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.
Highlights
Fracture is one of the most commonly encountered modes of failure in structural systems across a broad spectrum of applications spanning the civil, mechanical, and aerospace engineering fields
While the general topic of fracture mechanics is very complex in itself due to the coexistence of multiple physical processes occurring over multiple spatial scales, the specific topic of dynamic fracture is possibly even more challenging due to the occurrence of crack surface roughening, instabilities, and branching
The first two examples refer to the Kalthoff–Winkler experiment[45] and the classical crack-branching experiment[33]; both pertain to the dynamic fracture of brittle solids
Summary
Fracture is one of the most commonly encountered modes of failure in structural systems across a broad spectrum of applications spanning the civil, mechanical, and aerospace engineering fields. An important disadvantage of these models lies in their high computational cost, which follows from the need to solve a coupled system of partial differential equations for both the damage (phase) and the displacement fields[30] This limitation becomes even more significant when the phase-field approach is applied for fracture analysis in three-dimensional media. We extend this general approach to continuous systems by formulating a VO elastodynamic framework uniquely suited for the analysis of dynamic fracture and capable of detecting the formation and propagation of damage by means of strain-driven order variation laws. The introduction of VO operators in the continuum elastodynamic formulation allows the governing equations to evolve (from linear to nonlinear) and adapt (by capturing discontinuities) based on both the local response and the underlying damage mechanism while eliminating the need for explicitly tracking the damage front.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
