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Journal articles on the topic 'Modeling of multiple matrix cracking'

Author: Grafiati

Published: 4 June 2021

Last updated: 15 February 2022

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1

Li, Longbiao. "Modeling matrix fracture in fiber-reinforced ceramic-matrix composites with different fiber preforms." Textile Research Journal 90, no. 7-8 (October 21, 2019): 909–24. http://dx.doi.org/10.1177/0040517519883956.

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In this paper, the stress-dependent matrix multiple fracture in silicon carbide fiber-reinforced ceramic-matrix composites with different fiber preforms is investigated. The critical matrix strain energy criterion is used to determine the matrix multiple fracture considering the interface debonding. The effects of the fiber radius, fiber elastic modulus, matrix elastic modulus, fiber volume, interface shear stress, and interface debonded energy on the matrix multiple fracture and the interface debonding are analyzed. The experimental matrix multiple cracking and interface debonding of minicomposite, unidirectional, and two-dimensional woven SiC/SiC composites with different fiber volumes and interphases are predicted. The matrix cracking density increases with the increasing of the fiber volume, fiber elastic modulus, interface shear stress, and interface debonded energy, and the decreasing of the fiber radius and matrix elastic modulus.

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2

Longbiao, Li. "Modeling the Effect of Multiple Matrix Cracking Modes on Cyclic Hysteresis Loops of 2D Woven Ceramic-Matrix Composites." Applied Composite Materials 23, no. 4 (February 17, 2016): 555–81. http://dx.doi.org/10.1007/s10443-016-9474-7.

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3

Curosu, Iurie, Amr Omara, Ameer Hamza Ahmed, and Viktor Mechtcherine. "Probabilistic Finite Element Modeling of Textile Reinforced SHCC Subjected to Uniaxial Tension." Materials 14, no. 13 (June 29, 2021): 3631. http://dx.doi.org/10.3390/ma14133631.

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The paper presents a finite element investigation of the effect of material composition and the constituents’ interaction on the tensile behavior of strain-hardening cement-based composites (SHCC) both with and without textile reinforcement. The input material parameters for the SHCC and continuous reinforcement models, as well for their bond, were adopted from reference experimental investigations. The textile reinforcement was discretized by truss elements in the loaded direction only, with the constitutive relationships simulating a carbon and a polymer textile, respectively. For realistic simulation of macroscopic tensile response and multiple cracking patterns in hybrid fiber-reinforced composites subjected to tension, a multi-scale and probabilistic approach was adopted. SHCC was simulated using the smeared crack model, and the input constitutive law reflected the single-crack opening behavior. The probabilistic definition and spatial fluctuation of matrix strength and tensile strength of the SHCC enabled realistic multiple cracking and fracture localization within the loaded model specimens. Two-dimensional (2D) simulations enabled a detailed material assessment with reasonable computational effort and showed adequate accuracy in predicting the experimental findings in terms of macroscopic stress–strain properties, extent of multiple cracking, and average crack width. Besides material optimization, the model is suitable for assessing the strengthening performance of hybrid fiber-reinforced composites on structural elements.

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4

SCHLANGEN, ERIK, and ZHIWEI QIAN. "3D MODELING OF FRACTURE IN CEMENT-BASED MATERIALS." Journal of Multiscale Modelling 01, no. 02 (April 2009): 245–61. http://dx.doi.org/10.1142/s1756973709000116.

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In this article, a 3D lattice model is presented to simulate fracture in cement-based materials. In the paper, two applications are shown. The first application is modeling heterogeneous materials containing particle embedded in a matrix. A method is shown for coupling 3D information on the material structure obtained with CT-scanning to the material properties in the model. In the second application, fracture in fiber cement-based materials is modeled. Fibers are explicitly implemented as separate elements connected to the cement matrix via special interface elements. With the model, multiple cracking and ductile global behavior are simulated of the composite material. Variables in the model are the fiber dimensions and properties, the fiber volume in the composite, the bond behavior of fibers and matrix, and the cement matrix properties. These properties can be obtained by testing. Some examples of tests are given in the paper. The model can be used as a design tool for creating fiber (cement-based) composites with any desired mechanical behavior.

