, wherein the effect of a gradient in the intact strength of the material on damage propagation is studied. The results show that introducing different strength gradients can alter the location of the site of maximum damage. This may have important implications in the design of impact resistant materials and structures.

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45

Cleja-Ţigoiu, Sanda, and Victor Ţigoiu. "Strain Gradient Effect in Finite Elasto-plastic Damaged Materials." International Journal of Damage Mechanics 20, no. 4 (November 9, 2010): 484–514. http://dx.doi.org/10.1177/1056789510386816.

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In this article we propose a strain gradient model for elasto-plastic materials in which there exist zones with structural inhomogeneities, characterized by nonlocal deformations. We assume the existence of an anholonomic configuration, called damaged configuration, which is associated with the second-order plastic deformation. We proved how the damage may be coupled to the second-order plasticity introducing a tensorial damage variable, Qd, as a measure of the nonmetricity of the plastic Bilby-type part of the connection, which characterizes peculiar structural defects. The constitutive and evolution equations are subjected to be compatible with the principle of the imbalanced free energy, which is applied for isothermal processes. The free energy density function Ψ, is represented as a function of second-order elastic deformation and it depends on the damaged configuration, K, through the second-order plastic deformation. At the level of plastically deformed configuration, the effects of macro- and microforces are cumulated into the internal power. Two possible nonlocal evolution equations to describe plastic behavior are derived as a consequence of balance equation for microforces. Finally, we look at the influence of the strain gradient in a simple model.

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46

Sharma, L., R. H. J. Peerlings, P. Shanthraj, F. Roters, and M. G. D. Geers. "An FFT-based spectral solver for interface decohesion modelling using a gradient damage approach." Computational Mechanics 65, no. 4 (December 11, 2019): 925–39. http://dx.doi.org/10.1007/s00466-019-01801-4.

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AbstractThis work presents a fast Fourier transform (FFT) based method that can be used to model interface decohesion. The inability of an FFT solver to deal with sharp interfaces discards the use of conventional cohesive zones to model the interfacial mechanical behaviour within this framework. This limitation is overcome by approximating sharp interfaces (e.g. grain/phase boundaries) with an interphase. Within the interphase, the background plastic constitutive behaviour is inherited from the respective adjacent grains. The anisotropic kinematics of the decohesion process is modelled using a damage deformation gradient that is constructed by mapping the opening strains (in normal and tangential modes) to the associated projection tensors. The degradation (damage) of the interfacial opening resistances is modelled via a dimensionless nonlocal damage variable that prevents localisation of damage within the interphase. This nonlocal variable results from the solution of a gradient damage based regularisation equation within the interphase subdomain. The damage field is constrained to the interphase region by applying a relatively large penalisation on the damage gradients inside the interphase. The extent of nonlocality ensures that the damage is largely uniform in the direction perpendicular to the interphase, thus making its thickness the theoretical lengthscale for dissipation. To achieve model predictions that are objective with respect to the interphase thickness, scaling relations of the model parameters are proposed. The numerical performance is shown for a uniform opening case and then for a propagating crack. Finally, an application to an artificial polycrystal is shown.

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47

Son, Nguyen Quoc, and Nguyen Truong Giang. "Standard gradient models and crack simulation." Vietnam Journal of Mechanics 33, no. 4 (December 12, 2011): 293–301. http://dx.doi.org/10.15625/0866-7136/33/4/261.

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The standard gradient models have been intensively studied in the literature, cf. Fremond (1985) or Gurtin (1991) for various applications in plasticity, damage mechanics and phase change analysis. The governing equations for a solid have been introduced essentially from an extended version of the virtual equation. It is shown here first that these equations can also be derived from the formalism of energy and dissipation potentials and appear as a generalized Biot equation for the solid. In this spirit, the governing equations for higher gradient models can be straightforwardly given. The interest of gradient models is then discussed in the context of damage mechanics and crack simulation. The phenomenon of strain localization in a time-dependent or time-independent process of damage is explored as a convenient numerical method to simulate the propagation of cracks, in relation with some recent works of theliterature, cf. Bourdin & Marigo [3], Lorentz & al [5], Henry & al [12].

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Wolff, Michael, Michael Böhm, and Holm Altenbach. "Application of the Müller–Liu entropy principle to gradient-damage models in the thermo-elastic case." International Journal of Damage Mechanics 27, no. 3 (November 25, 2016): 387–408. http://dx.doi.org/10.1177/1056789516679495.

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A general damage-gradient model is developed within the framework of continuum mechanics, using balance relations. As a new item, a balance relation for totally damaged material is introduced, leading to a partial differential equation for the damage variable. The obtained model is evaluated using the Müller–Liu approach, yielding necessary and sufficient conditions for thermodynamic consistency. The widely spread damage model with a scalar damage variable is obtained as a special case of the general model considered here. As a special case, we deal with a thermo-elastic material, avoiding splitting of the strain as well as introduction of internal variables connected with inelastic behaviour.

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Lyn Dee, Goh, Norhisham Bakhary, Azlan Abdul Rahman, and Baderul Hisham Ahmad. "A Comparison of Artificial Neural Network Learning Algorithms for Vibration-Based Damage Detection." Advanced Materials Research 163-167 (December 2010): 2756–60. http://dx.doi.org/10.4028/www.scientific.net/amr.163-167.2756.

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This paper investigates the performance of Artificial Neural Network (ANN) learning algorithms for vibration-based damage detection. The capabilities of six different learning algorithms in detecting damage are studied and their performances are compared. The algorithms are Levenberg-Marquardt (LM), Resilient Backpropagation (RP), Scaled Conjugate Gradient (SCG), Conjugate Gradient with Powell-Beale Restarts (CGB), Polak-Ribiere Conjugate Gradient (CGP) and Fletcher-Reeves Conjugate Gradient (CGF) algorithms. The performances of these algorithms are assessed based on their generalisation capability in relating the vibration parameters (frequencies and mode shapes) with damage locations and severities under various numbers of input and output variables. The results show that Levenberg-Marquardt algorithm provides the best generalisation performance.

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Forest, Samuel. "Nonlinear regularization operators as derived from the micromorphic approach to gradient elasticity, viscoplasticity and damage." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472, no. 2188 (April 2016): 20150755. http://dx.doi.org/10.1098/rspa.2015.0755.

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The construction of regularization operators presented in this work is based on the introduction of strain or damage micromorphic degrees of freedom in addition to the displacement vector and of their gradients into the Helmholtz free energy function of the constitutive material model. The combination of a new balance equation for generalized stresses and of the micromorphic constitutive equations generates the regularization operator. Within the small strain framework, the choice of a quadratic potential w.r.t. the gradient term provides the widely used Helmholtz operator whose regularization properties are well known: smoothing of discontinuities at interfaces and boundary layers in hardening materials, and finite width localization bands in softening materials. The objective is to review and propose nonlinear extensions of micromorphic and strain/damage gradient models along two lines: the first one introducing nonlinear relations between generalized stresses and strains; the second one envisaging several classes of finite deformation model formulations. The generic approach is applicable to a large class of elastoviscoplastic and damage models including anisothermal and multiphysics coupling. Two standard procedures of extension of classical constitutive laws to large strains are combined with the micromorphic approach: additive split of some Lagrangian strain measure or choice of a local objective rotating frame. Three distinct operators are finally derived using the multiplicative decomposition of the deformation gradient. A new feature is that a free energy function depending solely on variables defined in the intermediate isoclinic configuration leads to the existence of additional kinematic hardening induced by the gradient of a scalar micromorphic variable.

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