The 8 references with contexts in paper A. Dumansky M., A. Ruslantsev N., А. Думанский М., А. Русланцев Н. (2016) “Модель нелинейного деформирования и накопление повреждений в полимерных композитах // A model of nonlinear strain and damage accumulation in polymer composites” / spz:neicon:technomag:y:2014:i:2:p:324-331

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Caddour A.S., Hinton M.J., Li S., Smith P.A. Damage prediction in polymeric composites: Up-date of Part (A) of the Third World-Wide Failure Exercise (WWFE-III).Proc. of the 18thInt. Conference on Composite Materials (ICCM18). QinetiQ Ltd, 2011. 5 p. Available at:http://www.iccm-central.org/Proceedings/ICCM18proceedings/data/2.%20Oral%20 Presentation/Aug23(Tuesday)/T45%20Mechanical%20and%20Physical%20Properties/T45-5IF1621.pdf, accessed 01.1.2013.
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    ÏÌÓ„Ëı ÔÓÂÍÚÓ‚ · ̊· · ̊ Ì‚ÓÁÏÓÊ̇, ÔÓ ̋ÚÓÏÛ ‡Á‡·ÓÚ͇ ÏÂÚÓ‰Ó‚, ÔÓÁ‚ÓΡ ̨ ̆Ëı ÓÔËÒ ̊‚‡Ú ̧ Ò‚ÓÈÒÚ‚‡ ÔÓÎËÏÂÌ ̊ı ÍÓÏÔÓÁÚÓ‚ Ò Û ̃ÂÚÓÏ ÒÚÛÍÚÛÌ ̊ı Ë ÚÂıÌÓÎÓ„Ë ̃ÂÒÍËı Ù‡ÍÚÓÓ‚ ˇ‚ΡÂÚÒˇ ‡ÍÚۇΠ̧ÌÓÈ Á‡‰‡ ̃ÂÈ. ¡ÓÎ ̧ ̄ËÌÒÚ‚Ó ÏÓ‰ÂÎÂÈ ‰ÂÙÓÏËÓ‚‡Ìˡ ÒÎÓËÒÚ ̊ı ÍÓÏÔÓÁËÚÓ‚ ÓÒÌÓ‚‡Ì ̊ ̇ ÒÓÁ‰‡ÌËË ÏÂÚÓ‰Ó‚ ‡Ò ̃ÂÚ‡ ‰ÂÙÓχˆËË Ï‡ÚÂˇ· Ò ÔÓËÁ‚ÓÎ ̧ÌÓÈ ÒıÂÏÓÈ ÛÍ·‰ÍË, ÓÒÌÓ‚ ̊‚‡ˇÒ ̧ ̇ ı‡‡ÍÚÂËÒÚË͇ı ÒÎÓˇ. ¬
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    ̋ÍÒÔÂËÏÂÌڇΠ̧ÌÓ ÔÓ͇Á‡ÌÓ, ̃ÚÓ ÏÂı‡ÌË ̃ÂÒÍË ҂ÓÈÒÚ‚‡ ÒÎÓˇ ‚ ̇Ô‡‚ÎÂÌËË ‡ÏËÓ‚‡Ìˡ Ò··Ó Á‡‚ËÒˇÚ ÓÚ Ì‡ÔˇÊÂÌËÈ, ‚ ÚÓ Ê ‚ÂÏˇ ÔË ‰ÂÙÓÏËÓ‚‡ÌËË ÒÎÓˇ ‚ ̇Ô‡‚ÎÂÌËË ÔÓÔÂÂÍ ‚ÓÎÓÍÓÌ Ë ÔË Ò‰‚Ë„Â ÔÓˇ‚ΡÂÚÒˇ ÌÂÎËÌÂÈ̇ˇ Á‡‚ËÒËÏÓÒÚ ̧E2 ËG12ÓÚ Ì‡ÔˇÊÂÌËÈ.

