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Favia, Pietro (2018) Study of the Fractures in Slowly Driven Dominated Threshold Systems. [Ph.D. thesis]

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Abstract (english)

Fracture mechanics plays an important role in the material science, structure design and industrial production due to the failure of materials and structures are paid high attention in human activities.
For this reason, the fracture mechanics can be considered today one of the most important research fields in engineering. The attempts to predict the failure of a material are able to link different disciplines: in this dissertation, a very deep use of the statistical physics will be done in order to try to introduce the disorder of the medium into the breaking and to a give a new point of view to the fracture mechanics.
In the following, we will introduce a new kind of model to evaluate the genesis of the crack: the statistical central force model. As we will see, this model tries to compute the genesis of the fracture in a medium by taking into account the presence of defects of the material that are the main cause of the differences between the critical theoretical strength of a material and the real one. This innovation introduced by this model which is difficult to find in other kinds of techniques existing today united to the fact that we try to predict the behaviour of a macro system by knowing exactly the statistical behaviour of the micro-components of the system itself (the trusses) like in complex systems happens, is the main innovation of the statistical central force model. The model consists of a truss structure in which each truss is representative of a little portion of the material. Since this model was already applied in static for a porous medium in literature, we will study it from a mathematical viewpoint and we will apply it to the study of the dynamic of a dry medium before (the applications could be for the study of the fracture in metals and composites with loads changing in time) and of a porous medium later (in order to study the fracking into soils and the fracture of the concrete). Further developments could bring us to develop the same method for the study of the spalling in the concrete because of the application of a thermal load. In the dissertation we will introduce the mathematical tools to understand this model and some simulation on generic media will be realized.
This dissertation consists basically of five chapters.
In chapter 1 a brief description of the state of the art will be given: we will leave from the birth of the classical elastic fracture mechanics and we will shortly talk about the fracture mechanics in a plastic field. After this we will describe two important techniques used today for the evaluation of the crack: the XFem and the Peridynamics; the first one is a numerical technique allowing the FEM to take into account the possibility to create a breaking into the material. This is done, as we will see, by adding further degrees of freedom to the finite elements. In this way a single finite element will have the possibility to “open” itself and to simulate a discontinuous field of displacements, which is the main problem concerning with FEM in calculating the fracture. The second one is a theory that postulates that each medium can be divided in particles and that each particle interacts with its own neighbours within a given horizon. From which we get the word “peri”. By this assumption it is possible to get some integro-equations that can be defined on the surfaces of the tips and of the cracks as well.
In chapter 2 we will talk about the so called Fiber Bundle Model which is the basis of our statistical model. We will talk about the dry FBM that was already studied at the beginning of ’90s from a mathematical viewpoint : it consists of a bundle of fibers clamped at one edge and free to move to the other one. The model is one dimensional and it is probably one of the most naïve models to begin to study the fracture; however, despite to its simplicity, it contains an important tool: the possibility to take into account the defects of the medium by introducing the concept of variable thresholds in stress. As we will see, these thresholds will be picked up by a probability density function. Then we will apply the theory of the statistical ensembles to study one of the extensions of the FBM: the continuous fiber bundle model. This is necessary to have an idea of how the micro-components of our model, the trusses, behave in a truss structure subject to an external load.
In chapter 3 we will report briefly the theory of the porous medium according to the mixture theories of De Boer. So an overview about the equations will be given and then we will discretize these equations according to the finite element technique. After this, we will briefly describe in which part of the algorithm the concept of imperfection/threshold in stress enters. We will do this for a dry medium and for a porous medium in dynamics.
In chapter 4 we will report the numerical results. Some simulations in dynamics will be done both for a dry medium and for a porous medium. Furthermore we will introduce in the end a new damage law that will have a precise statistical meaning: it will be the average among all the possible realizations of the constitutive laws of our truss structure and for a big number of trusses, it will become the constitutive behaviour of our structure from which to get the damage law. And this result will take into account the disorder of the medium.
In chapter 5 we will talk about a controversial argument: the Self Organized Criticality (SOC) that was sticked in previous papers to the statistical central model. We will try to understand what SOC is and if our system with our algorithm to compute the fracture gets the necessary and sufficient conditions to enter into the set of the SOC systems.
At the end of our journey we will have hopefully done a first step into the description of a new numerical tool to evaluate the crack into a generic medium without needing an initial discontinuity to develop the crack itself. The next steps will be to validate this technique for existing materials and to compare it to other numerical tools like XFem or Peridynamics. After this, the future will be to extend the technique passing from trusses to 2D elements.



