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Title: Variable-order fracture mechanics and its application to dynamic fracture
Abstract

This study presents the formulation, the numerical solution, and the validation of a theoretical framework based on the concept of variable-order mechanics and capable of modeling dynamic fracture in brittle and quasi-brittle solids. More specifically, the reformulation of the elastodynamic problem via variable and fractional-order operators enables a unique and extremely powerful approach to model nucleation and propagation of cracks in solids under dynamic loading. The resulting dynamic fracture formulation is fully evolutionary, hence enabling the analysis of complex crack patterns without requiring any a priori assumption on the damage location and the growth path, and without using any algorithm to numerically track the evolving crack surface. The evolutionary nature of the variable-order formalism also prevents the need for additional partial differential equations to predict the evolution of the damage field, hence suggesting a conspicuous reduction in complexity and computational cost. Remarkably, the variable-order formulation is naturally capable of capturing extremely detailed features characteristic of dynamic crack propagation such as crack surface roughening as well as single and multiple branching. The accuracy and robustness of the proposed variable-order formulation are validated by comparing the results of direct numerical simulations with experimental data of typical benchmark problems available in the literature.

 
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Award ID(s):
1825837 1761423
NSF-PAR ID:
10212806
Author(s) / Creator(s):
;
Publisher / Repository:
Nature Publishing Group
Date Published:
Journal Name:
npj Computational Materials
Volume:
7
Issue:
1
ISSN:
2057-3960
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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