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5

Wang, B. L., Y. G. Sun, and H. Y. Zhang. "Multiple cracking of fiber/matrix composites—Analysis of normal extension." International Journal of Solids and Structures 45, no. 14-15 (July 2008): 4032–48. http://dx.doi.org/10.1016/j.ijsolstr.2008.02.026.

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6

Longbiao, Li. "Modeling cyclic fatigue hysteresis loops of 2D woven ceramic-matrix composite at elevated temperatures in air considering multiple matrix cracking modes." Theoretical and Applied Fracture Mechanics 85 (October 2016): 246–61. http://dx.doi.org/10.1016/j.tafmec.2016.03.010.

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7

Leonovich, S. N. "Modeling of Capillary Shrinkage and Cracking in Early-Age Concrete." Science & Technique 17, no. 4 (July 31, 2018): 265–77. http://dx.doi.org/10.21122/2227-1031-2018-17-4-265-277.

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. Scientific hypothesis on moistening shrinkage mechanism for cement stone and concrete has been assumed as a basis for the present paper. Physical ideas on a mechanism for cracks volume increment in a concrete model presented as two-level structure have been accepted as a theoretical basis for a calculation method of crack resistance during capillary shrinkage. These ideas are the following: a matrix of hardening cement stone with inclusions and emptiness of various forms (cracks) as result of influences that change an intense deformed state in a point and a volume. The following assumptions have been accepted while making a theoretical justification for a calculation method of shrinkable concrete crack resistance. Following this methodology approaches of fracture mechanics according to a generalized criterion have been applied in the paper. Concrete is considered as an elastic quasi-homogeneous two-component medium which consists of the following parts:a) constructive part: a matrix – a cement stone with structural elements of crushed stone, sand; b) destructive part: emptiness – capillaries cracks and pores (cavities with initial cracks in walls). Emptiness in a matrix and contact zones are presented by a coordinated five-level system in the form and sizes which are multiple to a diameter due to impacts while reaching critical sizes. These critical sizes make it possible to pass from one level into another one according to the following scheme: size stabilization – accumulation delocalization – critical concentration in single volume – transition to the following level. Process of cracks formation and their growth are considered as a result of non-power influences on the basis of crack theory principles from a condition that fields of deformation and tension creating schemes of a normal separation and shift occur in the top part of each crack at its level in the initial concrete volume. Ксij(t) parameter as algebraic amount of critical values Kij in the whole system of all levels of cracks filling canonical volume up to critical concentration has been accepted as a generalized constant of property for concrete crack resistance in time, its resistance to formation, accumulation in volumes of micro-cracks and formation of trunk cracks with critical values. External temperature, moistening long influences create fields of tension in the top parts of cracks. Concrete destruction processes due to cracks are considered as generalized deformedintensed state in some initial volume having physical features which are inherent to a composite with strength and deformative properties. It is possible to realize analytical calculations for assessment of tension and crack resistance of concrete at early age on the basis of a generalized criterion in terms of stress intensity factor due to modern experimental data on capillary pressure value (70 kPa in 180 min after concrete placing). The developed algorithm of calculation allows to consider factors influencing on capillary pressure: type of cement, modifiers and mineral additives, concrete curing conditions.

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8

Kashtalyan, M., I. G. García, and V. Mantič. "Coupled stress and energy criterion for multiple matrix cracking in cross-ply composite laminates." International Journal of Solids and Structures 139-140 (May 2018): 189–99. http://dx.doi.org/10.1016/j.ijsolstr.2018.01.033.

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9

Chudoba, Rostislav, Yingxiong Li, Rostislav Rypl, Homam Spartali, and Miroslav Vořechovský. "Probabilistic multiple cracking model of brittle-matrix composite based on a one-by-one crack tracing algorithm." Applied Mathematical Modelling 92 (April 2021): 315–32. http://dx.doi.org/10.1016/j.apm.2020.10.041.

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10

El Yagoubi, Jalal, Jacques Lamon, and Jean Christophe Batsale. "Multiscale Modelling of the Influence of Damage on the Thermal Properties of Ceramic Matrix Composites." Advances in Science and Technology 73 (October 2010): 65–71. http://dx.doi.org/10.4028/www.scientific.net/ast.73.65.