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    χÚË ̃Ì ̊ı ‡Î„ÓËÚÏÓ‚ Ë ‡Ì‡ÎËÚË ̃ÂÒÍÓÈ ‡ÔÔÓÍÒËχˆËË ÍË‚ ̊ı ‰ÂÙÓÏËÓ‚‡Ìˡ ‚ ÔÎÓÒÍÓÒÚË ÒÎÓˇ ÔË Ò‰‚Ë„Â Ô‰·„‡ÂÚÒˇ ÏÂÚÓ‰ ÔÓÒÚÓÂÌˡ ÌÂÎËÌÂÈÌ ̊ı ÓÔ‰ÂΡ ̨ ̆Ëı ÒÓÓÚÌÓ ̄ÂÌËÈ Ô‡ÍÂÚ‡ ÔÓ ı‡‡ÍÚÂËÒÚËÍ‡Ï ÒÎÓˇ. 1. ÃÓ‰ÂÎ ̧ ÌÂÎËÌÂÈÌÓ„Ó ‰ÂÙÓÏËÓ‚‡Ìˡ ¬ ÏÂʉÛ̇Ó‰ÌÓÏ œÓÂÍÚ Third World-Wide Failure Exercise (WWFE-III), ÔÓÒ‚ˇ ̆ÂÌÌÓÏ ‡Á‡·ÓÚÍ ÏÓ‰ÂÎÂÈ ‰ÂÙÓÏËÓ‚‡Ìˡ Ë ‡ÁÛ ̄ÂÌˡ ÔÓÎËÏÂÌ ̊ı ÍÓÏÔÓÁËÚÓ‚
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    , Ô˂‰ÂÌ ̊ ËÒ.‰‡ÌÌ ̊ ÌÂÎËÌÂÈÌÓ„Ó ‰ÂÙÓÏËÓ‚‡Ìˡ ÔË Ò‰‚Ë„Â ‚ ÔÎÓÒÍÓÒÚË ÒÎÓˇ (ËÒ.1).1 –ËÒ. 1. Ë‚ ̊ ‰ÂÙÓÏËÓ‚‡Ìˡ ÔË Ò‰‚Ë„Â ‚ ÔÎÓÒÍÓÒÚË ÒÎÓˇ: 1 | Û„ÎÂÔ·ÒÚËÍË AS4/3501-6; 2 | IM7/8552; 3 | G40/800; 4 | ÒÚÂÍÎÓÔ·ÒÚËÍ LY556/60 œÓÒÍÓÎ ̧ÍÛ ÌÂÎËÌÂÈÌ ̊ ҂ÓÈÒÚ‚‡ ÒÎÓˇ Ë Ô‡ÍÂÚ‡ ‚ ÓÒÌÓ‚ÌÓÏ ÓÔ‰ÂΡ ̨ÚÒˇ ÌÂÎËÌÂÈÌ ̊ÏË Ò‚ÓÈÒÚ‚‡ÏË ÒÎÓˇ ÔË Ò‰‚Ë„Â ‚ ÔÎÓÒÍÓÒÚË ÒÎÓˇ [4], ‚ ̊ÔÓÎÌËÏ ‡ÔÔÓÍÒËχˆË ̨ ÍË‚ÓÈ ‰ÂÙ

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    −τ∗), „‰Âg066| ÏÓ‰ÛÎ ̧ Ò‰‚Ë„‡ ̇ ̇ ̃‡Î ̧ÌÓÏ Û ̃‡ÒÚÍÂ;H()| ÙÛÌÍˆËˇ ’ ̋‚Ë҇ȉ‡;f| ‡ÔÔÓÍÒËÏËÛ ̨ ̆‡ˇ ÙÛÌÍˆËˇ. ƒÎˇ Û„ÎÂÔ·ÒÚË͇ AS4/3501-6 ‰Îˇ ‡ÔÔÓÒÍËχˆËË · ̊· ËÒÔÓÎ ̧ÁÓ‚‡Ì‡ ̋ÍÒÔÓÌÂ̈ˇΠ̧̇ˇ ÙÛÌÍˆËˇ: f(τ) = 2.0 exp ( 0.024(τ−τ∗) ) H(τ−τ∗), „‰Âτ∗= 35Ãœ‡. –ËÒ. 2.¿ÔÔÓÍÒËχˆËˇ ÍË‚ÓÈ ‰ÂÙÓÏËÓ‚‡Ìˡ ‚ ÔÎÓÒÍÓÒÚË Ò‰‚Ë„‡ ‰Îˇ Û„ÎÂÔ·ÒÚË͇ AS4/3501-6. ÛÊ͇ÏË ÔÓ͇Á‡Ì‡ ̋ÍÒÔÂËÏÂÌڇΠ̧̇ˇ Á‡‚ËÒËÏÓÒÚ ̧
