{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:42:52Z","timestamp":1760244172675,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"18","license":[{"start":{"date-parts":[[2022,9,9]],"date-time":"2022-09-09T00:00:00Z","timestamp":1662681600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Department of Mechanical and Electro-Mechanical Engineering, National Sun Yat-sen University, Taiwan","award":["11TA303"],"award-info":[{"award-number":["11TA303"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>The distribution of stresses near holes is of great importance in fracture mechanics and material modeling. The present paper provides a general stress solution near a traction-free surface for an arbitrary piecewise linear yield criterion, assuming plane-strain conditions. The generalized method of moving coordinates is proven efficient in this case. In particular, the solution reduces to evaluating one ordinary integral. The boundary value problem solved is a Cauchy problem for a hyperbolic system of equations. Therefore, the stress solution in the plastic region is independent of other boundary conditions, though the occurrence of plastic yielding at a specific point is path-dependent. The general solution applies to calculating the stress field near an elliptic hole. It is shown that the parameter that controls the pressure-dependency of the yield criterion affects the stress field significantly. The aspect ratio is less significant as compared to that parameter. However, for a given material, the aspect ratio should also be considered to predict the stress field accurately, especially in the near vicinity of the hole. The solution reduces to an available solution for the pressure-independent yield criterion, which is a particular yield criterion of the considered class of yield criteria.<\/jats:p>","DOI":"10.3390\/ma15186266","type":"journal-article","created":{"date-parts":[[2022,9,9]],"date-time":"2022-09-09T04:54:41Z","timestamp":1662699281000},"page":"6266","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Application of the Generalized Method of Moving Coordinates to Calculating Stress Fields near an Elliptical Hole"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7289-0856","authenticated-orcid":false,"given":"Sergei","family":"Alexandrov","sequence":"first","affiliation":[{"name":"Ishlinsky Institute for Problems in Mechanics RAS, 101-1 Prospect Vernadskogo, 119526 Moscow, Russia"},{"name":"Department of Civil Engineering, Peoples\u2019 Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, 117198 Moscow, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2206-2563","authenticated-orcid":false,"given":"Marina","family":"Rynkovskaya","sequence":"additional","affiliation":[{"name":"Department of Civil Engineering, Peoples\u2019 Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, 117198 Moscow, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9668-3616","authenticated-orcid":false,"given":"Shang-Nan","family":"Tsai","sequence":"additional","affiliation":[{"name":"Department of Mechanical and Electro-Mechanical Engineering, National Sun Yat-sen University, No. 70 Lien-Hai Rd., Kaohsiung 804, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1115\/1.4011454","article-title":"On the stress distribution at the base of a stationary crack","volume":"24","author":"Williams","year":"1956","journal-title":"J. Appl. Mech."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1115\/1.3601206","article-title":"A path independent integral and the approximate analysis of strain concentration by notches and cracks","volume":"35","author":"Rice","year":"1968","journal-title":"J. Appl. Mech."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"711","DOI":"10.1016\/S0020-7683(98)00042-0","article-title":"Mode I and mixed mode fields with incomplete crack tip plasticity","volume":"36","author":"Li","year":"1999","journal-title":"Int. J. Solids Struct."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1539","DOI":"10.1016\/S0020-7683(00)00098-6","article-title":"Singular plastic fields in non-associative pressure sensitive solids","volume":"38","author":"Papanastasiou","year":"2001","journal-title":"Int. J. Solids Struct."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"678","DOI":"10.1115\/1.3424381","article-title":"Riemann-Integral solutions for the plastic slip-line fields around elliptical holes","volume":"45","author":"Thomason","year":"1978","journal-title":"J. Appl. Mech."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"763","DOI":"10.1016\/0001-6160(81)90119-X","article-title":"Ductile fracture and the stability of incompressible plasticity in the presence of microvoids","volume":"29","author":"Thomason","year":"1981","journal-title":"Acta Metall."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/j.engfracmech.2015.11.013","article-title":"Explicit solutions of an elliptic hole or a crack problem in thermoelectric materials","volume":"151","author":"Zhang","year":"2016","journal-title":"Eng. Fract. Mech."