Implementation of a new strain split to model unilateral contact within the phase field method

• Published in: International journal for numerical methods in engineering Vol. 121; no. 21; pp. 4717 - 4733
• Main Authors: Nguyen, Thanh‐Tung, Yvonnet, Julien, Waldmann, Danièle, He, Qi‐Chang
• Format: Journal Article
• Language: English
• Published: Hoboken, USA John Wiley & Sons, Inc 15.11.2020; Wiley Subscription Services, Inc; Wiley
• Subjects: Anisotropic media; anisotropy; Compressive properties; Computer simulation; Crack propagation; Elastic anisotropy; fracture; Mathematical analysis; Mechanics; Orthogonality; phase field model; Physics; Projectors; spectral decomposition; Strain; Tensors; unilateral contact condition; Phase field model; Fracture; Unilateral contact condition; Spectral decomposition; Anisotropy
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.6463

Summary A new orthogonal split of strain tensor into compressive and tensile parts is implemented within the phase field model to mimic unilateral contact condition with which any existing cracks and any crack propagation have to comply. The resulting phase field model offers several advantages as compared to other available schemes. First, it involves rigorous orthogonality between traction and compression parts. Second, it yields remarkably simple, new analytical expressions of the projectors which provide computational saving during the crack propagation simulation. Finally, it can be applied to arbitrary initial elastic anisotropic media, which is not the case of other available strain tensor split operators. A detailed comparison of the fracture responses predicted by the present model and other approaches is provided. It is shown that the present orthogonal decomposition is able to accurately predict experimental results and removes spurious effects found in other schemes for specific loads like compression.