Emmrich, Etienne; Puhst, Dimitri A short note on modeling damage in peridynamics. (English) Zbl 1334.35339 J. Elasticity 123, No. 2, 245-252 (2016). Summary: We extend the peridynamic model to inherit irreversible damage. The governing equation is both nonlocal in time and in space and yields an abstract differential equation of Volterra type. We present conditions under which unique global solutions exist. Cited in 12 Documents MSC: 35Q74 PDEs in connection with mechanics of deformable solids 74B20 Nonlinear elasticity 74H20 Existence of solutions of dynamical problems in solid mechanics Keywords:nonlocal continuum mechanics; nonlinear models; peridynamics; damage; existence PDFBibTeX XMLCite \textit{E. Emmrich} and \textit{D. Puhst}, J. Elasticity 123, No. 2, 245--252 (2016; Zbl 1334.35339) Full Text: DOI References: [1] Emmrich, E.; Lehoucq, R. B.; Puhst, D.; Griebel, M. (ed.); Schweitzer, M. A. (ed.), Peridynamics: a nonlocal continuum theory, No. 89 (2013), Berlin · Zbl 1311.74013 · doi:10.1007/978-3-642-32979-1_3 [2] Emmrich, E., Puhst, D.: Well-posedness of the peridynamic model with Lipschitz continuous pairwise force function. Commun. Math. Sci. 11, 1039-1049 (2013) · Zbl 1434.74016 · doi:10.4310/CMS.2013.v11.n4.a7 [3] Emmrich, E., Puhst, D.: Measure-valued and weak solutions to the nonlinear peridynamic model in nonlocal elastodynamics. Nonlinearity 28, 285-307 (2015) · Zbl 1312.35163 · doi:10.1088/0951-7715/28/1/285 [4] Gajewski, H., Gröger, K., Zacharias, K.: Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen. Akademie-Verlag, Berlin (1974) · Zbl 0289.47029 [5] Lipton, R.: Cohesive dynamics and fracture. arXiv:1411.4609v4 (2014) · Zbl 1386.74127 [6] Silling, S.A.: Reformulation of elasticity theory for discontinuities and long-range forces. J. Mech. Phys. Solids 48, 175-209 (2000) · Zbl 0970.74030 · doi:10.1016/S0022-5096(99)00029-0 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.