Bhattacharya, Debdeep; Lipton, Robert P. Quasistatic evolution with unstable forces. (English) Zbl 1524.74047 Multiscale Model. Simul. 21, No. 2, 598-623 (2023). MSC: 74A70 74A20 74A45 PDFBibTeX XMLCite \textit{D. Bhattacharya} and \textit{R. P. Lipton}, Multiscale Model. Simul. 21, No. 2, 598--623 (2023; Zbl 1524.74047) Full Text: DOI arXiv
Bhattacharya, Debdeep; Lipton, Robert P. Simulating grain shape effects and damage in granular media using PeriDEM. (English) Zbl 1512.74006 SIAM J. Sci. Comput. 45, No. 1, B1-B26 (2023). MSC: 74A45 74R10 74E20 74A70 74S99 PDFBibTeX XMLCite \textit{D. Bhattacharya} and \textit{R. P. Lipton}, SIAM J. Sci. Comput. 45, No. 1, B1--B26 (2023; Zbl 1512.74006) Full Text: DOI arXiv
Diehl, Patrick; Lipton, Robert Quasistatic fracture using nonlinear-nonlocal elastostatics with explicit tangent stiffness matrix. (English) Zbl 07768023 Int. J. Numer. Methods Eng. 123, No. 18, 4183-4208 (2022). MSC: 74Rxx 65Fxx 35Qxx PDFBibTeX XMLCite \textit{P. Diehl} and \textit{R. Lipton}, Int. J. Numer. Methods Eng. 123, No. 18, 4183--4208 (2022; Zbl 07768023) Full Text: DOI
Diehl, Patrick; Lipton, Robert; Wick, Thomas; Tyagi, Mayank A comparative review of peridynamics and phase-field models for engineering fracture mechanics. (English) Zbl 1505.74191 Comput. Mech. 69, No. 6, 1259-1293 (2022). MSC: 74R10 74A70 74S99 74-02 74-05 PDFBibTeX XMLCite \textit{P. Diehl} et al., Comput. Mech. 69, No. 6, 1259--1293 (2022; Zbl 1505.74191) Full Text: DOI
Jha, P. K.; Lipton, R. Finite element approximation of nonlocal dynamic fracture models. (English) Zbl 1465.74163 Discrete Contin. Dyn. Syst., Ser. B 26, No. 3, 1675-1710 (2021). MSC: 74S05 74R99 74A70 74S20 65M12 PDFBibTeX XMLCite \textit{P. K. Jha} and \textit{R. Lipton}, Discrete Contin. Dyn. Syst., Ser. B 26, No. 3, 1675--1710 (2021; Zbl 1465.74163) Full Text: DOI arXiv
Lipton, Robert P.; Jha, Prashant K. Nonlocal elastodynamics and fracture. (English) Zbl 1464.74012 NoDEA, Nonlinear Differ. Equ. Appl. 28, No. 3, Paper No. 23, 44 p. (2021). MSC: 74A45 74A70 74R10 PDFBibTeX XMLCite \textit{R. P. Lipton} and \textit{P. K. Jha}, NoDEA, Nonlinear Differ. Equ. Appl. 28, No. 3, Paper No. 23, 44 p. (2021; Zbl 1464.74012) Full Text: DOI arXiv
Jha, Prashant K.; Lipton, Robert Finite element convergence for state-based peridynamic fracture models. (English) Zbl 1463.74103 Commun. Appl. Math. Comput. 2, No. 1, 93-128 (2020). MSC: 74R99 74H55 74S05 PDFBibTeX XMLCite \textit{P. K. Jha} and \textit{R. Lipton}, Commun. Appl. Math. Comput. 2, No. 1, 93--128 (2020; Zbl 1463.74103) Full Text: DOI arXiv
Jha, Prashant K.; Lipton, Robert Numerical convergence of finite difference approximations for state based peridynamic fracture models. (English) Zbl 1441.74018 Comput. Methods Appl. Mech. Eng. 351, 184-225 (2019). MSC: 74A45 35Q74 74S20 65M06 65M12 65M15 74H55 PDFBibTeX XMLCite \textit{P. K. Jha} and \textit{R. Lipton}, Comput. Methods Appl. Mech. Eng. 351, 184--225 (2019; Zbl 1441.74018) Full Text: DOI arXiv
Lipton, Robert; Said, Eyad; Jha, Prashant Free damage propagation with memory. (English) Zbl 1403.74080 J. Elasticity 133, No. 2, 129-153 (2018). MSC: 74R05 74R10 PDFBibTeX XMLCite \textit{R. Lipton} et al., J. Elasticity 133, No. 2, 129--153 (2018; Zbl 1403.74080) Full Text: DOI
Jha, Prashant K.; Lipton, Robert Numerical analysis of nonlocal fracture models in Hölder space. (English) Zbl 1388.74054 SIAM J. Numer. Anal. 56, No. 2, 906-941 (2018). Reviewer: Vinod K. Arya (Dallas) MSC: 74H55 74S20 PDFBibTeX XMLCite \textit{P. K. Jha} and \textit{R. Lipton}, SIAM J. Numer. Anal. 56, No. 2, 906--941 (2018; Zbl 1388.74054) Full Text: DOI arXiv
Lipton, Robert Cohesive dynamics and brittle fracture. (English) Zbl 1386.74127 J. Elasticity 124, No. 2, 143-191 (2016); erratum ibid. 125, no. 1, 137 (2016). MSC: 74R10 35B27 35Q74 74H55 PDFBibTeX XMLCite \textit{R. Lipton}, J. Elasticity 124, No. 2, 143--191 (2016; Zbl 1386.74127) Full Text: DOI arXiv
Du, Qiang; Lipton, Robert; Mengesha, Tadele Multiscale analysis of linear evolution equations with applications to nonlocal models for heterogeneous media. (English) Zbl 1348.74287 ESAIM, Math. Model. Numer. Anal. 50, No. 5, 1425-1455 (2016). MSC: 74Q05 74E05 74H10 45F99 45P05 PDFBibTeX XMLCite \textit{Q. Du} et al., ESAIM, Math. Model. Numer. Anal. 50, No. 5, 1425--1455 (2016; Zbl 1348.74287) Full Text: DOI
Lipton, Robert Dynamic brittle fracture as a small horizon limit of peridynamics. (English) Zbl 1309.74065 J. Elasticity 117, No. 1, 21-50 (2014). MSC: 74R10 34A34 74H55 PDFBibTeX XMLCite \textit{R. Lipton}, J. Elasticity 117, No. 1, 21--50 (2014; Zbl 1309.74065) Full Text: DOI arXiv
Alali, Bacim; Lipton, Robert Multiscale dynamics of heterogeneous media in the peridynamic formulation. (English) Zbl 1320.74029 J. Elasticity 106, No. 1, 71-103 (2012). MSC: 74D10 74E05 74H15 74H20 74Q10 35Q74 49J45 PDFBibTeX XMLCite \textit{B. Alali} and \textit{R. Lipton}, J. Elasticity 106, No. 1, 71--103 (2012; Zbl 1320.74029) Full Text: DOI arXiv