Abstract
The description of crack propagation in structural materials is still a great challenge because the discontinuous nature of the phenomena conflicts with the underlying mathematical structure of classical continuum mechanics. Recently a new non-local continuum theory has been proposed, Peridynamics, with the specific goal to overcome the limitations of the classical theory. Peridynamics is based on integral equations and does not make use of spatial differentiation, for these reasons it is better suited to describe problems affected by discontinuities. The paper presents a series of applications of peridynamics-based computational methods to the solution of static and dynamic structural problems.
Similar content being viewed by others
References
Y. Mi, M. A. Crisfield, G. A. O Davies and H. B. Hellweg, “Progressive delamination using interface elements”, J Compos Mater, Vol. 32, pp. 1246–1272, 1998.
T. Belytschko, H. Chen, J. X. Xu and G. Zi, “Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment”, Int J Numer Meth Eng, Vol. 58, pp. 1873–1905, 2003.
C. Miehe, M. Hofacker, and F. Welschinger, “A phase field model for rate-independent crack propagation:Robust algorithmic implementation based on operator splits”, Comput. Methods Appl. Mech. Eng., Vol. 119, pp. 2765–2778, 2010.
M. J. Borden, C. V. Verhoosel, M. A. Scott, T. J. R. Hughes, and C. M. Landis, “A phase-field description of dynamic brittle fracture,”, Comput. Methods Appl. Mech. Eng., Vol. 217–210, pp. 77–95, 2012.
L. Kosteski, B. R. D’Ambra, and I. Iturrioz, “Crack propagation in elastic solids using the truss-like discrete element method”, Int J Fract, Vol. 174, pp. 139–161, 2012.
S. Silling, “Reformulation of elasticity theory for discontinuities and long-range forces”, J Mech Phys Solids, Vol. 48, pp. 175–209, 2000.
S. Silling, M. Epton, O. Weckner, J. Xu and E. Askari, “Peridynamic states and costitutive modeling”, J Elast, Vol. 88, pp. 151–184, 2007.
S. Oterkus, E. Madenci, A. Agwai, “Fully coupled peridynamic thermomechanics”, J Mech Phys Solids, Vol. 64, pp. 1–23, 2014.
A. Katiyar, J. T. Foster, H. Ouchi and M. Sharma, “A peridynamic formulation of pressure driven convective fluid transport in porous media”, J Comput Phys, Vol. 261, pp. 209–229, 2014.
M. Zaccariotto, F. Luongo, G. Sarego and U. Galvanetto, “Examples of applications of the peridynamic theory to the solution of static equilibrium problems”, The Aeronautical J., Vol. 119, pp. 1–24, 2015.
M. Duzzi, M. Zaccariotto, U. Galvanetto, “Application of Peridynamic Theory to Nanocomposite Materials”, Adv Mat Research, Vol. 1016, pp. 44–48, 2014.
D. Dipasquale, M. Zaccariotto, U. Galvanetto, “Crack propagation with adaptive grid refinement in 2D peridynamics”, Int. J. of Fracture, Vol. 190, No 1–2, pp. 1–22, 2014.
Y. D. Ha, F. Bobaru, “Characteristics of dynamic brittle fracture captured with peridynamics”, Eng. Frac. Mech, Vol. 78, No 6, pp. 1156–1168, 2011.
W. Hu, Y. Wang, J. Yu, C. F. Yen and F. Bobaru, “Impact damage on a thin glass plate with a thin polycarbonate backing”, Int. J Imp. Eng., Vol. 62, pp. 152–165, 2013.
E. Budyn, G. Zi, N. Moes and T. Belytschko, “A method for multiple crack growth in the brittle materials without remeshing”, Int. J. Num. Meth. Engin., Vol. 61, pp. 1741–1770, 2004.
E. Askari, F. Bobaru, R. Lehoucq, M. Parks, S. A. Silling and O. Weckner, “Peridynamics for multiscale materials modeling”, J Phys Conf Ser, Vol. 125, pp. 1–11, 2008.
R. Rahman, J. T. Foster, “Bridging the length scales through nonlocal hierarchical multiscale modeling scheme”, Computational Materials Science, Vol. 92, pp. 401–415, 2014.
V. P. Nguyen, M. Stroeven and L. J. Sluys, “Multiscale continuous modeling of heterogeneous materials: a review on recent developments”, J. Multiscale Modelling, Vol. 3, No 4, pp. 1–42, 2011.
