2023/02/07 by Ren, Huilong, Zhuang, Xiaoying, Rabczuk, Timon
#FOS: Mathematics #FOS: Physical sciences #Materials Science (cond-mat.mtrl-sci) #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2302.13783
A phase field model for ductile fracture considering Hencky strain and finite J2 plasticity is presented using the nonlocal operator method. A variational derivation of J2 plasticity at finite strain with a phase field model is performed. The method includes a logarithmic strain tensor and an exponential mapping in the plasticity evolution. A spectral decomposition based algorithm for computing the first and second order derivatives of the composite matrix function is implemented. A consistent tangential stiffness matrix is derived and used in Newton-Raphson iterations. Several numerical examples are performed to validate the method, including notched single-edged plates with brittle fracture or ductile fracture and necking of a bar with/without phase field model.