Development of a damage propagation analysis system based on level set XFEM using the cohesive zone model

Experimental and numerical study on open-hole tension/compression properties of carbon-fiber-reinforced thermoplastic laminates

“…The CZM for delamination was introduced by interface elements, 26 and that for intralaminar cracks was introduced by quasi-3D XFEM. 33 In the elements containing crack lines, discontinuity functions were enriched at the nodes to reproduce the discontinuity in the displacement field. Furthermore, these crack elements were divided into several subdomains and one interface element for numerical integration.…”

“…The OHC analysis was terminated when the compressive stress decreased by 5% relative to the maximum value. The detailed formulations of the quasi-3D XFEM 12,33 and the descriptions of the CZM for delamination, 38 Weibull criterion, 25 and LaRC03 failure criterion 34 can be referred elsewhere.…”

Compression-after-impact test analysis of CFRP skin-stringer specimen by FEM using a zig-zag type cohesive zone model

“…In the future, CAI test analyses of the specimens considering different size of impact damage will be conducted and compared with the experimental results, and XFEM (Nagashima and Sawada, 2016;Nagashima. 2020;Wang and Nagashima, 2021) will be used to model multiple matrix cracks for each layer of the laminated structure to improve the accuracy of the analysis model.…”

“…In order to solve this problem, Higuchi et al (2017) introduced the CZM considering the zig-zag softening law (zig-zag CZM) to improve convergence with reference to the study on CDM (Ridha et al, 2014). In addition, one of the authors proposed a quasi-three-dimensional extended FEM (XFEM) analysis method (Nagashima and Sawada, 2016) that models delamination with interface elements used in FEM as well as matrix cracking by establishing enrichment of the displacement field with discontinuous functions by XFEM. In the proposed method, it is possible to model matrix cracking independently of finite element division.…”

معادلات تنش در روش اجزامحدود توسعه یافته بر اساس انتگرال گیری عددی نیروهای داخلی ذخیره شده با استفاده از توابع چندجمله ای معادل