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Ceramic matrix composites (CMC) are very attractive materials for structural applications at high temperatures. Not only must CMC be damage tolerant, but they must also allow thermal management. For this purpose heat transfers must be controlled even in the presence of damage. Damage consists in multiple cracks that form in the matrix and ultimately in the fibers, when the stresses exceed the proportional limit. Therefore the thermal conductivity dependence on applied load is a factor of primary importance for the design of CMC components. This original approach combines a model of matrix cracking with a model of heat transfer through an elementary cracked volume element containing matrix crack and an interfacial crack. It was applied to 1D composites subject to tensile ant thermal loading parallel to fiber direction in a previous paper. The present paper compares predictions to experimental results.

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11

Li, S., S. R. Reid, and Z. Zou. "Modelling damage of multiple delaminations and transverse matrix cracking in laminated composites due to low velocity lateral impact." Composites Science and Technology 66, no. 6 (May 2006): 827–36. http://dx.doi.org/10.1016/j.compscitech.2004.12.019.

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12

Kashtalyan, M., and C. Soutis. "Modelling of stiffness degradation due to cracking in laminates subjected to multi-axial loading." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 374, no. 2071 (July 13, 2016): 20160017. http://dx.doi.org/10.1098/rsta.2016.0017.

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The paper presents an analytical approach to predicting the effect of intra- and interlaminar cracking on residual stiffness properties of the laminate, which can be used in the post-initial failure analysis, taking full account of damage mode interaction. The approach is based on a two-dimensional shear lag stress analysis and the equivalent constraint model of the laminate with multiple damaged plies. The application of the approach to predicting degraded stiffness properties of multidirectional laminates under multi-axial loading is demonstrated on cross-ply glass/epoxy and carbon/epoxy laminates with transverse and longitudinal matrix cracks and crack-induced transverse and longitudinal delaminations. This article is part of the themed issue ‘Multiscale modelling of the structural integrity of composite materials’.

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13

Pineda, E. J., and A. M. Waas. "Modelling progressive failure of fibre reinforced laminated composites: mesh objective calculations." Aeronautical Journal 116, no. 1186 (December 2012): 1221–46. http://dx.doi.org/10.1017/s0001924000007612.

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Abstract A thermodynamically-based work potential theory for modelling progressive damage and failure in fibre-reinforced laminates is presented. The current, multiple-internal state variable (ISV) formulation, enhanced Schapery theory, utilises separate ISVs for modelling the effects of damage and failure. Damage is considered to be the effect of any structural changes in a material that manifest as pre-peak non-linearity in the stress versus strain response. Conversely, failure is taken to be the effect of the evolution of any mechanisms that results in post-peak strain softening. It is assumed, matrix microdamage is the dominant damage mechanism in continuous, fibre-reinforced, polymer matrix laminates, and its evolution is captured with a single ISV. Three additional ISVs are introduced to account for failure due to mode I transverse cracking, mode II transverse cracking, and mode I axial failure. Using the stationarity of the total work potential with respect to each ISV, a set of thermodynamically consistent evolution equations for the ISVs is derived. Typically, failure evolution (i.e. post-peak strain softening) results in pathologically mesh dependent solutions within a finite element method numerical setting. Therefore, consistent characteristic element lengths are introduced into the formulation of of the three failure potentials. The theory is implemented into commercial FEM software. The model is verified against experimental results from a laminated, quasi-isotropic, T800/3900-2 panel containing a central notch. Global load versus displacement, global load versus local strain gauge data, and macroscopic failure paths obtained from the models are compared to the experiments. Finally, a sensitivity study is performed on the failure parameters used in the model.

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14

Curtin, W. A. "Multiple matrix cracking in brittle matrix composites." Acta Metallurgica et Materialia 41, no. 5 (May 1993): 1369–77. http://dx.doi.org/10.1016/0956-7151(93)90246-o.

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15

Li, Longbiao. "Effect of Cyclic Fatigue Loading on Matrix Multiple Fracture of Fiber-Reinforced Ceramic-Matrix Composites." Ceramics 2, no. 2 (May 13, 2019): 327–46. http://dx.doi.org/10.3390/ceramics2020027.

