Variable-order fracture mechanics and its application to dynamic fracture

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 variableorder formulation are validated by comparing the results of direct numerical simulations with experimental data of typical benchmark problems available in the literature.

On the role of the microstructure in the deformation of porous solids

This study explores the role that the microstructure plays in determining the macroscopic static response of porous elastic continua and exposes the occurrence of position-dependent nonlocal effects that are strictly correlated to the configuration of the microstructure.Then,a nonlocal continuum theory based on variable-order fractional calculus is developed in order to accurately capture the complex spatially distributed nonlocal response.The remarkable potential of the fractional approach is illustrated by simulating the nonlinear thermoelastic response of porous beams.The performance,evaluated both in terms of accuracy and computational efficiency,is directly contrasted with high-fidelity finite element models that fully resolve the pores’geometry.Results indicate that the reduced-order representation of the porous microstructure,captured by the synthetic variable-order parameter,offers a robust and accurate representation of the multiscale material architecture that largely outperforms classical approaches based on the concept of average porosity.