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

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...

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Bibliographic Details
Published in:arXiv.org 2019-11
Main Authors: Suzuki, Jorge L, Zhou, Yongtao, D'Elia, Marta, Zayernouri, Mohsen
Format: Article
Language:English
Subjects:
Algorithms
Constitutive equations
Constitutive relationships
Damage
Elastoplasticity
Energy dissipation
Energy release rate
Fast Fourier transformations
Finite difference method
Fourier transforms
Mapping
Mathematical analysis
Mathematical models
Matrix algebra
Matrix methods
Nonlinear equations
Nonlinear systems
Plastic memory
Rheological properties
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Summary: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.
ISSN:2331-8422