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In this paper, the effect of cyclic fatigue loading on matrix multiple fracture of fiber-reinforced ceramic-matrix composites (CMCs) is investigated using the critical matrix strain energy (CMSE) criterion. The relationships between multiple matrix cracking, cyclic fatigue peak stress, fiber/matrix interface wear, and debonding are established. The effects of fiber volume fraction, fiber/matrix interface shear stress, and applied cycle number on matrix multiple fracture and fiber/matrix interface debonding and interface wear are discussed. Comparisons of multiple matrix cracking with/without cyclic fatigue loading are analyzed. The experimental matrix cracking of unidirectional SiC/CAS, SiC/SiC, SiC/Borosilicate, and mini-SiC/SiC composites with/without cyclic fatigue loading are predicted.

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16

Le, M. Q., H. Bainier, D. Néron, C. Ha-Minh, and P. Ladevèze. "On matrix cracking and splits modeling in laminated composites." Composites Part A: Applied Science and Manufacturing 115 (December 2018): 294–301. http://dx.doi.org/10.1016/j.compositesa.2018.10.002.

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17

Spearing, S. M., and F. W. Zok. "Stochastic Aspects of Matrix Cracking in Brittle Matrix Composites." Journal of Engineering Materials and Technology 115, no. 3 (July 1, 1993): 314–18. http://dx.doi.org/10.1115/1.2904224.

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A computer simulation of multiple cracking in fiber-reinforced brittle matrix composites has been conducted, with emphasis on the role of the matrix flaw distribution. The simulations incorporate the effect of bridging fibers on the stress required for cracking. Both short and long (steady-state) flaws are considered. Furthermore, the effects of crack interactions (through the overlap of interface slip lengths) are incorporated. The influence of the crack distribution on the tensile response of such composites is also examined.

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18

Baran, G., W. Shin, A. Abbas, and S. Wunder. "Indentation Cracking of Composite Matrix Materials." Journal of Dental Research 73, no. 8 (August 1994): 1450–56. http://dx.doi.org/10.1177/00220345940730080901.

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Composite restorative materials wear by a fatigue mechanism in the occlusal contact area. Here, tooth cusps and food debris cyclically indent the restoration. Modeling this phenomenon requires an understanding of material response to indentation. The question in this study was whether material response depends on indenter size and geometry, and also, whether polymers used in restorative materials should be considered elastic and brittle, or plastic and ductile for modeling purposes. Three resins used as matrices in proprietary restorative composites were the experimental materials. To ascertain the influence of glass transition temperature, liquid sorption, and small amounts of filler on indentation response, we prepared materials with various degrees of cure; some samples were soaked in a 50/50 water/ethanol solution, and 3 vol% silica was added in some cases. Indentation experiments revealed that no cracking occurred in any material after indentation by Vickers pyramid or spherical indenters with diameters equal to or smaller than 0.254 mm. Larger spherical indenters induced subsurface median and surface radial and/or ring cracks. Critical loads causing subsurface cracks were measured. Indentation with suitably large spherical indenters provoked an elastoplastic response in polymers, and degree of cure and Tg had less influence on critical load than soaking in solution. Crack morphology was correlated with yield strain. Commonly held assumptions regarding the brittle elastic behavior of composite matrix materials may be incorrect.

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19

Kuo, Wen-Shyong, and Tsu-Wei Chou. "Multiple Cracking of Unidirectional and Cross-PlyCeramic Matrix Composites." Journal of the American Ceramic Society 78, no. 3 (March 1995): 745–55. http://dx.doi.org/10.1111/j.1151-2916.1995.tb08242.x.

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20

Iarve, Endel V., Mark R. Gurvich, David H. Mollenhauer, Cheryl A. Rose, and Carlos G. Dávila. "Mesh-independent matrix cracking and delamination modeling in laminated composites." International Journal for Numerical Methods in Engineering 88, no. 8 (April 14, 2011): 749–73. http://dx.doi.org/10.1002/nme.3195.

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21

Zhang, J., and K. P. Herrmann. "Modeling Matrix Cracking in Composite Laminates Under Thermo-mechanical Loading." PAMM 1, no. 1 (March 2002): 203. http://dx.doi.org/10.1002/1617-7061(200203)1:1<203::aid-pamm203>3.0.co;2-z.

