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

Technical Report ·
DOI:https://doi.org/10.2172/1575111· OSTI ID:1575111
 [1];  [2];  [3];  [1]
  1. Michigan State University, East Lansing, MI (United States)
  2. University of Science and Technology, Wuhan (China); Michigan State University, East Lansing, MI (United States)
  3. Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
+ Show Author Affiliations

We develop a thermodynamically consistent, fractional visco-elastoplastic 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(N3) to O(N2) 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.

Research Organization:
Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA)
DOE Contract Number:
AC04-94AL85000; NA0003525
OSTI ID:
1575111
Report Number(s):
SAND--2019-14071R; 681585
Country of Publication:
United States
Language:
English

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Related Subjects

36 MATERIALS SCIENCE
Hankel matrices
fractional mechanical dissipation
fractional return-mapping algorithms
memory-dependent damage
memory-dependent free-energy density