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    ÇÚËˆÛ ÊÂÒÚÍÓÒÚË ÒÎÓˇ Ô‰ÒÚ‡‚ËÏ ‚ ÒÎÂ‰Û ̨ ̆ÂÈ ÙÓÏÂ:[G12] = [G012]−[G0]f, „‰Â [G012]| χÚˈ‡ ÊÂÒÚÍÓÒÚË ÒÎÓˇ ·ÂÁ Û ̃ÂÚ‡ ÌÂÎËÌÂÈÌÓÒÚË; [G0] =    0 0 0 0 0 0 0 0 1   | ‚ÒÔÓÏÓ„‡ÚÂÎ ̧̇ˇ χÚˈ‡. œÂÂıÓ‰ Í Ï‡Úˈ ÊÂÒÚÍÓÒÚË Ô‡ÍÂÚ‡ ÓÒÛ ̆ÂÒڂΡÂÚÒˇ ÔÓ ÚÂÓËË ÒÎÓËÒÚ ̊ı Ô·ÒÚËÌ: [Gxy] = ∑ i [Ti][G12][Ti]T ̄hi= [G0xy]−[G]f, „‰Â[G0xy] = ∑ i [Ti][G012][Ti]T ̄hi;[G] = ∑ i [Ti][G0][Ti]T ̄hi;[Ti]

2
Lagace P.A. Nonlinear stress-strain behavior of graphite/epoxy laminates.AIAA Journal, 1985, vol. 223, no. 10, pp. 1583{1589.
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    ‚‡Ì ̊ ̇ ÒÓÁ‰‡ÌËË ÏÂÚÓ‰Ó‚ ‡Ò ̃ÂÚ‡ ‰ÂÙÓχˆËË Ï‡ÚÂˇ· Ò ÔÓËÁ‚ÓÎ ̧ÌÓÈ ÒıÂÏÓÈ ÛÍ·‰ÍË, ÓÒÌÓ‚ ̊‚‡ˇÒ ̧ ̇ ı‡‡ÍÚÂËÒÚË͇ı ÒÎÓˇ. ¬ [1] ̋ÍÒÔÂËÏÂÌڇΠ̧ÌÓ ÔÓ͇Á‡ÌÓ, ̃ÚÓ ÏÂı‡ÌË ̃ÂÒÍË ҂ÓÈÒÚ‚‡ ÒÎÓˇ ‚ ̇Ô‡‚ÎÂÌËË ‡ÏËÓ‚‡Ìˡ Ò··Ó Á‡‚ËÒˇÚ ÓÚ Ì‡ÔˇÊÂÌËÈ, ‚ ÚÓ Ê ‚ÂÏˇ ÔË ‰ÂÙÓÏËÓ‚‡ÌËË ÒÎÓˇ ‚ ̇Ô‡‚ÎÂÌËË ÔÓÔÂÂÍ ‚ÓÎÓÍÓÌ Ë ÔË Ò‰‚Ë„Â ÔÓˇ‚ΡÂÚÒˇ ÌÂÎËÌÂÈ̇ˇ Á‡‚ËÒËÏÓÒÚ ̧E2 ËG12ÓÚ Ì‡ÔˇÊÂÌËÈ. ¬ ‡·ÓÚÂ
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    ÔÓ͇Á‡ÌÓ ÌÂÁ̇ ̃ËÚÂÎ ̧ÌÓ ÛÔÓ ̃ÌÂÌË ÔË ‡ÒÚˇÊÂÌËË ÒÎÓˇ ‚ ̇Ô‡‚ÎÂÌËË ‡ÏËÓ‚‡Ìˡ. ¬Ó ÏÌÓ„Ëı ‡·ÓÚ‡ı ÔÓ͇Á‡ÌÓ, ̃ÚÓ ÌÂÎËÌÂÈÌ ̊ ҂ÓÈÒÚ‚‡ Ô‡ÍÂÚ‡ ‚ ÓÒÌÓ‚ÌÓÏ ÓÔ‰ÂΡ ̨ÚÒˇ ÌÂÎËÌÂÈÌÓÒÚ ̧ ̨ Ò‰‚Ë„Ó‚ ̊ı ı‡‡ÍÚÂËÒÚËÍ ÒÎÓˇ [3,4,5].

