Numerical Study On Damage Fracture And Dynamic Instability Of Continuum

Understanding the dynamic fracture and instability of continuous medium is an ongoing challenge in physics and materials science.With the rapid development of computer technology,numerical simulation plays a crucial role in current scientific research.In recent years,a method termed phase field method(PFM)has demonstrated extraordinary capabilities in dealing with complex fractures.However,the phase field modeling of fracture is computationally demanding,due to the high temporal-spatial resolution required for crack tracking.Besides,the vast majority of the previous reports concentrated on brittle fracture.The few reports on the phase field modeling of fractures at large deformations are also limited to quasi-static.To our knowledge,at least in the mechanics community,research related to the coupling of phase field modeling and nonlinear elastic dynamics is scarce.In this context,My PhD work exactly started by proposing some novel models and algorithms.After laying the foundations of the methodology,further research is committed to uncovering the physical origins of rapid fracture instability and limit crack velocity.In addition to solid fractures,the research in this thesis also involves the hydrodynamic instability of non-Newtonian fluids.The research of this thesis is summarized in the following aspects:(1)To cope with the expensive computational cost of phase field modeling of fracture,a novel hybrid adaptive finite element phase-field method(ha-PFM)is developed.ha-PFM can dynamically track the propagation of the cracks and adaptively refine(coarsen)the meshes based on a novel crack tip identification strategy.This scheme prominently reduces the computational cost,e.g.CPU time and memory usage.Unlike the previous adaptive phase field method(APFM),multi-level hybrid triangular and quadrilateral elements were developed to discretize the computational domain,which eliminates hanging nodes and ensures that the meshes in the vicinity of the crack tip are highly isotropic.Several representative benchmarks containing quasi-static and dynamic fracture were re-investigated with ha-PFM.Compared with the standard phase field method,it was found that ha-PFM can increase the speed by 15 to 30 times.(2)Based on the proposed ha-PFM,we investigated the dynamic brittle fracture of poly(methyl methacrylate)(PMMA)through computer simulation.Without the explicit fracture criterion,current simulations not only successfully reproduced the crucial experimental observations on crack propagation,such as crack patterns,velocity evolutions and limit crack velocity but also discovered some new features not reported in the experimental study yet.Through quantifying the energy flux into the crack tip and fracture energy,the long-standing challenge of limit crack velocity in experiments is successfully predicted by continuum theory,which unveils that crack bifurcation sets the upper limit for crack velocity.Combining the crack bifurcation criterion and continuum theory provides a rational explanation for complex path selection of cracks.(3)With the groundwork of brittle fracture,this work presents the Griffith-type phase-field formation at large deformation in the framework of adaptive edge-based smoothed finite element method(ES-FEM)for the first time.The ES-FEM is an excellent member of the S-FEM family developed in combination with meshless ideas and finite element method(FEM),which is characterized by higher accuracy,‘softer'stiffness,and insensitive to mesh distortion.Given that,the advantages of the phase-field method(PFM)and ES-FEM are fully combined by the approach proposed in this paper.With the costly computational overhead of PFM and ES-FEM in mind,a well-designed multi-level adaptive mesh strategy was developed,which considerably improved the computational efficiency(about 20 times faster).Furthermore,the detailed numerical implementation for the coupling of PFM and ES-FEM is outlined.Several representative numerical examples were recalculated based on the proposed method,and its effectiveness is verified by comparison with the results in experiments and literature.In particular,an experiment in which cracks deflected in rubber due to impinging on a weak interface was firstly reproduced.(4)Numerical experiments on phase field modeling of the fracture in hyperelastic materials reveal that the classical mechanical-based dynamic phase field model is ineffective in the framework of non-linear deformation.The aspiration to gain insight into rapid fracture instability motivated us to develop a novel dynamic phase field model characterized by wave velocity invariance,enabling crack propagation at a velocity approach to the asymptotic limit.Given that the numerical treatment of rapid fractures involves extremely high spatiotemporal resolution,robust explicit dynamics and a tried-and-tested ha-PFM are invoked.More crucially,an original adaptive distorted mesh removal scheme(ADMR)was developed to cope with the intractable finite element mesh distortion problem in large deformation fractures.The detailed numerical implementation for entire procedures is outlined,and its reliability is verified by two quasi-static fracture benchmarks.Utilizing the proposed model and innovative algorithms,the arresting ultrahigh-speed crack oscillation and tip-splitting instabilities captured in the fracture experiments of brittle gels were successfully reproduced.(5)In this research,a well-known Phan-Thien and Tanner(PTT)differential viscoelastic constitutive equation has been employed to analyze the nonlinear stability and dynamics of non-isothermal film casting.Finite element method(FEM)combined with stabilization techniques including discrete elastic viscous stress splitting(DEVSS)and streamline upwind Petrov-Galerkin(SUPG)were first performed for numerical calculation of transient film casting.Therefore,the stability analysis of film casting was carried out based on a wider parameter space of processing and rheological properties of the polymer melt.Unlike the results predicted by Upper-Convected Maxwell(UCM)model,the stabilizing region upon an upper critical draw ratio is nonexistent,while more than one peak of Drc was observed with varying aspect ratio,which was dominated by two deformation types named planar and transitional deformations,respectively.Our simulation results show that elongational rheological behavior plays a dominant role on the stability of flow for both extensional-thickening and extensional-thinning fluids,while the effects of processing parameters like extrusion rate and cooling,and rheological parameters like relaxation time on Drc all can be attributed to elongational viscosity.