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"184","DOI":"10.1016\/j.ijthermalsci.2017.03.020","article-title":"Two-dimensional problem of thermoelectric materials with an elliptic hole or a rigid inclusion","volume":"117","author":"Zhang","year":"2017","journal-title":"Int. J. Therm. Sci."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"113003","DOI":"10.1016\/j.compstruct.2020.113003","article-title":"Stress distribution around an elliptic hole in a plate with \u2018implicit\u2019 and \u2018explicit\u2019 non-local models","volume":"256","author":"Tuna","year":"2021","journal-title":"Compos. Struct."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"214","DOI":"10.3103\/S002565441002007X","article-title":"Stress-strain state and stress intensity factors of an inclined elliptic defect in a plate under biaxial loading","volume":"45","author":"Ostsemin","year":"2010","journal-title":"Mech. Solids"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Wang, W., Yuan, H., Li, X., and Shi, P. (2019). Stress concentration and damage factor due to central elliptical hole in functionally graded panels subjected to uniform tensile traction. Materials, 12.","DOI":"10.3390\/ma12030422"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1016\/0020-7225(68)90025-6","article-title":"The stress field around an elliptical crack in an anisotropic elastic medium","volume":"6","author":"Willis","year":"1968","journal-title":"Int. J. Eng. Sci."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1341","DOI":"10.1111\/ffe.12990","article-title":"Cracking process of a granite specimen that contains multiple pre-existing holes under uniaxial compression","volume":"42","author":"Huang","year":"2019","journal-title":"Fatigue Fract. Eng. Mater. Struct."},{"key":"ref_14","first-page":"e219","article-title":"Stress concentration due to the presence of a hole within the context of elastic bodies","volume":"3","author":"Murru","year":"2021","journal-title":"Mat. Des. Process. Commun."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"e202100103","DOI":"10.1002\/zamm.202100103","article-title":"Stress concentration due to the bi-axial deformation of a plate of a porous elastic body with a hole","volume":"101","author":"Murru","year":"2021","journal-title":"Z. Angew. Math. Mech."},{"key":"ref_16","first-page":"427","article-title":"The elasto-plastic plate with a hole: Analytical solutions derived by singular perturbations","volume":"46","author":"Meyer","year":"1995","journal-title":"Z. Angew. Math. Phys."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"3206","DOI":"10.1080\/15397734.2020.1801461","article-title":"Analytical method for determining the elastoplastic interface of a circular hole subjected to biaxial tension-compression loads","volume":"50","author":"Lu","year":"2022","journal-title":"Mech. Based Des. Struct. Mach."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1243\/030932405X12858","article-title":"Mechanical analysis of streamlined tubes with non-uniform wall thickness for heat exchangers","volume":"40","author":"Li","year":"2005","journal-title":"J. Strain Anal. Eng. Des."},{"key":"ref_19","first-page":"189","article-title":"Mechanical behavior and optimization of functionally graded hollow cylinder with an elliptic hole","volume":"7","author":"Roghani","year":"2020","journal-title":"Mech. Adv. Compos. Struct."},{"key":"ref_20","unstructured":"Druyanov, B. (1993). Technological Mechanics of Porous Bodies, Clarendon Press."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"060802","DOI":"10.1115\/1.2987874","article-title":"Coulomb\u2013Mohr Granular Materials: Quasi-static flows and the highly frictional limit. ASME","volume":"61","author":"Cox","year":"2008","journal-title":"Appl. Mech. Rev."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"791","DOI":"10.3103\/S0025654420060059","article-title":"Piecewise linear plastic potentials as a tool for calculating plane transient temperature stresses","volume":"55","author":"Burenin","year":"2020","journal-title":"Mech. Solids"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1016\/0022-5096(64)90029-8","article-title":"A theory of the kinematics of ideal soils under plane strain conditions","volume":"12","author":"Spencer","year":"1964","journal-title":"J. Mech. Phys. Solids"},{"key":"ref_24","unstructured":"Hill, R. (1950). The Mathematical Theory of Plasticity, Clarendon Press."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1016\/S0022-5096(99)00033-2","article-title":"Experimental analysis of near-crack-tip plastic flow and deformation characteristics (I): Polycrystalline aluminum","volume":"48","author":"Bastawros","year":"2000","journal-title":"J. Mech. Phys. 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