A New Unified Solution for Circular Opening considering Different Strength Criteria and the Postpeak Elastic Strain Form

Table 1

A summary on the yield criterion under plane strain conditions.

Failure criterion	Initial yield criterion	Simplified yield criterion	Linearity	Intermediate principal stress
Mohr–Coulomb (MC) [1, 14]		;	Linear	No
Tresca (TR) [15]			Linear	No
Generalized Lade–Duncan (GLD) [18–23]	;		Nonlinear	Yes
Mogi–Coulomb (GMC) [2, 24, 25]			Linear	Yes
von Mises (VM) [15, 26]			Nonlinear	Yes
Generalized SMP criterion (GSMP) [18, 27]			Nonlinear	Yes
Circumscribe Drucker–Prager (CDP) [1, 3, 4, 28–30]			Nonlinear	Yes
Middle Circumscribe Drucker–Prager (MDP) [28]	The expression form is the same as CDP.			Yes
Inscribe Drucker–Prager (IDP) [31]	The expression form is the same as CDP.			Yes
Unified strength theory (UST) [5, 6, 32–34]	If; ; If		Linear	Yes
Generalized twin shear stress criterion (GTSS) [5, 6]	When b = 1, UST is equal to GTSS.		Linear	Yes

The compressive stress is positive and the tensile stress is negative ; b is the intermediate principal stress coefficient; ; ; .