Rapid strain energy density evaluation for V-notches under mode I loading conditions

Improvement of Mixed-Mode I/II Fracture Toughness Modeling Prediction Performance by Using a Multi-Fidelity Surrogate Model Based on Fracture Criteria

“… and are the strain energy density generated from the applied external load. The values of and can be rewritten in terms of stress intensity factor, which is considered an elementary prediction of fracture toughness of the ASED criteria ( and ) following Equations (14) and (15) where and are given by Lazzarin et al [ 29 ] as 0.1186 and 0.3332, respectively, and are specific values of mixed-mode I/II fracture toughness obtained from the ASED criteria, and are mode I and II Williams’ eigenvalues, which are equal to 0.5 [ 30 ], and and are mode I and mode II radii under plane strain conditions, which can be calculated following Equations (16) and (17). where …”

Rapid evaluation of notch stress intensity factors using the peak stress method with 3D tetrahedral finite element models: Comparison of commercial codes

“…The comparison between Equations (4)–(6) and previous Equations (1)–(3) shows that the PSM has a further advantage in addition to the coarse FE mesh: only a single linear‐elastic peak stress evaluated at the singularity location is necessary to estimate each NSIF‐term, instead of a number of stress versus distance results, which require a post‐processing analysis. Other methods 52–56 are available in the literature to rapidly estimate the NSIF‐terms using coarse meshes. Lazzarin et al 53 suggested to take advantage of the averaged SED calculated by adopting coarse meshes inside a structural volume of radius R 0 .…”

“…Lazzarin et al 53 suggested to take advantage of the averaged SED calculated by adopting coarse meshes inside a structural volume of radius R 0 . The need for the geometrical modeling of the structural volume has been removed in very recent contributions by Foti et al, 56 Campagnolo et al, 57 and Zappalorto et al 54,55 in case of 2D problems. It is worth noting that the values of K * FE , K ** FE , and K *** FE calibrated under pure modes of loading using 2D four‐node plane elements, 3D eight‐node brick elements, four‐node as well as ten‐node tetrahedral elements of Ansys Mechanical APDL element library have been successfully checked also against mixed mode problems 58–61 …”

Energy‐based evaluation of the stress concentration factor with highly non‐regular coarse meshes: Theoretical formulation and practical validation

“…Different from Meneghetti's approach, in the past and recent literature some other authors proposed to use the Averaged Strain Energy Density (ASED) or the Total Strain Energy to indirectly assess local stress field parameters, such as the NSIF at pointed V-notches, weld roots or toes. 17,18 In particular, Lazzarin and co-workers 17,18 and Berto and collaborators [19][20][21][22] proved that the ASED evaluated over a circular sector surrounding the pointed V-notch tip is almost mesh insensitive, and used such a property to indirectly compute NSIFs, as well as the stress concentration factor of holes. 18 Zappalorto and co-workers, 23,24 instead, proposed to use the elemental strain energy (ESE) or elemental averaged stresses (EASs) to compute NSIFs in notched solids and welded joints under different loading conditions.…”