Abstract (italian)

Fracture mechanics plays an important role in the material science, structure design and industrial production due to the failure of materials and structures are paid high attention in human activities.
For this reason, the fracture mechanics can be considered today one of the most important research fields in engineering. The attempts to predict the failure of a material are able to link different disciplines: in this dissertation, a very deep use of the statistical physics will be done in order to try to introduce the disorder of the medium into the breaking and to a give a new point of view to the fracture mechanics.
In the following, we will introduce a new kind of model to evaluate the genesis of the crack: the statistical central force model. As we will see, this model tries to compute the genesis of the fracture in a medium by taking into account the presence of defects of the material that are the main cause of the differences between the critical theoretical strength of a material and the real one. This innovation introduced by this model which is difficult to find in other kinds of techniques existing today united to the fact that we try to predict the behaviour of a macro system by knowing exactly the statistical behaviour of the micro-components of the system itself (the trusses) like in complex systems happens, is the main innovation of the statistical central force model. The model consists of a truss structure in which each truss is representative of a little portion of the material. Since this model was already applied in static for a porous medium in literature, we will study it from a mathematical viewpoint and we will apply it to the study of the dynamic of a dry medium before (the applications could be for the study of the fracture in metals and composites with loads changing in time) and of a porous medium later (in order to study the fracking into soils and the fracture of the concrete). Further developments could bring us to develop the same method for the study of the spalling in the concrete because of the application of a thermal load. In the dissertation we will introduce the mathematical tools to understand this model and some simulation on generic media will be realized.
This dissertation consists basically of five chapters.
In chapter 1 a brief description of the state of the art will be given: we will leave from the birth of the classical elastic fracture mechanics and we will shortly talk about the fracture mechanics in a plastic field. After this we will describe two important techniques used today for the evaluation of the crack: the XFem and the Peridynamics; the first one is a numerical technique allowing the FEM to take into account the possibility to create a breaking into the material. This is done, as we will see, by adding further degrees of freedom to the finite elements. In this way a single finite element will have the possibility to “open” itself and to simulate a discontinuous field of displacements, which is the main problem concerning with FEM in calculating the fracture. The second one is a theory that postulates that each medium can be divided in particles and that each particle interacts with its own neighbours within a given horizon. From which we get the word “peri”. By this assumption it is possible to get some integro-equations that can be defined on the surfaces of the tips and of the cracks as well.
In chapter 2 we will talk about the so called Fiber Bundle Model which is the basis of our statistical model. We will talk about the dry FBM that was already studied at the beginning of ’90s from a mathematical viewpoint : it consists of a bundle of fibers clamped at one edge and free to move to the other one. The model is one dimensional and it is probably one of the most naïve models to begin to study the fracture; however, despite to its simplicity, it contains an important tool: the possibility to take into account the defects of the medium by introducing the concept of variable thresholds in stress. As we will see, these thresholds will be picked up by a probability density function. Then we will apply the theory of the statistical ensembles to study one of the extensions of the FBM: the continuous fiber bundle model. This is necessary to have an idea of how the micro-components of our model, the trusses, behave in a truss structure subject to an external load.
In chapter 3 we will report briefly the theory of the porous medium according to the mixture theories of De Boer. So an overview about the equations will be given and then we will discretize these equations according to the finite element technique. After this, we will briefly describe in which part of the algorithm the concept of imperfection/threshold in stress enters. We will do this for a dry medium and for a porous medium in dynamics.
In chapter 4 we will report the numerical results. Some simulations in dynamics will be done both for a dry medium and for a porous medium. Furthermore we will introduce in the end a new damage law that will have a precise statistical meaning: it will be the average among all the possible realizations of the constitutive laws of our truss structure and for a big number of trusses, it will become the constitutive behaviour of our structure from which to get the damage law. And this result will take into account the disorder of the medium.
In chapter 5 we will talk about a controversial argument: the Self Organized Criticality (SOC) that was sticked in previous papers to the statistical central model. We will try to understand what SOC is and if our system with our algorithm to compute the fracture gets the necessary and sufficient conditions to enter into the set of the SOC systems.
At the end of our journey we will have hopefully done a first step into the description of a new numerical tool to evaluate the crack into a generic medium without needing an initial discontinuity to develop the crack itself. The next steps will be to validate this technique for existing materials and to compare it to other numerical tools like XFem or Peridynamics. After this, the future will be to extend the technique passing from trusses to 2D elements.



