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Soft materials often exhibit a distinctive power-law viscoelastic response arising from broad distribution of time-scales present in their complex internal structure. A promising tool to accurately describe the rheological behaviour of soft…
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 the evolving anomalous rheology to the nonlinear dynamics of…
A rising wave of technologies and instruments are enabling more labs and clinics to make a variety of measurements related to tissue viscoelastic properties. These instruments include elastography imaging scanners, rheological shear…
We develop a fractional return-mapping framework for power-law visco-elasto-plasticity. In our approach, the fractional viscoelasticity is accounted through canonical combinations of Scott-Blair elements to construct a series of well-known…
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…
Understanding the rheological properties of soft biological tissue is a key issue for mechanical systems used in the healthcare field. We propose a simple empirical model using Fractional Dynamics and Exponential Nonlinearity (FDEN) to…
Recently, a non-linear model of viscoelasticity based on Rational Extended Thermodynamics was proposed in [arXiv:2312.05116]. This theory extends the evolution of the viscous stress beyond the linear framework of the Maxwell model to the…
This paper examines the oscillatory behaviour of complex viscoelastic systems with power law-like relaxation behaviour. Specifically, we use the fractional Maxwell model, consisting of a spring and fractional dashpot in series, which…
Understanding the visocoelastic properties of soft biological tissues is important for progress in the field of human healthcare. This study analyzes the viscoelastic properties of soft biological tissues using a fractional dynamics model.…
Anomalous relaxation and diffusion processes have been widely characterized by fractional derivative models, where the definition of the fractional-order derivative remains a historical debate due to the singular memory kernel that…
Mathematical models describing the behavior of viscoelastic materials are often based on evolution equations that measure the change in stress depending on its material parameters such as stiffness, viscosity or relaxation time. In this…
We study the particle-scale dynamics that give rise to bulk flow behaviours of highly concentrated particle-fluid mixtures using discrete element method (DEM) simulations. We utilize boundary conditions of a stress-controlled shear cell and…
The purpose of this paper is twofold: from one side we provide a general survey to the viscoelastic models constructed via fractional calculus and from the other side we intend to analyze the basic fractional models as far as their creep,…
Physically-inspired latent force models offer an interpretable alternative to purely data driven tools for inference in dynamical systems. They carry the structure of differential equations and the flexibility of Gaussian processes,…
We propose a general hybrid physics-informed machine learning framework for modeling nonlinear, history-dependent viscoelastic behavior under multiaxial cyclic loading. The approach is built on a generalized internal state variable-based…
Complex physical systems which exhibit fluid-like behavior are often modeled as non-Newtonian fluids. A crucial element of a non-Newtonian model is the rheology, which relates inner stresses with strain-rates. We propose a framework for…
Traumatic axonal injury occurs when loads experienced on the tissue-scale are transferred to the individual axons. Mechanical characterization of axon deformation especially under dynamic loads however is extremely difficult owing to their…
In this note we analyze a model for a unidirectional unsteady flow of a viscous incompressible fluid with time dependent viscosity. A possible way to take into account such behaviour is to introduce a memory formalism, including thus the…
Polycrystalline materials have a viscoelastic rheology where the strains produced by stresses depend on the timescale of deformation. Energy can be stored elastically within grain interiors and dissipated by a variety of different…
We propose a new material viscoelastic model and mathematical solution to simulate relaxation modulus and viscoelastic response. The model formula of relaxation modulus is extended from sigmoidal function considering nonlinear strain…