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

TL;DR

This paper introduces a novel thermodynamically consistent fractional visco-elasto-plastic model with memory-dependent damage for anomalous materials, featuring advanced numerical algorithms for efficient simulation.

Contribution

It develops a new fractional model incorporating damage with a semi-implicit fractional return-mapping algorithm and efficient fractional damage energy computation.

Findings

Fractional orders significantly influence damage evolution.

The model captures the competition between plastic slip and damage energy.

Computational complexity is reduced from O(N^3) to O(N^2) using FFT.

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 $\mathcal{O}(N^3)$ to $\mathcal{O}(N^2)$ 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.