Interaction between a Macrocrack and a Cluster of Microcracks by Muskhelishvili’s Complex Potential Method

<div>A crack subjected to concentrated forces. (a) <span class="nowrap"><svg height="12.3655pt" id="M38" style="vertical-align:-3.129351pt" version="1.1" viewbox="-0.0498162 -9.23615 48.3973 12.3655" width="48.3973pt" 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="M475 445L452 468C423 436 401 426 385 426S352 427 305 436C268 443 216 448 185 448C156 448 128 425 102 382C89 360 77 338 64 304L89 291C117 340 143 380 190 380C214 380 268 376 295 373C320 370 344 371 362 374L70 101C32 65 23 36 23 18C23 5 27 -3 31 -8C36 -8 39 -6 42 -1C52 15 67 31 80 40S110 49 143 33C195 8 257 -20 290 -20C339 -20 382 11 439 129L416 148C366 74 334 55 305 55C278 55 236 68 203 81C169 94 141 100 122 96C205 170 348 308 411 376L475 445Z" id="g113-123"></path></g><g transform="matrix(.013,0,0,-0.013,9.381,0)"><path d="M535 230V280H52V230H535Z" id="g117-33"></path></g><g transform="matrix(.013,0,0,-0.013,19.917,0)"><path d="M169 380V459C122 440 66 423 24 416V392C86 384 90 382 90 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421 449 310 449C298 449 279 444 261 433L169 380ZM169 346C196 367 237 389 269 389C341 389 403 329 403 221C403 109 347 37 263 37C228 37 191 53 169 76V346Z" id="g121-110"></path></g><g transform="matrix(.013,0,0,-0.013,26.054,0)"><path d="M238 0V26C174 32 166 38 166 104V712C132 700 70 683 18 677V653C81 647 87 645 87 577V104C87 38 78 32 15 26V0H238Z" id="g121-106"></path></g><g transform="matrix(.013,0,0,-0.013,29.382,0)"><path d="M433 39L423 65C413 59 399 54 387 54C370 54 352 69 352 114V299C352 352 342 392 307 422C285 440 255 449 225 449C168 437 102 399 75 379C56 365 44 353 44 339C44 315 69 296 87 296C101 296 111 303 116 319C124 349 133 371 145 385C156 397 171 404 190 404C241 404 275 364 275 291V274C253 256 180 229 120 209C65 190 39 159 39 110C39 47 88 -12 159 -12C189 -12 237 25 277 52C282 35 288 21 301 8C312 -3 333 -12 348 -12L433 39ZM275 84C256 65 221 48 195 48C164 48 124 73 124 124C124 161 146 180 185 198C206 208 254 229 275 240V84Z" id="g121-95"></path></g><g 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Mathematical Problems in Engineering

fig3

Figure 3

Figure 3: Interaction between a Macrocrack and a Cluster of Microcracks by Muskhelishvili’s Complex Potential Method 