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Hahn H.T., Tsai S.W. Nonlinear Elastic Behavior of Unidirectional Composite Laminate.Journal of Composite Materials, 1973, vol. 7, pp. 102{118. DOI:10.1177/002199837300700108
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    ¬ ‡·ÓÚ [2] ÔÓ͇Á‡ÌÓ ÌÂÁ̇ ̃ËÚÂÎ ̧ÌÓ ÛÔÓ ̃ÌÂÌË ÔË ‡ÒÚˇÊÂÌËË ÒÎÓˇ ‚ ̇Ô‡‚ÎÂÌËË ‡ÏËÓ‚‡Ìˡ. ¬Ó ÏÌÓ„Ëı ‡·ÓÚ‡ı ÔÓ͇Á‡ÌÓ, ̃ÚÓ ÌÂÎËÌÂÈÌ ̊ ҂ÓÈÒÚ‚‡ Ô‡ÍÂÚ‡ ‚ ÓÒÌÓ‚ÌÓÏ ÓÔ‰ÂΡ ̨ÚÒˇ ÌÂÎËÌÂÈÌÓÒÚ ̧ ̨ Ò‰‚Ë„Ó‚ ̊ı ı‡‡ÍÚÂËÒÚËÍ ÒÎÓˇ
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    . ¬ ‡·ÓÚ [6] ÓÔËÒ‡ÌË ÌÂÎËÌÂÈÌ ̊ı Ò‚ÓÈÒÚ‚ ÓÒÛ ̆ÂÒڂΡÂÚÒˇ ÔË ÔÓÏÓ ̆Ë ÒÓÓÚÌÓ ̄ÂÌˡ –‡Ï·Â„‡ | ŒÒ„Û‰‡. ¬ [7] Ô‰ÔÓ·„‡ÂÚÒˇ, ̃ÚÓ ÌÂÎËÌÂÈÌÓÒÚ ̧ ‚ ̊Á‚‡Ì‡ ‡ÒÚÂÒÍË‚‡ÌËÂÏ Ï‡Úˈ ̊. ¬ [5] ÌÂÎËÌÂÈÌ ̊ ҂ÓÈÒÚ‚‡ ÒÎÓˇ ÔË Ò‰‚Ë„Â ‡ÔÔÓÍÒËÏËÛ ̨ÚÒˇ ÔÓÎËÌÓÏÓÏ ‚ÚÓÓÈ ÒÚÂÔÂÌË.

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Dumanskiy A.M., Ruslantsev A.N., Karaseva A.A. Raschet nelineynogo deformirovaniya perekrestno armirovannykh ugleplastikov [Calculation of nonlinear deformation of crossreinforced carbon plastics].Materialy 9 Mezhdunarodnoy konferentsii po neravnovesnym protsessam v soplakhistruyakh (NPNJ'2012)[Proc. of the 9thInternational Conference on Nonequilibrium Processes in Nozzles and Jets (NPNJ'2012)], Russia, Alushta, 25-31 May 2012. Moscow, MAI Publ., 2012, pp. 363{365.
