A Hamiltonian‐based analytical method for fracture analysis of linear thermo‐viscoelastic media. Issue 4 (3rd November 2017)

• Record Type: Journal Article
• Authors: Tong, Zhenzhen; Cheng, Xianhe; Rong, Dalun; Xu, Chenghui; Zhou, Zhenhuan; Xu, Xinsheng
• Is Part Of: Zeitschrift für angewandte Mathematik und Mechanik. Volume 98:Issue 4(2018)
• Page Start: 542
• Page End: 553
• Publication Date: 2017-11-03
• Subjects: Thermo‐viscoelasticity -- symplectic method -- Hamiltonian system -- fracture analysis; Mathematics -- Periodicals; Mechanics, Applied -- Periodicals; Engineering -- Periodicals; 519
• DOI: 10.1002/zamm.201600058
• Languages: English
• ISSNs: 0044-2267

Abstract

Abstract: A Hamiltonian‐based methodology is presented to study the fracture behaviors of the thermo‐viscoelastic materials based on the Laplace transform. The governing equations and associated boundary conditions are rebuilt in a Hamiltonian form by using the symplectic mathematics in the frequency domain ( s ‐domain). The fundamental unknown vector composed of both displacements and stresses variables is expanded in terms of the symplectic eigensolutions. The corresponding unknown coefficients of the symplectic series are determined from the outer boundary conditions. Thus, the main unknowns are obtained and transformed into the time domain ( t ‐domain). The fracture parameters including stress intensity factors (SIFs) and J ‐integrals are derived simultaneously. Numerical examples as well as convergence studies are given and are found to be in good agreement with the ANSYS results. A parametric study of thermo‐viscoelastic parameters is included also. Abstract : A Hamiltonian‐based methodology is presented to study the fracture behaviors of the thermo‐viscoelastic materials based on the Laplace transform. The governing equations and associated boundary conditions are rebuilt in a Hamiltonian form by using the symplectic mathematics in the frequency domain ( s ‐domain). The fundamental unknown vector composed of both displacements and stresses variables is expanded in terms of the symplectic eigensolutions. The corresponding unknown coefficients of the symplectic series are determined from the outer boundary conditions. Thus, the main unknowns are obtained and transformed into the time domain ( t ‐domain). The fracture parameters including stress intensity factors (SIFs) and J ‐integrals are derived simultaneously. Numerical examples as well as convergence studies are given and are found to be in good agreement with the ANSYS results. A parametric study of thermo‐viscoelastic parameters is included also.