Derivation of Finite Strain Damage Model for Simulation of Low-Cycle Fatigue of Steel Structures

摘要

Low-cycle fatigue of constructural steel is closely related to the accumulation of plastic strain under cyclic loading and eventually leads to the formation of cracks or even failure of a structure. Low-cycle fatigue is very important in seismic design where for economical reasons localized damage is allowed and structure is subjected to cyclic loading. Usually very rough models are used to access damage accumulation e.g. accumulated plastic strain or accumulated plastic work. In the paper a new approach to the assessment of low-cycle fatigue based on damage mechanics is presented. A Pedersen-Tvegaard material model for tool materials, that combines kinematic and isotropic hardening with damage evolution is extended for finite strains. Owing to specific properties of constructural steel the material model had to be additionally modified. A three-dimensional finite element for large strain is developed based on the derived material model. Shear and volumetric locking is treated by Taylor expansion of shape functions. Formulation leads to the system of 28 nonlinear algebraic equations for each material (integration) point that have to be solved and consistently linearized. Symbolic manipulations, more precisely, automatic generator of numerical codes AceGen, has been used to that end. The generator is aMathematica package able to resolve the mayor problem of symbolic generation of nonlinear finite elements arrays (e.g. stiffness matrix, etc.), which is an exponential growth of the size of derived expressions. An approach, implemented in AceGen, avoids this problem by combining: symbolic and algebraic capabilities of Mathematica, automatic differentiation technique, simultaneous optimization of expressions and theorem proving . The generator translates final symbolic formulas in a compiled language and incorporates the code into a nonlinear finite element analysis environment.The 3D numerical analysis of low-cycle fatigue of the structural details for which test results are available is presented. The numerical analysis show good agreement with the experiments in the case of small plastic strains as well as in the case of local buckling at the locations of plastic hinges. The presented numerical model permits a life prediction of the structural details for arbitrary loading histories.