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    ¬ ‡·ÓÚ [2] ÔÓ͇Á‡ÌÓ ÌÂÁ̇ ̃ËÚÂÎ ̧ÌÓ ÛÔÓ ̃ÌÂÌË ÔË ‡ÒÚˇÊÂÌËË ÒÎÓˇ ‚ ̇Ô‡‚ÎÂÌËË ‡ÏËÓ‚‡Ìˡ. ¬Ó ÏÌÓ„Ëı ‡·ÓÚ‡ı ÔÓ͇Á‡ÌÓ, ̃ÚÓ ÌÂÎËÌÂÈÌ ̊ ҂ÓÈÒÚ‚‡ Ô‡ÍÂÚ‡ ‚ ÓÒÌÓ‚ÌÓÏ ÓÔ‰ÂΡ ̨ÚÒˇ ÌÂÎËÌÂÈÌÓÒÚ ̧ ̨ Ò‰‚Ë„Ó‚ ̊ı ı‡‡ÍÚÂËÒÚËÍ ÒÎÓˇ
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    . ¬ ‡·ÓÚ [6] ÓÔËÒ‡ÌË ÌÂÎËÌÂÈÌ ̊ı Ò‚ÓÈÒÚ‚ ÓÒÛ ̆ÂÒڂΡÂÚÒˇ ÔË ÔÓÏÓ ̆Ë ÒÓÓÚÌÓ ̄ÂÌˡ –‡Ï·Â„‡ | ŒÒ„Û‰‡. ¬ [7] Ô‰ÔÓ·„‡ÂÚÒˇ, ̃ÚÓ ÌÂÎËÌÂÈÌÓÒÚ ̧ ‚ ̊Á‚‡Ì‡ ‡ÒÚÂÒÍË‚‡ÌËÂÏ Ï‡Úˈ ̊. ¬ [5] ÌÂÎËÌÂÈÌ ̊ ҂ÓÈÒÚ‚‡ ÒÎÓˇ ÔË Ò‰‚Ë„Â ‡ÔÔÓÍÒËÏËÛ ̨ÚÒˇ ÔÓÎËÌÓÏÓÏ ‚ÚÓÓÈ ÒÚÂÔÂÌË.

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    Ë‚ ̊ ‰ÂÙÓÏËÓ‚‡Ìˡ ÔË Ò‰‚Ë„Â ‚ ÔÎÓÒÍÓÒÚË ÒÎÓˇ: 1 | Û„ÎÂÔ·ÒÚËÍË AS4/3501-6; 2 | IM7/8552; 3 | G40/800; 4 | ÒÚÂÍÎÓÔ·ÒÚËÍ LY556/60 œÓÒÍÓÎ ̧ÍÛ ÌÂÎËÌÂÈÌ ̊ ҂ÓÈÒÚ‚‡ ÒÎÓˇ Ë Ô‡ÍÂÚ‡ ‚ ÓÒÌÓ‚ÌÓÏ ÓÔ‰ÂΡ ̨ÚÒˇ ÌÂÎËÌÂÈÌ ̊ÏË Ò‚ÓÈÒÚ‚‡ÏË ÒÎÓˇ ÔË Ò‰‚Ë„Â ‚ ÔÎÓÒÍÓÒÚË ÒÎÓˇ
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    , ‚ ̊ÔÓÎÌËÏ ‡ÔÔÓÍÒËχˆË ̨ ÍË‚ÓÈ ‰ÂÙÓÏËÓ‚‡Ìˡ ÔË Ò‰‚Ë„Â. ƒÎˇ ÔËÏÂ‡ ‡ÒÒÏÓÚËÏ ÌËÁÍÓÏÓ‰ÛÎ ̧Ì ̊È ‚ ̊ÒÓÍÓÔÓ ̃Ì ̊È Û„ÎÂÔ·ÒÚËÍ AS4/3501-6, ÔÓÎÛ ̃Ë‚ ̄ËÈ ̄ËÓÍÓ ‡ÒÔÓÒÚ‡ÌÂÌË ‚ ‡‚ˇˆËÓÌÌÓÈ Ë ‡ÍÂÚÌÓ-ÍÓÒÏË ̃ÂÒÍÓÈ ÚÂıÌËÍÂ.

