Forms of Energy Release Rate and J Internal Increase Rate Based on Finite Deformation Theory
To study the crack propagation problem,a model in terms of incremental deformation represents the real propagation mechanism by taking instantaneous configuration as a reference.It requires an accurate definition of incremental deformation on a fresh crack.However,it is difficult to make the instantaneous configuration including zones around the crack tip satisfy the relevant equilibrium equations with regards to the initial configuration.Generally,energy methods such as crack tip energy release rate G and J-integral are powerful in analyzing and solving crack problems.Therefore the focus is on the determination of the form of the increase rate of energy release rate,G·,and that of J-integral,J·,regarding instantaneous configuration.Because the classical theory of small deformation takes initial configuration as a reference,the formulae for G· and J· are derived by using the energy principle and variational principle in the finite deformation theory in the present study.This work provides a new theoretical line for studying crack propagation.