A Thermodynamically Consistent Fractional Visco-Elasto-Plastic Model with Memory-Dependent Damage for Anomalous Materials

Abstract

We develop a thermodynamically consistent, fractional visco-elasto-plastic model coupled with damage for anomalous materials. The model utilizes Scott-Blair rheological elements for both visco-elastic/plastic parts. The constitutive equations are obtained through Helmholtz free-energy potentials for Scott-Blair elements, together with a memory-dependent fractional yield function and dissipation inequalities. A memory-dependent Lemaitre-type damage is introduced through fractional damage energy release rates. For time-fractional integration of the resulting nonlinear system of equations, we develop a first-order semi-implicit fractional return-mapping algorithm. We also develop a finite-difference discretization for the fractional damage energy release rate, which results into Hankel-type matrix-vector operations for each time-step, allowing us to reduce the computational complexity from O(N 3 ) to O(N 2 ) through the use of Fast Fourier Transforms. Our numerical results demonstrate that the fractional orders for visco-elasto-plasticity play a crucial role in damage evolution, due to the competition between the anomalous plastic slip and bulk damage energy release rates.

Data-Driven Failure Prediction in Brittle Materials: A Phase-Field Based Machine Learning Framework

“…Future works will focus on addressing the noted issues. Besides, the focus of future studies will be on the evaluation of the developed framework with the inclusion of plasticity/visco-elasto-plasticity [45,46,50,48] in the damage and fatigue phase-field model, combined with efficient and stable long time integration schemes [47,56].…”

Anomalous Features in Internal Cylinder Flow Instabilities subject to Uncertain Rotational Effects

“…Uncertainty in modeling procedure and also inaccuracy of the measured data are two main factors in arising epistemic uncertainty. The uncertainty in modeling could be the result of a variety of possibilities including the effects of geometry [30][31][32][33][34] , constitutive laws [35][36][37][38][39][40][41][42][43][44][45][46][47][48] , rheological models [49][50][51] , low-fidelity and reduced-order modeling [52][53][54][55][56][57][58][59][60][61][62][63][64] , and random forcing sources in addition to the random field boundary/initial conditions [65][66][67][68][69][70][71] . In the current work, we seek to fill a gap in the rich literature of investigating flow instabilities inside rotating flow systems by emphasizing on the stochastic modeling of the fluid dynamics and later focusing on the anomalies in the anomalous transport features of such system through statistical and scaling analysis of the response.…”