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Rotem A., Hashin Z. Failure Modes of Angle Ply Laminates.Journal of Composite Materials, 1975, vol. 9, pp. 191{206. DOI:10.1177/002199837500900209
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    ¬ ‡·ÓÚ [2] ÔÓ͇Á‡ÌÓ ÌÂÁ̇ ̃ËÚÂÎ ̧ÌÓ ÛÔÓ ̃ÌÂÌË ÔË ‡ÒÚˇÊÂÌËË ÒÎÓˇ ‚ ̇Ô‡‚ÎÂÌËË ‡ÏËÓ‚‡Ìˡ. ¬Ó ÏÌÓ„Ëı ‡·ÓÚ‡ı ÔÓ͇Á‡ÌÓ, ̃ÚÓ ÌÂÎËÌÂÈÌ ̊ ҂ÓÈÒÚ‚‡ Ô‡ÍÂÚ‡ ‚ ÓÒÌÓ‚ÌÓÏ ÓÔ‰ÂΡ ̨ÚÒˇ ÌÂÎËÌÂÈÌÓÒÚ ̧ ̨ Ò‰‚Ë„Ó‚ ̊ı ı‡‡ÍÚÂËÒÚËÍ ÒÎÓˇ
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    . ¬ ‡·ÓÚ [6] ÓÔËÒ‡ÌË ÌÂÎËÌÂÈÌ ̊ı Ò‚ÓÈÒÚ‚ ÓÒÛ ̆ÂÒڂΡÂÚÒˇ ÔË ÔÓÏÓ ̆Ë ÒÓÓÚÌÓ ̄ÂÌˡ –‡Ï·Â„‡ | ŒÒ„Û‰‡. ¬ [7] Ô‰ÔÓ·„‡ÂÚÒˇ, ̃ÚÓ ÌÂÎËÌÂÈÌÓÒÚ ̧ ‚ ̊Á‚‡Ì‡ ‡ÒÚÂÒÍË‚‡ÌËÂÏ Ï‡Úˈ ̊. ¬ [5] ÌÂÎËÌÂÈÌ ̊ ҂ÓÈÒÚ‚‡ ÒÎÓˇ ÔË Ò‰‚Ë„Â ‡ÔÔÓÍÒËÏËÛ ̨ÚÒˇ ÔÓÎËÌÓÏÓÏ ‚ÚÓÓÈ ÒÚÂÔÂÌË.

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    ¬Ó ÏÌÓ„Ëı ‡·ÓÚ‡ı ÔÓ͇Á‡ÌÓ, ̃ÚÓ ÌÂÎËÌÂÈÌ ̊ ҂ÓÈÒÚ‚‡ Ô‡ÍÂÚ‡ ‚ ÓÒÌÓ‚ÌÓÏ ÓÔ‰ÂΡ ̨ÚÒˇ ÌÂÎËÌÂÈÌÓÒÚ ̧ ̨ Ò‰‚Ë„Ó‚ ̊ı ı‡‡ÍÚÂËÒÚËÍ ÒÎÓˇ [3,4,5]. ¬ ‡·ÓÚ [6] ÓÔËÒ‡ÌË ÌÂÎËÌÂÈÌ ̊ı Ò‚ÓÈÒÚ‚ ÓÒÛ ̆ÂÒڂΡÂÚÒˇ ÔË ÔÓÏÓ ̆Ë ÒÓÓÚÌÓ ̄ÂÌˡ –‡Ï·Â„‡ | ŒÒ„Û‰‡. ¬ [7] Ô‰ÔÓ·„‡ÂÚÒˇ, ̃ÚÓ ÌÂÎËÌÂÈÌÓÒÚ ̧ ‚ ̊Á‚‡Ì‡ ‡ÒÚÂÒÍË‚‡ÌËÂÏ Ï‡Úˈ ̊. ¬
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    ÌÂÎËÌÂÈÌ ̊ ҂ÓÈÒÚ‚‡ ÒÎÓˇ ÔË Ò‰‚Ë„Â ‡ÔÔÓÍÒËÏËÛ ̨ÚÒˇ ÔÓÎËÌÓÏÓÏ ‚ÚÓÓÈ ÒÚÂÔÂÌË. ¬ ‰‡ÌÌÓÈ ‡·ÓÚÂ Ò ÔÓÏÓ ̆ ̧ ̨ χÚË ̃Ì ̊ı ‡Î„ÓËÚÏÓ‚ Ë ‡Ì‡ÎËÚË ̃ÂÒÍÓÈ ‡ÔÔÓÍÒËχˆËË ÍË‚ ̊ı ‰ÂÙÓÏËÓ‚‡Ìˡ ‚ ÔÎÓÒÍÓÒÚË ÒÎÓˇ ÔË Ò‰‚Ë„Â Ô‰·„‡ÂÚÒˇ ÏÂÚÓ‰ ÔÓÒÚÓÂÌˡ ÌÂÎËÌÂÈÌ ̊ı ÓÔ‰ÂΡ ̨ ̆Ëı ÒÓÓÚÌÓ ̄ÂÌËÈ Ô‡ÍÂÚ‡ ÔÓ ı‡‡ÍÚÂËÒÚËÍ‡Ï ÒÎÓˇ. 1.