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22

Pollayi, Hemaraju, and Wenbin Yu. "Modeling matrix cracking in composite rotor blades within VABS framework." Composite Structures 110 (April 2014): 62–76. http://dx.doi.org/10.1016/j.compstruct.2013.11.012.

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23

Longbiao, Li. "Modeling first matrix cracking stress of fiber-reinforced ceramic-matrix composites considering fiber fracture." Theoretical and Applied Fracture Mechanics 92 (December 2017): 24–32. http://dx.doi.org/10.1016/j.tafmec.2017.05.004.

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24

Walls, D. P., J. C. McNulty, and F. W. Zok. "Multiple matrix cracking in a fiber-reinforced titanium matrix composite under high-cycle fatigue." Metallurgical and Materials Transactions A 27, no. 7 (July 1996): 1899–907. http://dx.doi.org/10.1007/bf02651939.

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25

Li, Longbiao. "Effect of temperature on matrix multicracking evolution of C/SiC fiber-reinforced ceramic-matrix composites." High Temperature Materials and Processes 39, no. 1 (June 9, 2020): 189–99. http://dx.doi.org/10.1515/htmp-2020-0044.

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AbstractIn this paper, the temperature-dependent matrix multicracking evolution of carbon-fiber-reinforced silicon carbide ceramic-matrix composites (C/SiC CMCs) is investigated. The temperature-dependent composite microstress field is obtained by combining the shear-lag model and temperature-dependent material properties and damage models. The critical matrix strain energy criterion assumes that the strain energy in the matrix has a critical value. With increasing applied stress, when the matrix strain energy is higher than the critical value, more matrix cracks and interface debonding occur to dissipate the additional energy. Based on the composite damage state, the temperature-dependent matrix strain energy and its critical value are obtained. The relationships among applied stress, matrix cracking state, interface damage state, and environmental temperature are established. The effects of interfacial properties, material properties, and environmental temperature on temperature-dependent matrix multiple fracture evolution of C/SiC composites are analyzed. The experimental evolution of matrix multiple fracture and fraction of the interface debonding of C/SiC composites at elevated temperatures are predicted. When the interface shear stress increases, the debonding resistance at the interface increases, leading to the decrease of the debonding fraction at the interface, and the stress transfer capacity between the fiber and the matrix increases, leading to the higher first matrix cracking stress, saturation matrix cracking stress, and saturation matrix cracking density.

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26

Nguyen, B. N. "A Three-Dimensional Modeling of Transverse Matrix Cracking in Laminated Composites." Key Engineering Materials 127-131 (November 1996): 1117–26. http://dx.doi.org/10.4028/www.scientific.net/kem.127-131.1117.

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27

Pawar, Prashant M., and Ranjan Ganguli. "Modeling Multi-Layer Matrix Cracking in Thin Walled Composite Rotor Blades." Journal of the American Helicopter Society 50, no. 4 (October 1, 2005): 354–66. http://dx.doi.org/10.4050/1.3092872.

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28

Sulym, H. T., O. P. Yasnii, and Ya M. Pasternak. "Modeling of Multiple Cracking Under the Conditions of Thermomechanical Fatigue." Materials Science 51, no. 6 (May 2016): 765–72. http://dx.doi.org/10.1007/s11003-016-9901-9.

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29

Wang, Yi, Ning Zhang, Chongqing Kang, Daniel S. Kirschen, Jingwei Yang, and Qing Xia. "Standardized Matrix Modeling of Multiple Energy Systems." IEEE Transactions on Smart Grid 10, no. 1 (January 2019): 257–70. http://dx.doi.org/10.1109/tsg.2017.2737662.

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30

Longbiao, Li. "Modeling matrix cracking of fiber-reinforced ceramic-matrix composites under oxidation environment at elevated temperature." Theoretical and Applied Fracture Mechanics 87 (February 2017): 110–19. http://dx.doi.org/10.1016/j.tafmec.2016.11.003.

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31

Sun, Yongjian, and Raj N. Singh. "The generation of multiple matrix cracking and fiber–matrix interfacial debonding in a glass composite." Acta Materialia 46, no. 5 (March 1998): 1657–67. http://dx.doi.org/10.1016/s1359-6454(97)00347-9.