“…C=k}kLD xJN} Q=D w xtOkt "1 xi=[= =@ OWQ p=L QO lQD w xOv=t |k=@ Q}}eD uwO@ OWQ p=L QO lQD |xUOvy |= Q@ Q=@ u}rw= VwQ u}= "OvwW|t pOt |}=Hx@=H u=O}t x@ X=N |a@=wD uOQm |=yxv}tR QO TBU w [31] OW KQ]t LEFM |]N CUmW l}v=mt p=Ut : : : w |m}t=v}O CUmW '|Oa@xU lQD VQDUo 'C}RwBt=m O=wt Ovv=t hrDNt [74] "OW xO=iDU= 'xDi=}xaUwD OwOLt |= RH= VwQ Ovv=ty '|OOa |=yVwQ R= xO=iDU= CQwY QO "OvwW = Qoty xOt; CUO x@ G}=Dv CU= sRq pY=L G}=Dv R= u=v}t]= Qw_vt x@ %OQm s}UkD xDUO xU x@ u=wD|t = Q |UOvyt p=Ut ?re= QO |}=Qoty |=yQ=}at Q=}at R= xar=]t u}= QO [8] " 4 VvD Q=}at "3 w 3 |}=Hx@=H Q=}at "2 & 2 wQ}v Q=}at "1 xDi=}xaUwD OwOLt |= RH= VwQ QO O}OH |=yVvD |xaUwD |= Q@ wQ}v |}=Qoty QO 5 xOW xQ}NP |rN=O |=ywQ}v 'wQ}v |}=Qoty Q=}at |=v@t Q@ "CU= xOW xO=iDU= =@ O}=@ Ov};|t CUO x@ u=tr= |xvt=O QO VvD |=yxirwt |Q}op= QoDv= R= xm u=tr= xOW x@U=Lt K}LY |=yVvD ' , =@k=aDt "OvW=@ pO=aD QO |r=ta= |HQ=N |=yQ=@ "OwW|t |rN=O w |HQ=N |=yQ=@ u}@ pO=aD x@ QHvt j}kO |R=UpOt Qw_vt x@ 'OwOLt |= RH= l}Uqm VwQ C}@ w@Lt OwHw =@ CU= sRq = Q} R CU= |}=yC}OwOLt |= Q=O VwQ u}= 'lQLDt |=y|oDUw}B=v =y|oDUw}B=v O}OH |xUOvy =@ =D OvwW KqY= xrUt pL u}L QO |O}rwD |=yVt "CU= xrUt |xvt=O OOHt |Ov@Vt '?r=e VwQ \}=QW u}= QO "OvW=@ j@]vt |O= R; C=HQO O=OaD = Q} R 'CU= Q@u=tR w CNU |Qt= xrUt OOHt |Ov@Vt |rw "OW=@ QUOQOQB |Qt= O}OH |=yVt O}rwD =} Ovm Q}}eD CU= umtt xrUt OwOLt |= RH= VwQ 'pmWt u}= pL |= Q@ xOW x=Q= OOaDt |=yVwQ u=}t QO |xO}= "CU=yVwQ u} QD?w@Lt w u} QDOvtCQOk R= |m} 1 XFEM xDi=}xaUwD |}xvwox@ xOw@ lQD VQDUo =@ u=tRsy |Ov@u=tr= O}OHD pmWt pL 'VwQ u}= |rY= OwOLt |= RH= VwQ "OvwW|t pOt lQD |xUOvy x@ xHwD uwO@ =y|oDUw}B=v xm R= dQ=i |Ov@Vt u; QO xm CU= l}Uqm OwOLt |= RH= VwQ s}taD 'xDi=}xaUwD VwQ \U@ R= xm pO=at |}xrtHOvJ `@=wD R= xO=iDU= =@ 'Qw_vt u}O@ "CU= xOt; xQ}NP |=ywQ}v |OOa p= QoDv= 'xOt; CUO x@ xOW KqY= |}xrB `@=wD |= Q@ = QwDvw u}@ pO=aD 'VvD |= Q@ |O=yvW}B CqO=at |HvUCLY Qw_vt x@ "OW x@U=Lt xOW |=ypwtQi 'C}=yv QO "OW |@=} RQ= |HQ=N '`@QtQ}R VwQ QO "Ov=j@]vt lQD xHw wO Q@ |O}rwD |=yErFtQ}R [9] "OwW|t s}UkD VwoQ=yJ p=mW= R= |}xm@W x@ lQD \UwD xOW xOW xQ}NP |=ywQ}v p= QoDv= |OOa pL |= Q@ u=wD|t q=@ VwQ wO R= 13 O}=U} wy R=U|ve `@=D |=yu=tr= |= Q@ =t= 'Ow@ j}kO 14 |R=wt wQx@wQ `q[= =@ |yQoQ=yJ |Oa@wO |=yu=tr= VwQ = QwDvw 'xt=O= QO [10] "CW=O |yHwD p@=k |=y=]N s_vt=v |yQoQ=yJ |Oa@wO [11] "O=O xaUwD G=Hwa= |= Q=O |=yu=tr= |= Q@ = Q OwN |O=yvW}B 16 piwDU} Qm RDQ=wW T}Oty CW=ov R= xO=iDU= =@ u= Q=mty w 15 u=H= Q=D=v R=}v uwO@ = Q h}a[ w |wk |oDUw}B=v |= Q=O |=y\}Lt p= QoDv= |x@U=Lt |xwLv =yv; |=yvW}B VwQ OyO|t u=Wv =yv; |=yQ=m G}=Dv "OvOQm x=Q= |Ov@x}L=vQ}R x@ w 17 |}x_Lr VR= Q@ VwQ T=U= Q@ u= Q=mty w u=}}qwH [1312] "OQ=O |}q=@ CkO |xDUw}B=v |=y\}Lt |= Q@ |O}OH QJ=QO=wm Oa=wk Tv=SQw}O |x}[k R= xO=iDU= =@ xO=iDU= p@=k |R=UxDUUo VwQ `wv Qy |= Q@ xm OvOQm x=Q= x=wNrO |Oa@xU w |Oa@wO |O}OH QJ=QO=wm VwQ '|OOa |R=Uxv}y@ |Q}oQ=m x@ =@ u= Q=mty w |wUwt [14] "CU= =yv; VwQ QO "OvOQm x=Q= |oDUw}B=v |= Q=O |Oa@wO |ar[OvJ |=yu=tr= |= Q@ = Q |Ov@x}L=v x@ =yv; |O=yvW}B VwQ "CU= xOW xO=iDU= 18 \=kv hPL sD} Qwor= R= CkO ^iL =@ |Q}op= QoDv= \=kv O=OaD Vy=m p}rO ...…”