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EPrint type:Ph.D. thesis
Tutor:Pesavento, Francesco
Supervisor:Pruessner, Gunnar
Ph.D. course:Ciclo 30 > Corsi 30 > SCIENZE DELL'INGEGNERIA CIVILE E AMBIENTALE
Data di deposito della tesi:14 January 2018
Anno di Pubblicazione:14 January 2018
Key Words:truss lattice fracture mechanics porous media
Settori scientifico-disciplinari MIUR:Area 08 - Ingegneria civile e Architettura > ICAR/08 Scienza delle costruzioni
Struttura di riferimento:Dipartimenti > Dipartimento di Ingegneria Civile, Edile e Ambientale
Codice ID:10791
Depositato il:25 Oct 2018 16:35
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Le url contenute in alcuni riferimenti sono raggiungibili cliccando sul link alla fine della citazione (Vai!) e tramite Google (Ricerca con Google). Il risultato dipende dalla formattazione della citazione.

1. Abaimov, S., Statistical Physics of non- thermal phase transitions. From foundations to applications. Springer Cerca con Google

2. Ahmed, A. eXtended Finite Element Method ( XFEM ) - Modeling arbitrary discontinuities and Failure analysis. 196 (2009). Cerca con Google

3. Bak, P., Tang, C. & Wiesenfeld, K. Self-organized criticality. Phys. Rev. A 38, 364–374 (1988). Cerca con Google

4. Bak, P., How nature works: the science of self organised criticality, Per Bak Cerca con Google

5. Bar-Yam, Y. Dynamics of Complex Systems (Studies in Nonlinearity) Variational Principles and the Numerical Solution of Scattering Problems. Computers in Physics 12, (1998). Cerca con Google

6. Baxevanis, T. & Katsaounis, T. Scaling of the size and temporal occurrence of burst sequences in creep rupture of fiber bundles. Eur. Phys. J. B 61, 153–157 (2008). Cerca con Google

7. Bhattacharyya, P., Pradhan, S. & Chakrabarti, B. Phase transition in fiber bundle models with recursive dynamics. Phys. Rev. E 67, 46122 (2003). Cerca con Google

8. Belytschko, T., Liu, W.K., Moran, B., Elkhodary, K., Non linear Finite elements for Continua and Structure, Wiley, 2014 Cerca con Google

9. Hansen, A., Hemmer,P., Pradhan, S., The Fiber Bundle Model: Modeling Failure in Materials, Wiley, 2015 Cerca con Google

10. Hemmer, P. C., Hansen, A. & Pradhan, S. Rupture processes in fibre bundle models. Lect. Notes Phys. 705, 27–55 (2006). Cerca con Google

11. Hemmer, P. C. & Hansen, A. The Distribution of Simultaneous Fiber Failures in Fiber Bundles. J. Appl. Mech. 59, 909 (1992). Cerca con Google

12. Hidalgo, R. C., Kovacs, K., Pagonabarraga, I. & Kun, F. Universality class of fiber bundles with strong heterogeneities. Epl 81, 54005 (2008). Cerca con Google

13. Hidalgo, R. C., Kun, F. & Herrmann, H. J. Bursts in a fiber bundle model with continuous damage. Phys. Rev. E 64, 66122 (2001). Cerca con Google

14. Huang, K. Statistical Mechanics, 2nd Edition. Statistical Mechanics 512 (1987). doi:citeulike-article-id:712998 Cerca con Google

15. Garelli, M.,. Propagazione di cricche e impatti con la teoria della Peridinamica in Abaqus Laureando : Matteo Garelli Matricola n . 1041163. , Università degli studi di Padova(2015). Cerca con Google

16. Klein, W., Gould, H. & Tobochnik, J. Phenomenological Theories of Nucleation. V, (2012). Cerca con Google

17. Kloster, M., Hansen, A. & Hemmer, P. C. Burst avalanches in solvable models of fibrous materials. Phys. Rev. E 56, 2615 (1997). Cerca con Google

18. Krenk, S. Non-linear modeling and analysis of solids and structures. Igarss 2014 (2009). doi:10.1007/s13398-014-0173-7.2 Cerca con Google

19. Kun, F., Raischel, F., Hidalgo, R. C. & Herrmann, H. J. Extensions of fiber bundle models. Model. Crit. Catastrophic Phenom. Geosci. - A Stat. Phys. Approach 705, 57–92 (2007). Cerca con Google

20. Kun, F., Zapperi, S., Herrmann, H. J., Sapienza, L. & Roma, P. a M. PHYSICAL JOURNAL B Damage in fiber bundle models. 279, 269–279 (2000). Cerca con Google