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Bogetti T., Hoppel C., Harik V., Newill J., Burns B. Chapter 5.12 | Predicting the Nonlinear Response and Progressive Failure of Composite Laminates: Correlation with experimental results. In:Failure Criteria in Fibre Reinforced Polymer Composites: The World-Wide Failure Exercise. Elsevier, 2004, pp. 961{975. DOI:10.1016/B978-008044475-8/50034-2
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    ¬ ‡·ÓÚ [2] ÔÓ͇Á‡ÌÓ ÌÂÁ̇ ̃ËÚÂÎ ̧ÌÓ ÛÔÓ ̃ÌÂÌË ÔË ‡ÒÚˇÊÂÌËË ÒÎÓˇ ‚ ̇Ô‡‚ÎÂÌËË ‡ÏËÓ‚‡Ìˡ. ¬Ó ÏÌÓ„Ëı ‡·ÓÚ‡ı ÔÓ͇Á‡ÌÓ, ̃ÚÓ ÌÂÎËÌÂÈÌ ̊ ҂ÓÈÒÚ‚‡ Ô‡ÍÂÚ‡ ‚ ÓÒÌÓ‚ÌÓÏ ÓÔ‰ÂΡ ̨ÚÒˇ ÌÂÎËÌÂÈÌÓÒÚ ̧ ̨ Ò‰‚Ë„Ó‚ ̊ı ı‡‡ÍÚÂËÒÚËÍ ÒÎÓˇ [3,4,5]. ¬ ‡·ÓÚÂ
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    ÓÔËÒ‡ÌË ÌÂÎËÌÂÈÌ ̊ı Ò‚ÓÈÒÚ‚ ÓÒÛ ̆ÂÒڂΡÂÚÒˇ ÔË ÔÓÏÓ ̆Ë ÒÓÓÚÌÓ ̄ÂÌˡ –‡Ï·Â„‡ | ŒÒ„Û‰‡. ¬ [7] Ô‰ÔÓ·„‡ÂÚÒˇ, ̃ÚÓ ÌÂÎËÌÂÈÌÓÒÚ ̧ ‚ ̊Á‚‡Ì‡ ‡ÒÚÂÒÍË‚‡ÌËÂÏ Ï‡Úˈ ̊. ¬ [5] ÌÂÎËÌÂÈÌ ̊ ҂ÓÈÒÚ‚‡ ÒÎÓˇ ÔË Ò‰‚Ë„Â ‡ÔÔÓÍÒËÏËÛ ̨ÚÒˇ ÔÓÎËÌÓÏÓÏ ‚ÚÓÓÈ ÒÚÂÔÂÌË.

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Schueker C., Petterman H.E. Combining elastic brittle damage with plasticity to model the non-linear behavior of fiber reinforced laminates. In: Camanho P.P., Davila C.G., Pinho S.T., Remmers J.J.T., eds.Mechanical response of composites. Springer, 2008, pp. 99{117. (Ser. Computational methods in applied sciences; vol. 10). DOI:10.1007/978-1-4020-8584-05