D. L. Shi, X. Q. Feng, Y. Y. Huang, K. C. Hwang and H. Gao, “The effect of Nanotube waviness and agglomeration on the elastic property of carbon nanotube-reinforced compositess”, J. Eng. Mater. Technol., Vol. 126, No 3, pp. 250–257, 2004.
Y. L. Hu, E. Madenci,“Bond-based peridynamic modeling of composite laminates with arbitrary fiber orientation and stacking sequence”, Composite Struct, Vol. 153, pp. 139–175, 2016.
Y. L. Hu, N. V. De Carvalho, E. Madenci,“Peridynamic modeling of delamination growth in composite laminates”, Composite Struct, Vol. 132, pp. 610–620, 2015.
Y. L. Hu, Y. Yu, H. Wang,“Peridynamic analytical method for progressive damage in notched composite laminates”, Composite Struct, Vol. 108, pp. 801–810, 2014.
S. A. Silling, E. Askari, “A meshfree method based on the peridynamic model of solid mechanics”, Comput Struct, Vol. 83, pp. 1526–1535, 2005.
M. B. Nooru-Mohamed, E. Schlangen and J. G. M. Van Mier, “Experimental and numerical study on the behavior of concrete subjected to biaxial tension and shear”, Advanced cement based materials, Vol. 1, No 1, pp. 22–37, 1993.
R. W. Macek, S. A. Silling, “Peridynamics via finite element analysis”, Finite Elements in Analysis and Design, Vol. 43, pp. 1169–1178, 2007.
ABAQUS-Explicit Version 6. 6 User’s Manual, ABAQUS Inc., Providence, Rhode Island, 2006.
B. Kilic and E. Madenci, “Coupling of peridynamic theory and the finite element method”, J. of Mech. of Mat. and Struct., Vol. 5, No 5, pp. 707–733, 2010.
W. Liu and J. W. Hong, “A coupling approach of discretized peridynamics with finite element method”, Comp. Meth. in Appl. Mech. and Eng., Vol. 245–246, pp. 163–175, 2012.
G. Lubineau, Y. Azdoud, F. Han, C. Rey and A. Askari, “A morphing strategy to couple non-local to local continuum mechanics”, J. Mech. and Ph. of Solids, Vol. 60, No 6, pp. 1088–1102, 2012.
A. Shojaei, B. Boroomand, and F. Mossaiby, “A simple meshless method for challenging engineering problems”, Eng. Comput., Vol. 32, No 6, pp. 1567–1600, 2015.
W. H. Gerstle, N. Sau, and S. A. Silling, “Peridynamic modeling of plain and reinforced concrete structures”, 18th International Conference on Structural Mechanics in Reactor Technology, Beijing, China, 2005.
U. Galvanetto, T. Mudric, A. Shojaei, M. Zaccariotto, “An effective way to couple FEM meshes and Peridynamics grids for the solution of static equilibrium problems”, Mech Res Comm, Vol. 76, pp. 41–47, 2016.
M. Zaccariotto, D. Tomasi, U. Galvanetto, “An enhanced coupling of PD grids to FE meshes”, Mech Res Comm, in press, 2017.
M. Zaccariotto, T. Mudric, D. Tomasi, A. Shojaei U. Galvanetto, “Coupling of FEM meshes with Peridynamic grids”, submitted for publication.
R. H. J. Peerlings, W. A. M. Brekelmans, R. de Borst and M. G. D. Geers, “Gradient-enhanced damage modelling of highcycle fatigue”, Int. J. Num. Meth. Engin., Vol. 49, No 12, pp. 1547–1569, 2000.
U. Galvanetto, P. Robinson, A. Cerioni and C. L. Armas, “A Simple Model for the Evaluation of Constitutive Laws for the Computer Simulation of Fatigue-Driven Delamination in Composite Materials”, SDHM, Vol. 5, No 2, pp. 161–189, 2009.
M. Zaccariotto, F. Luongo, G. Sarego, D. Dipasquale and U. Galvanetto, “Fatigue Crack Propagation with Peridynamics: a sensitivity study of Paris law parameters”, CEAS 2013, Innov Eur Sweden, Linkoping, Sweden 2013.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Zaccariotto, M., Sarego, G., Dipasquale, D. et al. Discontinuous mechanical problems studied with a peridynamics-based approach. Aerotec. Missili Spaz. 96, 44–55 (2017). https://doi.org/10.1007/BF03404736
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF03404736