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32

Thornburgh, Robert, and Aditi Chattopadhyay. "Unified Approach to Modeling Matrix Cracking and Delamination in Laminated Composite Structures." AIAA Journal 39, no. 1 (January 2001): 153–60. http://dx.doi.org/10.2514/2.1283.

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33

Thornburgh, Robert, and Aditi Chattopadhyay. "Unified approach to modeling matrix cracking and delamination in laminated composite structures." AIAA Journal 39 (January 2001): 153–60. http://dx.doi.org/10.2514/3.14709.

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34

Deng, Yong, Weiguo Li, Jiaxing Shao, Xuyao Zhang, Haibo Kou, Jianzuo Ma, Yong Tao, and Ruzhuan Wang. "Modeling the temperature-dependent non-steady state first matrix cracking stress for fiber ceramic matrix composites." Journal of Alloys and Compounds 740 (April 2018): 987–96. http://dx.doi.org/10.1016/j.jallcom.2018.01.063.

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35

Zheng, Xuan, Jun Zhang, and Zhenbo Wang. "Effect of multiple matrix cracking on crack bridging of fiber reinforced engineered cementitious composite." Journal of Composite Materials 54, no. 26 (May 4, 2020): 3949–65. http://dx.doi.org/10.1177/0021998320923145.

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In the present paper, a modified micromechanics based model that describes the crack bridging stress in randomly oriented discontinuous fiber reinforced engineered cementitious composite is developed. In the model, effect of multiple matrix cracking on fiber embedded length, which in turn influencing fiber bridging in the composite, is taken into consideration. First, crack spacing of high strength-low shrinkage engineered cementitious composite was experimentally determined by photographing the specimen surface at some given loading points during uniaxial tensile test. The diagram of average cracking spacing and loading time of each composite is obtained based on above data. Then, fiber bridging model is modified by introducing a revised fiber embedment length as a function of crack spacing. The model is verified with uniaxial tensile test on both tensile strength and crack opening. Good agreement between model and test results is obtained. The modified model can be used in design and prediction of tensile properties of fiber reinforced cementitious composites with characteristics of multiple matrix cracking.

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36

Wang, Fang, Lu Li, Zhiqian Chen, and Xiangguo Zeng. "Statistical modeling for the accumulation of transverse matrix cracking in cross-ply laminates." Polymer Composites 33, no. 6 (May 3, 2012): 912–17. http://dx.doi.org/10.1002/pc.22211.

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37

Li, Shuxin, Cangru Jiang, and Songlin Han. "Modeling of the characteristics of fiber-reinforced composite materials damaged by matrix-cracking." Composites Science and Technology 43, no. 2 (January 1992): 185–95. http://dx.doi.org/10.1016/0266-3538(92)90008-q.

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38

Longbiao, Li. "Synergistic effects of fiber/matrix interface wear and fibers fracture on matrix multiple cracking in fiber-reinforced ceramic-matrix composites." Composite Interfaces 26, no. 3 (June 21, 2018): 193–219. http://dx.doi.org/10.1080/09276440.2018.1488490.

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39

OMAGARI, Kazuomi, Akira TODOROKI, Yoshinobu SHIMAMURA, and Hideo KOBAYASHI. "Detection of Matrix Cracking of CFRP by Electrical Resistance Change Using Multiple Electrodes." Proceedings of the JSME annual meeting 2004.6 (2004): 245–46. http://dx.doi.org/10.1299/jsmemecjo.2004.6.0_245.

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40

Wu, Hwai-Chung, and Vicror C. Li. "Stochastic Process of Multiple Cracking in Discontinuous Random Fiber Reinforced Brittle Matrix Composites." International Journal of Damage Mechanics 4, no. 1 (January 1995): 83–102. http://dx.doi.org/10.1177/105678959500400105.

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41

Huang, Y., N. Y. Li, H. W. Zhang, and K. C. Hwang. "Interactive Growth of Multiple Fiber-Bridged Matrix Cracks in Unidirectional Composites." Journal of Engineering Materials and Technology 118, no. 3 (July 1, 1996): 295–301. http://dx.doi.org/10.1115/1.2806809.

