A COUPLING STRATEGY FOR CLASSICAL AND NONLOCAL ELASTICITY MODELS

Transcription

1 A COUPLING STRATEGY FOR CLASSICAL AND NONLOCAL ELASTICITY MODELS Nonlocal School on Fractional Equations Iowa State University, August 17 19, 2017 Marta D'Elia, P. Bochev, D. Littlewood, M. Perego Sandia National Labs, NM Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE NA

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4 A COUPLING STRATEGY FOR CLASSICAL AND NONLOCAL ELASTICITY MODELS Nonlocal School on Fractional Equations Iowa State University, August 17 19, 2017 Marta D'Elia, P. Bochev, D. Littlewood, M. Perego Sandia National Labs, NM Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE NA

5 NONLOCAL MODELS

6 NONLOCAL MODELS

7 NONLOCAL MODELS

8 NONLOCAL MODELS

9 NONLOCAL MODELS

10 NONLOCAL MODELS

11 COUPLING

12 COUPLING

13 COUPLING

14 COUPLING

15 COUPLING

16 COUPLING

17 OUTLINE

18 A NONLOCAL VECTOR CALCULUS Q. Du, M.D. Gunzburger, R. Lehoucq, and K. Zhou, Analysis and approximation of nonlocal diffusion problems with volume constraints. SIAM Review, 54, , 2012 Q. Du, M. Gunzburger, R. Lehoucq, and K. Zhou, A nonlocal vector calculus, nonlocal volume constrained problems, and nonlocal balance laws. Math. Model. Meth. Appl. Sci, 23, , 2013

19 NONLOCAL VECTOR CALCULUS

20 NONLOCAL VECTOR CALCULUS

21 NONLOCAL VECTOR CALCULUS

22 NONLOCAL VECTOR CALCULUS

23 NONLOCAL VECTOR CALCULUS

24 NONLOCAL VECTOR CALCULUS

25 NONLOCAL VECTOR CALCULUS

26 THE LtN OPTIMIZATION PROBLEM M. D'Elia, M. Perego, P. Bochev, D. Littlewood, A coupling strategy for local and nonlocal diffusion models with mixed volume constraints and boundary conditions, Computers and Mathematics with applications, 2015 M. D'Elia, P. Bochev, Formulation, analysis and computation of an optimization based local to nonlocal coupling method, submitted, 2016

27 MODEL PROBLEMS (Poisson Dirichlet)

28 MODEL PROBLEMS (Poisson Dirichlet)

29 MODEL PROBLEMS (Poisson Dirichlet)

30 LtN COUPLING

31 LtN COUPLING

32 LtN COUPLING

33 LtN COUPLING

34 IS THE SOLUTION UNIQUE?

35 IS THE SOLUTION UNIQUE?

36 IS THE SOLUTION UNIQUE?

37 IS THE SOLUTION UNIQUE?

38 IS THE SOLUTION UNIQUE?

39 FINITE DIMENSIONAL APPROXIMATION M. D'Elia, M. Perego, P. Bochev, D. Littlewood, A coupling strategy for local and nonlocal diffusion models with mixed volume constraints and boundary conditions, Computers and Mathematics with applications, 2015 M. D'Elia, P. Bochev, Formulation, analysis and computation of an optimization based local to nonlocal coupling method, submitted, 2016

40 FINITE ELEMENT DISCRETIZATIONS

41 FINITE ELEMENT DISCRETIZATIONS

42 MODEL PROBLEMS (Poisson Dirichlet & Neumann)

43 MODEL PROBLEMS (Poisson Dirichlet & Neumann)

44 COUPLING CONFIGURATION

45 THE DISCRETIZATION

46 THE DISCRETIZATION

47 THE DISCRETIZATION LK A T 'S O L PAB

48 QUICK EXAMPLE

49 STATIC PERIDYNAMICS D. Littlewood, M. Perego, M. D'Elia, P. Bochev, A coupling approach for static peridynamics and classical elasticity, in preparation M. D'Elia, P. Bochev, D. Littlewood, M. Perego, Optimization based coupling of local and nonlocal models: Applications to peridynamics, Chapter in Handbook of nonlocal continuum mechanics for materials and structures, Springer, 2017

50 THE PERIDYNAMIC MODEL

51 THE PERIDYNAMIC MODEL LK A T O' S L B PA

52 THE PERIDYNAMIC MODEL LK A T O' S L B PA

53 THE LOCAL MODEL

54 THE COUPLING STRATEGY

55 THE COUPLING STRATEGY

56 SOFTWARE* peridigm.sandia.gov * advertisement slide software.sandia.gov/albany/ trilinos.org/packages/rol

57 THE GEOMETRY

58 THE PATCH TEST

59 THE PATCH TEST

60 THE PATCH TEST

61 THE PATCH TEST

62 CRACK TEST

63 CRACK TEST

64 TENSILE BAR

65 TENSILE BAR WITH CRACK

66 ANOTHER CRACK TEST

67 ANOTHER CRACK TEST

68 ANOTHER CRACK TEST

69 ANOTHER CRACK TEST

70 WHAT IS KEEPING US BUSY...

71 WHAT IS KEEPING US BUSY... WHAT IS KEEPING ME BUSY...

72 MANNA Modeling, Analysis and Numerics for Nonlocal Applications, Santa Fe, NM, Dec , 2017 sites.google.com/site/manna2017abq

73 Thank you