48 citations · 215 across the 26 of their papers we have counts for
13 papers · 1 filter
A General Return-Mapping Framework for Fractional Visco-Elasto-Plasticity
Jorge L. Suzuki, Maryam Naghibolhosseini, Mohsen Zayernouri
We develop a fractional return-mapping framework for power-law visco-elasto-plasticity. In our approach, the fractional viscoelasticity is accounted through canonical combinations…
A Data-Driven Memory-Dependent Modeling Framework for Anomalous Rheology: Application to Urinary Bladder Tissue
Jorge L. Suzuki, Tyler G. Tuttle, Sara Roccabianca +1
We introduce a data-driven fractional modeling framework aimed at complex materials, and particularly bio-tissues. From multi-step relaxation experiments of distinct anatomical loc…
Anomalous Nonlinear Dynamics Behavior of Fractional Viscoelastic Structures
Jorge L. Suzuki, Pegah Varghaei, Ehsan Kharazmi +1
Fractional models and their parameters are sensitive to changes in the intrinsic micro-structures of anomalous materials. We investigate how such physics-informed models propagate…
A Thermodynamically Consistent Fractional Visco-Elasto-Plastic Model with Memory-Dependent Damage for Anomalous Materials
Jorge L. Suzuki, Yongtao Zhou, Marta D'Elia +1
We develop a thermodynamically consistent, fractional visco-elasto-plastic model coupled with damage for anomalous materials. The model utilizes Scott-Blair rheological elements fo…
Fast IMEX Time Integration of Nonlinear Stiff Fractional Differential Equations
Yongtao Zhou, Jorge L. Suzuki, Chengjian Zhang +1
Efficient long-time integration of nonlinear fractional differential equations is significantly challenging due to the integro-differential nature of the fractional operators. In a…
Vibration Analysis of Geometrically Nonlinear and Fractional Viscoelastic Cantilever Beams
Pegah Varghaei, Ehsan Kharazmi, Jorge L. Suzuki +1
We investigate the nonlinear vibration of a fractional viscoelastic cantilever beam, subject to base excitation, where the viscoelasticity takes the general form of a distributed-o…
An Automated Singularity-Capturing Scheme for Fractional Differential Equations
Jorge L. Suzuki, Mohsen Zayernouri
Solutions to fractional models inherently exhibit non-smooth behavior, which significantly deteriorates the accuracy and therefore efficiency of existing numerical methods. We deve…
Fractional Sensitivity Equation Method: Applications to Fractional Model Construction
Ehsan Kharazmi, Mohsen Zayernouri
Fractional differential equations provide a tractable mathematical framework to describe anomalous behavior in complex physical systems, yet they introduce new sensitive model para…
Operator-Based Uncertainty Quantification of Stochastic Fractional PDEs
Ehsan Kharazmi, Mohsen Zayernouri
Fractional calculus provides a rigorous mathematical framework to describe anomalous stochastic processes by generalizing the notion of classical differential equations to their fr…
Petrov-Galerkin Method for Fully Distributed-Order Fractional Partial Differential Equations
Mehdi Samiee, Ehsan Kharazmi, Mohsen Zayernouri +1
Distributed-order PDEs are tractable mathematical models for complex multiscaling anomalous transport, where derivative orders are distributed over a range of values. We develop a…
A Petrov-Galerkin Spectral Element Method for Fractional Elliptic Problems
Ehsan Kharazmi, Mohsen Zayernouri, George Em Karniadakis
We develop a new -continuous Petrov-Galerkin spectral element method for one-dimensional fractional elliptic problems of the form ${}_{0}{\mathcal{D}}_{x}^α u(x) - λu(x) =…
A Tunably-Accurate Laguerre Petrov-Galerkin Spectral Method for Multi-Term Fractional Differential Equations on the Half Line
Anna Lischke, Mohsen Zayernouri, George Em Karniadakis
We present a new tunably-accurate Laguerre Petrov-Galerkin spectral method for solving linear multi-term fractional initial value problems with derivative orders at most one and co…
Petrov-Galerkin and Spectral Collocation Methods for distributed Order Differential Equations
Ehsan Kharazmi, Mohsen Zayernouri, George Em Karniadakis
Distributed order fractional operators offer a rigorous tool for mathematical modelling of multi-physics phenomena, where the differential orders are distributed over a range of va…