[1]
F. Bobaru, J. T. Foster, P. H. Geubelle and S. A. Silling. Handbook of Peridynamic Modeling. Advances in Applied Mathematics (CRC Press, 2016).
[2]
L. Beuth. Formulation and Application of a Quasi-Static Material Point Method. PhD thesis, Institut für Geotechnik, Universität Stuttgart (Stuttgart, 2012).
[3]
D. J. Littlewood, M. L. Parks, J. T. Foster, J. A. Mitchell and P. Diehl. The Peridigm Meshfree Peridynamics Code. Journal of Peridynamics and Nonlocal Modeling (2023).
[4]
C. Willberg, L. Wiedemann and M. Rädel. A mode-dependent energy-based damage model for peridynamics and its implementation. Journal of Mechanics of Materials and Structures 14, 193–217 (2019).
[5]
C. Willberg, J.-T. Hesse, M. Garbade, M. Rädel, F. Heinecke, A. Schuster and A. Pernatii. A user material interface for the Peridynamic Peridigm framework. SoftwareX 21, 101322 (2023).
[6]
J.-T. Hesse, C. Willberg, R. Hein and F. Winkelmann. Peridynamic framework to model additive manufacturing processes. PAMM n/a, e202300033 (2023).
[7]
C. Willberg, J.-T. Hesse and A. Pernatii. PeriLab - Peridynamic Laboratory. SoftwareX 26 (2024).
[8]
[9]
[10]
[11]
J. Trageser and P. Seleson. Bond-Based Peridynamics: a Tale of Two Poisson's Ratios. Journal of Peridynamics and Nonlocal Modeling 2, 278–288 (2020).
[12]
J. Guan and L. Guo. A unified bond-based peridynamic model without limitation of Poisson's ratio. Applied Mathematical Modelling 128, 609–629 (2024).
[13]
J. Guan, W. Li, X. Yan and L. Guo. An incremental bond-based peridynamic method for elastoplastic problems. International Journal for Numerical Methods in Engineering 124, 3875–3902 (2023).
[14]
S. A. Silling, M. Epton, O. Weckner, J. Xu and E. Askari. Peridynamic States and Constitutive Modeling. Journal of Elasticity 88, 151–184 (2007).
[15]
M. R. Tupek. Extension of the peridynamic theory of solids for the simulation of materials under extreme loadings. Ph.D. Thesis, Massachusetts Intitute of Technology (2014).
[16]
M. Breitenfeld, P. Geubelle, O. Weckner and S. A. Silling. Non-ordinary state-based peridynamic analysis of stationary crack problems. Computer Methods in Applied Mechanics and Engineering 272, 233–250 (2014).
[17]
H. Chen. Bond-associated deformation gradients for peridynamic correspondence model. Mechanics Research Communications 90, 34–41 (2018).
[18]
[19]
M. Tupek and R. Radovitzky. An extended constitutive correspondence formulation of peridynamics based on nonlinear bond-strain measures. Journal of the Mechanics and Physics of Solids 65, 82–92 (2014).
[20]
[21]
[22]
J. Wan, Z. Chen, X. Chu and H. Liu. Improved method for zero-energy mode suppression in peridynamic correspondence model. Acta Mechanica Sinica 35, 1021–1035 (2019).
[23]
S. A. Silling. Stability of peridynamic correspondence material models and their particle discretizations. Computer Methods in Applied Mechanics and Engineering 332, 42–57 (2017).
[24]
S. Oterkus, E. Madenci and A. Agwai. Fully coupled peridynamic thermomechanics. Journal of the Mechanics and Models of Solids 64, 1–23 (2014).
[25]
O. C. Zienkiewicz, R. L. Taylor and J. Z. Zhu. The Finite Element Method: Its Basis and Fundamentals. 7th Edition (Butterworth-Heinemann, 2013).
[26]
C. Willberg. Development of a new isogeometric finite element and its application for Lamb wave based structural health monitoring. Dissertation, Otto von Guericke University Magdeburg (2012). Open-Access-Publikation.
[27]
M. Abramowitz and I. A. Stegun. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Vol. 55 of Applied Mathematics Series (United States Department of Commerce, National Bureau of Standards; Dover Publications, Washington D.C.; New York, 1983); p. 878. [June 1964], Ninth reprint with additional corrections of tenth original printing with corrections (December 1972); first edition.
[28]
A. Pernatii, U. Gabbert, K. Naumenko, J.-T. Hesse and C. Willberg. A Penalty Method for Coupling of Finite-Element and Peridynamic Models. PAMM 22, e202200151 (2023).
[29]
[30]
[31]
D. J. Littlewood, J. D. Thomas and T. Shelton. Estimation of the Critical Time Step for Peridynamic Models. In: Proceedings of the 12th U.S. National Congress on Computational Mechanics (2013).
[32]
E. Madenci and E. Oterkus. Peridynamic Theory and Its Applications (Springer New York, 2014).
[33]
J. T. Foster, S. A. Silling and W. Chen. An Energy based Failure Criterion for use with Peridynamic States. International Journal for Multiscale Computational Engineering 9, 675–688 (2011).