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A model is developed for monotonic and cyclic fiber sliding in a fiber-reinforced composite containing multiple cracks. The model is used to study the fatigue growth of multiple cracks in a matrix reinforced with aligned, continuous fibers, where cracks are bridged by frictionally constrained fibers. It is established that the crack tip stress intensity factor is significantly reduced in multiple cracking due to interactions among cracks and among slip zones. The fatigue crack does not grow as fast as that for a single bridged crack or for multiple nonbridged cracks, thus the approach to steady-state crack growth is significantly delayed.

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42

Åberg, Mats, and Peter Gudmundson. "Micromechanical modeling of transient waves from matrix cracking and fiber fracture in laminated beams." International Journal of Solids and Structures 37, no. 30 (July 2000): 4083–102. http://dx.doi.org/10.1016/s0020-7683(99)00147-x.

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43

Genin, Guy M., and John W. Hutchinson. "Composite Laminates in Plane Stress: Constitutive Modeling and Stress Redistribution due to Matrix Cracking." Journal of the American Ceramic Society 80, no. 5 (January 21, 2005): 1245–55. http://dx.doi.org/10.1111/j.1151-2916.1997.tb02971.x.

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44

Liu, Jia, Yi Xue, Qi Zhang, Kai Yao, Xin Liang, and Songhe Wang. "Micro-cracking behavior of shale matrix during thermal recovery: Insights from phase-field modeling." Engineering Fracture Mechanics 239 (November 2020): 107301. http://dx.doi.org/10.1016/j.engfracmech.2020.107301.

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45

Kumar, Deepak, Rene Roy, Jin-Hwe Kweon, and Jin-ho Choi. "Numerical Modeling of Combined Matrix Cracking and Delamination in Composite Laminates Using Cohesive Elements." Applied Composite Materials 23, no. 3 (October 2, 2015): 397–419. http://dx.doi.org/10.1007/s10443-015-9465-0.

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46

Hoos, Kevin, Endel V. Iarve, Michael Braginsky, Eric Zhou, and David H. Mollenhauer. "Static strength prediction in laminated composites by using discrete damage modeling." Journal of Composite Materials 51, no. 10 (June 2, 2016): 1473–92. http://dx.doi.org/10.1177/0021998316651986.

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Discrete Damage Modeling of complex local failure patterns in laminated composites including matrix cracking, delamination, and fiber failure was performed. Discrete Damage Modeling uses the Regularized eXtended Finite Element Method for the simulation of matrix cracking at initially unknown locations and directions independent of the mesh orientation. Cohesive interface model is used both for Mesh Independent Cracking as well as delamination propagation. The fiber failure mode is modeled by two different methods in tension and compression. Tensile failure is predicted by Critical Failure Volume criterion, which takes into account volumetric scaling of tensile strength. Compression fiber failure is simulated with a single parameter continuum damage mechanics model with non-compressibility condition in the failed region. Ply level characterization input data were used for prediction of notched and unnotched laminate strength. All input data required for model application is directly measured by ASTM tests except tensile fiber scaling parameter and compression fiber failure fracture toughness, which were taken from literature sources. The model contains no internal calibration parameters. Tensile and compressive strength of unnotched and open hole composite laminates IM7/977-3 has been predicted and compared with experimental data. Three different layups, [0/45/90/−45]2S, [30/60/90/−60/−30]2S, and the [60/0/−60]3S, were modeled and tested and showed good agreement with experiment in the case of tensile loading, whereas the compressive strength was generally under predicted for unnotched laminates and overpredicted for open hole laminates.

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GHOSH, SOMNATH, D. M. VALIVETI, CHAO HU, and JIE BAI. "A MULTISCALE FRAMEWORK FOR CHARACTERIZATION AND MODELING DUCTILE FRACTURE IN HETEROGENEOUS ALUMINUM ALLOYS." Journal of Multiscale Modelling 01, no. 01 (January 2009): 21–55. http://dx.doi.org/10.1142/s1756973709000050.