21. Kun, F., Zapperi, S. & Herrmann, H. J. Damage in Fiber Bundle Models. (1999). doi:10.1007/PL00011084 Cerca con Google

22. Latente, C., Ordine, P., Specie, P., Latente, C. & Il, A. Transizioni di fase 3.1. 1–34 Cerca con Google

23. Lewis, R. & Schrefler, B. Finite Element Method in the Deformation and Consolidation of Porous Media. Osti.Gov (1998). doi:10.1137/1031039 Cerca con Google

24. Madenci, E. Oterkus, E Peridynamics: Theory and its applications.. Springer, New York, 2014 Cerca con Google

25. Milanese, E., Yılmaz, O., Molinari, J. F. & Schrefler, B. A. Avalanches in dry and saturated disordered media at fracture in shear and mixed mode scenarios. Mech. Res. Commun. 80, 58–68 (2017). Cerca con Google

26. Pagonabarraga, I. & Mart, C. Avalanche dynamics of the continuous damage fiber bundle model. (2009). Cerca con Google

27. Pradhan, S., Bhattacharyya, P. & Chakrabarti, B. K. Dynamic critical behavior of failure and plastic deformation in the random fiber bundle model. Phys. Rev. E - Stat. Nonlinear, Soft Matter Phys. 66, (2002). Cerca con Google

28. Pradhan, S., Hansen, A. & Chakrabarti, B. K. Failure processes in elastic fiber bundles. Rev. Mod. Phys. 82, 499–555 (2010). Cerca con Google

29. Pradhan, S., Hansen, A. & Hemmer, P. C. Crossover behavior in failure avalanches. Phys. Rev. E - Stat. Nonlinear, Soft Matter Phys. 74, 1–9 (2006). Cerca con Google

30. Pradhan, S., Hansen, A. & Hemmer, P. C. Crossover behavior in burst avalanches: Signature of imminent failure. Phys. Rev. Lett. 95, 1–4 (2005). Cerca con Google

31. Pride, S. R. & Toussaint, R. Thermodynamics of fiber bundles. Phys. A Stat. Mech. its Appl. 312, 159–171 (2002). Cerca con Google

32. Raether, F. Ceramic Matrix Composites – an Alternative for Challenging Construction Tasks. Ceram. Appications 1, 45–49 (2013). Cerca con Google

33. Raischel, F., Kun, F. & Herrmann, H. J. Continuous damage fiber bundle model for strongly disordered materials. Phys. Rev. E - Stat. Nonlinear, Soft Matter Phys. 77, 1–10 (2008). Cerca con Google

34. Roylance, D., Introduction to fracture mechanics, Department of Material Science and Engineering, 2001 Cerca con Google

35. Sabhapandit, S. Hysteresis and Avalanches in the Random Field Ising Model. Physics (College. Park. Md). 74 (2002). Cerca con Google

36. Silling, S. A. & Lehoucq, R. B. Peridynamic theory of solid mechanics. Advances in Applied Mechanics. Adv. Appl. Mech. 44, 73–168 (2010). Cerca con Google

37. Silling, S. Defects and Interfaces in Peridynamics: A Multiscale Approach. Sandia Natl. Lab. Report, SAND2014-19128C, Albuquerque, New Mex. (2014). Cerca con Google

38. Vespignani, A. & Zapperi, S. How self-organized criticality works: A unified mean-field picture. Phys. Rev. E 57, 6345–6362 (1998). Cerca con Google

39. Yaner Bam Yam, Dynamics of complex systems, Wesley, 1992 Cerca con Google

40. Watkins, N. W., Pruessner, G., Chapman, S. C., Crosby, N. B. & Jensen, H. J. 25 Years of Self-organized Criticality: Concepts and Controversies. Space Sci. Rev. 198, 3–44 (2016). Cerca con Google

41. Zapperi, S., Ray, P., Stanley, H. E. & Vespignani, a. Avalanches in breakdown and fracture processes. Phys. Rev. E. Stat. Phys. Plasmas. Fluids. Relat. Interdiscip. Topics 59, 5049–5057 (1999). Cerca con Google

42. Zapperi, S., Vespignani, A. & Stanley, E. H. Plasticity and avalanche behaviour in microfracturing phenomena. Nature 388, 658–660 (1997). Cerca con Google

43. Zienkiewicz, O. C. & Taylor, R. L. The finite element method - Solid mechanics, 1989. Cerca con Google

44.Zienkiewicz, O. C. & Taylor, R. L., Zhu,J.Z. The Finite Element Method. Its Basis & fundamentals, 1982. Cerca con Google

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