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    ¬Ó ÏÌÓ„Ëı ‡·ÓÚ‡ı ÔÓ͇Á‡ÌÓ, ̃ÚÓ ÌÂÎËÌÂÈÌ ̊ ҂ÓÈÒÚ‚‡ Ô‡ÍÂÚ‡ ‚ ÓÒÌÓ‚ÌÓÏ ÓÔ‰ÂΡ ̨ÚÒˇ ÌÂÎËÌÂÈÌÓÒÚ ̧ ̨ Ò‰‚Ë„Ó‚ ̊ı ı‡‡ÍÚÂËÒÚËÍ ÒÎÓˇ [3,4,5]. ¬ ‡·ÓÚ [6] ÓÔËÒ‡ÌË ÌÂÎËÌÂÈÌ ̊ı Ò‚ÓÈÒÚ‚ ÓÒÛ ̆ÂÒڂΡÂÚÒˇ ÔË ÔÓÏÓ ̆Ë ÒÓÓÚÌÓ ̄ÂÌˡ –‡Ï·Â„‡ | ŒÒ„Û‰‡. ¬
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    Ô‰ÔÓ·„‡ÂÚÒˇ, ̃ÚÓ ÌÂÎËÌÂÈÌÓÒÚ ̧ ‚ ̊Á‚‡Ì‡ ‡ÒÚÂÒÍË‚‡ÌËÂÏ Ï‡Úˈ ̊. ¬ [5] ÌÂÎËÌÂÈÌ ̊ ҂ÓÈÒÚ‚‡ ÒÎÓˇ ÔË Ò‰‚Ë„Â ‡ÔÔÓÍÒËÏËÛ ̨ÚÒˇ ÔÓÎËÌÓÏÓÏ ‚ÚÓÓÈ ÒÚÂÔÂÌË. ¬ ‰‡ÌÌÓÈ ‡·ÓÚÂ Ò ÔÓÏÓ ̆ ̧ ̨ χÚË ̃Ì ̊ı ‡Î„ÓËÚÏÓ‚ Ë ‡Ì‡ÎËÚË ̃ÂÒÍÓÈ ‡ÔÔÓÍÒËχˆËË ÍË‚ ̊ı ‰ÂÙÓÏËÓ‚‡Ìˡ ‚ ÔÎÓÒÍÓÒÚË ÒÎÓˇ ÔË Ò‰‚Ë„Â Ô‰·„‡ÂÚÒˇ ÏÂÚÓ‰ ÔÓÒÚÓÂÌˡ ÌÂÎËÌÂÈÌ ̊ı ÓÔ‰ÂΡ ̨ ̆Ëı ÒÓÓÚÌÓ ̄ÂÌËÈ Ô‡ÍÂÚ‡ ÔÓ ı‡‡ÍÚÂËÒÚËÍ‡Ï ÒÎÓˇ. 1.

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2. DOI:10.1016/B978-008044475-8/50030-5 9.Lancaster P.Theory of matrices. New York, Academic Press, 1969. (Russ. ed.: Lancaster P. Teoriya matrits. Moscow, Nauka, 1978. 280 p.).
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    Õ‡ÔËÏÂ, ÔË ‰ÂÙÓÏËÓ‚‡ÌËË ‚ ÎËÌÂÈÌÓÈ Ó·Î‡ÒÚË ÙÛÌÍˆËˇf‡‚̇ ÌÛÎ ̨, χÚˈ‡[∆S]| ‰ËÌË ̃̇ˇ, Ë, ÒÓÓÚ‚ÂÚÒÚ‚ÂÌÌÓ, Ì Ó͇Á ̊‚‡ÂÚ ‚ÎˡÌˡ ̇ ‚ÂÎË ̃ËÌÛ ‰ÂÙÓχˆËÈ. ÕÓχ χÚˈ ̊‖∆S‖ÓÔ‰ÂΡÂÚÒˇ  ÒÓ·ÒÚ‚ÂÌÌ ̊ÏË ̃ËÒ·ÏË Ë ‡‚̇ ÌÓÏ χÚˈ ̊ diag ( 1 1−λif )
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    . ÃÓÊÌÓ ‚ˉÂÚ ̧, ̃ÚÓ ‚ ̇ ̃‡Î ̧Ì ̊È ÏÓÏÂÌÚ ÌÓχ χÚˈ ̊ ‡‚̇ ‰ËÌˈÂ, ‡ Ò ÓÒÚÓÏ ÙÛÌ͈ËËfÛ‚ÂÎË ̃Ë‚‡ÂÚÒˇ Ë ÌÓχ‖S‖. Œ‰Ì‡ÍÓ ‚ÂÎË ̃Ë̇ ̇ÍÓÔÎÂÌÌ ̊ı ÔÓ‚ÂʉÂÌËÈ ‚ ̇ ̃‡Î ̧Ì ̊È ÏÓÏÂÌÚ ‡‚̇ ÌÛÎ ̨, ÔÓ ̋ÚÓÏÛ ‰Îˇ ÓˆÂÌÍË ‚ÂÎË ̃ËÌ ̊ ̇ÍÓÔÎÂÌÌ ̊ı ÔÓ‚ÂʉÂÌËÈ, ÏÓÊÌÓ ËÒÔÓÎ ̧ÁÓ‚‡Ú ̧ ÒÎÂ‰Û ̨ ̆ ‚ ̊‡ÊÂÌËÂ: W= 1− 1 ‖S‖ .