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This paper develops three components contributing to the overall framework of multiscale modeling of ductile fracture in aluminum alloys. The first module is morphology-based domain partitioning (MDP) as a pre-processor to the multiscale modeling. This module delineates regions of statistical homogeneity and inhomogeneity with a systematic three-step process that is based on geometric features of morphology. The second module is detailed micromechanical analysis of particle fragmentation and matrix cracking of heterogeneous microstructures. A locally enriched VCFEM or LE-VCFEM is developed to incorporate ductile failure through matrix cracking in the form of void growth and coalescence using nonlocal Gurson–Tvergaard–Needleman (GTN) model. The third module develops a homogenized anisotropic plasticity-damage model in the form of GTN model for macroscopic analysis. Parameters in this GTN model are calibrated from results of homogenization of microstructural variables obtained from microstructural RVE. Numerical examples elucidate the strength of components of the overall framework.

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Jalalvand, Meisam, Hossein Hosseini-Toudeshky, and Bijan Mohammadi. "Numerical modeling of diffuse transverse cracks and induced delamination using cohesive elements." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 227, no. 7 (September 19, 2012): 1392–405. http://dx.doi.org/10.1177/0954406212460974.

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This article is devoted to the modeling of spread kind of damages such as matrix cracking and induced delamination in symmetric and asymmetric cross-ply laminates of composite materials using cohesive elements. For matrix crack modeling, parallel rows of cohesive elements are used between every row of 2D elements in 90° layers. Delamination is also modeled by cohesive elements at the 90°/0° interface. Since matrix cracking is a diffuse kind of damage mechanism, application of cohesive elements is not straightforward, and special techniques are necessary to resolve the modeling difficulties. For this purpose, two techniques of “bisecting” and “random distribution of strength of cohesive elements” are proposed here. Both techniques are applied to various symmetric laminates of [0/903]s and [90n/0]s (n = 1 to 3). The predicted stiffness and damage progresses from both techniques are in good agreement with the experimental results. Then, asymmetric cross-ply laminates of [90n/0] (n = 1 to 3) are analyzed to show the capability of this method in progressive damage analyses. The proposed method is less restricted in comparison with available micromechanical methods and is able to predict damage initiation, propagation and damage-mode transition for any symmetric and asymmetric cross-ply sequence. Therefore, this method can be used for development of “in-plane damage” of constitutive laws especially when specimens are subjected to complex loading and boundary conditions.

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Pecat, Oliver, Rüdiger Rentsch, Martin Garbrecht, and Ekkard Brinksmeier. "Modeling and Simulation of the Machining of Unidirectional CFRP." Advanced Materials Research 907 (April 2014): 55–62. http://dx.doi.org/10.4028/www.scientific.net/amr.907.55.

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The machining process of carbon fiber reinforced plastics is very complex due to its inhomogeneous material structure and anisotropic properties. Experimental investigation can be very demanding and time consuming because of the different fiber/matrix compositions and the influence of the fiber volume content which needs to be considered. In this work milling of unidirectional CFRP was simulated using two different material models with implicit and explicit description of fiber and matrix. The objective is to improve the knowledge of the physical mechanism of the cutting process and to predict the cutting forces and surface damage. For this purpose machining of unidirectional CFRP with fiber orientations 90°, 0°, +45° and-45° was simulated, verified by experiments. A significant influence of the fiber orientation on all determined variables was found. The cutting mechanism is dominated by matrix crushing for the fiber orientations 90°, 0° and +45°. Surface damage is caused by either matrix cracking and/or failure of fiber/matrix interface and is occurring in orientations 90° and-45° only. Additionally the evolution of a saw-tooth shaped surface could be identified for the-45° orientation.

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Pechprasarn, Suejit, and Naphat Albutt. "Multiple Reflections Modeling for Multi-Layered Optical Structures." Applied Mechanics and Materials 891 (May 2019): 299–303. http://dx.doi.org/10.4028/www.scientific.net/amm.891.299.

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Fresnel equations and transfer matrix approach are usually employed to solve for exact solution to Maxwell’s equations for multi-layered optical structures. In this paper, we demonstrate that the Fresnel equations and transfer matrix approach can be expanded using Geometric series. This geometric series give an insight to how the light is trapped and behaves in multi-layered optical structures. It also allows us to calculate multiple reflections and count the number of round-trip inside the structure. One main issue in optical calculation is that layers are usually treated as an infinitely large layer. This is, of course, not practical in term of device fabrication. We also demonstrate how this simple geometric calculation will enable us to calculate a smallest practical size that can accommodate a required optical resonant effect.

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