Numerical Implementation of Spatial Elastoplastic Damage Model of Concrete in the Framework of Isogeometric Analysis Approach

<table class="figure-group"><tr class="fig-image" id="a"><td><object data="https://static.hindawi.com/articles/mpe/volume-2016/4273024/figures/4273024.fig.005a.svgz" name="4273024.fig.005a" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(a) </b>Influence of <svg height="11.927pt" id="M171" style="vertical-align:-3.291101pt" version="1.1" viewbox="-0.0498162 -8.6359 18.498 11.927" width="18.498pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M686 28C612 35 607 44 591 112C563 234 541 360 519 489L489 666L457 658L147 121C100 40 89 36 24 28L17 0H240L250 28C168 34 159 41 190 101L262 237H482C495 180 503 137 510 91C517 47 514 35 441 28L433 0H677L686 28ZM475 280H285L429 541H431L475 280Z" id="g113-66"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="703" vert-adv-y="703"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,10.244,3.132)"><path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z" id="g50-51"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,14.676,3.132)"><path d="M329 433H203L239 587L230 596L147 534L123 433H57L30 395L34 388H115L61 129C37 16 59 -12 85 -12C147 -12 222 58 260 98L241 125C212 95 160 62 144 62C132 62 127 71 138 126L192 386L305 394L329 433Z" id="g50-117"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="347" vert-adv-y="347"></glyph.data></g></svg></td></tr><tr class="fig-image" id="b"><td><object data="https://static.hindawi.com/articles/mpe/volume-2016/4273024/figures/4273024.fig.005b.svgz" name="4273024.fig.005b" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(b) </b>Influence of <svg 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xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M578 512C578 619 494 650 387 650H140L134 622C219 615 223 609 210 542L127 119C112 40 104 34 23 28L17 0H235C317 0 387 7 444 33C515 65 564 122 564 195C564 289 495 335 412 352V354C505 373 578 422 578 512ZM486 510C486 422 423 367 314 367H257L294 565C299 591 305 602 315 608C324 614 339 617 362 617C421 617 486 595 486 510ZM466 200C466 100 393 35 296 35C222 35 198 51 212 127L250 333H303C388 333 466 303 466 200Z" id="g113-67"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="601" vert-adv-y="601"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,7.748,3.132)"><path d="M290 377C321 398 342 415 358 430C378 450 389 473 389 502C389 578 329 635 238 635H237C184 635 137 610 109 578L64 515L88 493C112 529 154 573 208 573S303 542 303 482C303 409 233 370 141 341L149 308C165 313 190 319 215 319C272 319 341 283 341 193C342 98 292 43 222 43C163 43 122 72 96 94C88 101 79 100 70 94C61 87 47 73 46 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<div>Influences of <svg height="11.927pt" id="M168" style="vertical-align:-3.291101pt" version="1.1" viewbox="-0.0498162 -8.6359 22.2339 11.927" width="22.2339pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M686 28C612 35 607 44 591 112C563 234 541 360 519 489L489 666L457 658L147 121C100 40 89 36 24 28L17 0H240L250 28C168 34 159 41 190 101L262 237H482C495 180 503 137 510 91C517 47 514 35 441 28L433 0H677L686 28ZM475 280H285L429 541H431L475 280Z" id="g113-66"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="703" vert-adv-y="703"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,10.244,3.132)"><path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z" id="g50-51"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,14.676,3.132)"><path d="M701 56L582 175V262C582 360 583 449 668 449C690 461 701 496 701 517L601 581C541 619 539 623 528 665H501C493 654 473 605 473 592C473 574 500 557 520 544L607 488C539 424 536 325 536 221L235 523C175 583 162 623 162 665H135C127 653 102 585 98 553L224 425C170 370 148 288 148 208C148 164 152 120 170 80H93C67 67 55 30 55 -15H71C75 -6 84 0 94 0H272C298 13 310 50 310 71C205 107 194 187 194 270C194 321 226 368 250 398L655 -15H663C689 -2 701 35 701 56Z" id="g50-17"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="756" vert-adv-y="756"></glyph.data></g></svg> and <svg height="11.927pt" id="M169" style="vertical-align:-3.291101pt" version="1.1" viewbox="-0.0498162 -8.6359 19.7285 11.927" width="19.7285pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M578 512C578 619 494 650 387 650H140L134 622C219 615 223 609 210 542L127 119C112 40 104 34 23 28L17 0H235C317 0 387 7 444 33C515 65 564 122 564 195C564 289 495 335 412 352V354C505 373 578 422 578 512ZM486 510C486 422 423 367 314 367H257L294 565C299 591 305 602 315 608C324 614 339 617 362 617C421 617 486 595 486 510ZM466 200C466 100 393 35 296 35C222 35 198 51 212 127L250 333H303C388 333 466 303 466 200Z" id="g113-67"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="601" vert-adv-y="601"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,7.748,3.132)"><path d="M290 377C321 398 342 415 358 430C378 450 389 473 389 502C389 578 329 635 238 635H237C184 635 137 610 109 578L64 515L88 493C112 529 154 573 208 573S303 542 303 482C303 409 233 370 141 341L149 308C165 313 190 319 215 319C272 319 341 283 341 193C342 98 292 43 222 43C163 43 122 72 96 94C88 101 79 100 70 94C61 87 47 73 46 60C44 47 48 37 62 23C76 10 118 -12 165 -12C238 -12 430 62 430 223C430 297 379 359 290 375V377Z" id="g50-52"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,12.18,3.132)"><path d="M701 56L582 175V262C582 360 583 449 668 449C690 461 701 496 701 517L601 581C541 619 539 623 528 665H501C493 654 473 605 473 592C473 574 500 557 520 544L607 488C539 424 536 325 536 221L235 523C175 583 162 623 162 665H135C127 653 102 585 98 553L224 425C170 370 148 288 148 208C148 164 152 120 170 80H93C67 67 55 30 55 -15H71C75 -6 84 0 94 0H272C298 13 310 50 310 71C205 107 194 187 194 270C194 321 226 368 250 398L655 -15H663C689 -2 701 35 701 56Z" id="g50-17"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="756" vert-adv-y="756"></glyph.data></g></svg> on the evolution discipline of <svg height="12.5794pt" id="M170" style="vertical-align:-3.29107pt" version="1.1" viewbox="-0.0498162 -9.28833 14.68 12.5794" width="14.68pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g 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152 120 170 80H93C67 67 55 30 55 -15H71C75 -6 84 0 94 0H272C298 13 310 50 310 71C205 107 194 187 194 270C194 321 226 368 250 398L655 -15H663C689 -2 701 35 701 56Z" id="g50-17"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="756" vert-adv-y="756"></glyph.data></g></svg>.</div>

Mathematical Problems in Engineering

fig5

Figure 5

Figure 5: Numerical Implementation of Spatial Elastoplastic Damage Model of Concrete in the Framework of Isogeometric Analysis Approach 