Multiscale Simulation of Failure Based on Space-Time Finite Element Method and Non-Ordinary State-Based Peridynamics




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Engineering materials such as rubbers are widely used in industrial applications and are often exposed to cyclic stress and strain conditions while in service. To ensure safety and reliability, quantifying the effect of loads on the life is an important but challenging task, due to the combination of geometric/material nonlinearities and loading conditions for extended time durations. In this work, a novel simulation-based approach based on space-time finite element method (FEM) is presented with a goal to capture fatigue failure in rubbery material subjected to cyclic loads and dynamic fracture in general elastic solids. It is established by integrating the time discontinuous Galerkin (TDG) formulation with either nonlinear material constitutive laws or peridynamics models. In the first implementation, nonlinear space-time FEM framework is established and integrated with a continuum damage mechanics (CDM) model to account for the damage evolution due to cyclic loading. CDM parameters for synthetic rubber are calibrated based on fatigue experiment. The nonlinear system in space-time FEM is solved using Newton’s method in which the system Jacobian is approximated with a finite difference approach. The developed approach is then employed to solve a set of benchmark problems involving fracture and low cycle fatigue in rubber. Additional tests on notched rubber sheet specimen are carried out to validate the simulation predictions. The simulation predictions yield good agreement with the tests. In addition, it is shown that responses to fatigue load with 106 cycles can be captured using the proposed approach. In the second case, a multiscale method that couples the space-time FEM based on the time discontinuous Galerkin method with non-ordinary state-based peridynamics (NOPD) is developed for dynamic fracture simulation. A concurrent coupling scheme is presented for the coupling, in which the whole domain is discretized by finite elements, and a local domain of interest is simulated with NOPD. The space-time FEM approach allows flexible choice of time step size and this makes the computation more effective. As a meshfree method, NOPD is introduced as a fine scale representation to capture the initiation and propagation of the crack. Through coupling to space-time FEM, NOPD simulation domain moves with the propagating crack front, leading to an adaptive multiscale simulation scheme. The robustness of this methodology is demonstrated through examples of a linear elastic material, in which comparisons are made to the full scale NOPD simulation. In summary, the proposed space-time approach introduces the key capability to establish approximations in the temporal domain, thus enabling prediction of nonlinear responses that are strongly time-dependent. This is demonstrated in two cases in this dissertation: the first involves fatigue failure prediction at extended time scale, and the second deals with dynamic fracture at small time scale. Based on the implementation and results, it is concluded the established space-time FEM framework is both efficient and accurate, and overcomes the critical limit of the traditional FEM approach using semi-discrete time integration schemes. The presented framework is ideal for many engineering problems featured by a multitude of temporal scales.



Finite element method, Continuum damage mechanics, Galerkin methods, Materials—Fatigue, Rubber—Testing


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