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Published January 2015 | metadata_only
Journal Article

A micromechanical damage and fracture model for polymers based on fractional strain-gradient elasticity


We formulate a simple one-parameter macroscopic model of distributed damage and fracture of polymers that is amenable to a straightforward and efficient numerical implementation. We show that the macroscopic model can be rigorously derived, in the sense of optimal scaling, from a micromechanical model of chain elasticity and failure regularized by means of fractional strain-gradient elasticity. In particular, we derive optimal scaling laws that supply a link between the single parameter of the macroscopic model, namely, the critical energy-release rate of the material, and micromechanical parameters pertaining to the elasticity and strength of the polymer chains and to the strain-gradient elasticity regularization. We show how the critical energy-release rate of specific materials can be determined from test data. Finally, we demonstrate the scope and fidelity of the model by means of an example of application, namely, Taylor-impact experiments of polyurea 1000 rods.

Additional Information

© 2014 Elsevier B.V. Received date: 11 January 2014; Revised date: 6 June 2014; Accepted date: 21 August 2014. Available online 30 October 2014. SH and MO gratefully acknowledge support from the Office of Naval Research through grant N00014-11-1-0547. SH and MO also gratefully acknowledge the support of the U.S. National Science Foundation through the Partnership for International Research and Education (PIRE) on Science at the Triple Point Between Mathematics, Mechanics and Materials Science, Award Number 0967140. SH gratefully acknowledges support provided by the Institute for Applied Mathematics (IAM), University of Bonn, Germany.

Additional details

August 22, 2023
August 22, 2023