Article
Geochemistry & Geophysics
R. Myhill
Summary: This paper presents a strategy for extending scalar equations of state to model anisotropic materials under nearly hydrostatic conditions. The method involves defining scalar equations and a tensor state variable, and provides expressions to describe their relationship and derive related physical properties.
GEOPHYSICAL JOURNAL INTERNATIONAL
(2022)
Article
Nanoscience & Nanotechnology
C. Paoletti, E. Santecchia, M. Cabibbo, M. Regev, S. Spigarelli
Summary: A physical model was used to study the dependence of minimum creep rate on stress and temperature for ETP copper. The model took into account the role of grain boundaries and the effect of grain growth. Experimental testing confirmed the model's predictions, showing that the grain size and dislocation density have an impact on creep behavior.
MATERIALS SCIENCE AND ENGINEERING A-STRUCTURAL MATERIALS PROPERTIES MICROSTRUCTURE AND PROCESSING
(2022)
Article
Geochemistry & Geophysics
Nicolas Brantut, Leo Petit
Summary: Under compressive stress, rock damage is coupled to slip on microscopic interfaces. Triaxial cyclic loading experiments on Westerly granite show hysteresis in stress-strain behavior explained by slip. Irrecoverable volumetric strain and elastic wave velocity drop with increasing stress and recover over time due to friction along shear interfaces.
GEOPHYSICAL JOURNAL INTERNATIONAL
(2023)
Article
Automation & Control Systems
Ratika Rastogi, O. P. Misra, Rajshree Mishra
Summary: This paper proposes a numerical method that uses Chebyshev polynomials and metaheuristic optimization algorithms to find approximate solutions of differential equations. The effectiveness of the method is demonstrated through graphical comparison and the performance is shown to be better than existing methods based on the Root Mean Square Error (RMSE).
ENGINEERING APPLICATIONS OF ARTIFICIAL INTELLIGENCE
(2023)
Article
Geochemistry & Geophysics
Qiang Xu, Yanghua Wang
Summary: This paper proves the causality and stability of the generalized wave equation by deriving the rate-of-relaxation function, providing a theoretical foundation for the applicability of the equation in seismic simulations. The proposed relationships between the viscoelastic parameter and the constant Q model and between the viscoelastic velocity and the reference velocity improve the accuracy of numerical simulations of the generalized viscoelastic wave equation.
GEOPHYSICAL JOURNAL INTERNATIONAL
(2023)
Article
Mathematics, Applied
Fabio Sozio, Arash Yavari
Summary: This paper presents a geometric field theory for dislocation dynamics and finite plasticity in single crystals. The theory describes the distorted lattice structure using differential forms and the primary fields are the dislocation fields. The evolution equations for the internal variables are derived based on the kinematics of the dislocation forms and coupled with the lattice structure through Orowan's equation. The governing equations are obtained using a two-potential approach and constraints are enforced to formulate the dynamics of dislocations on slip systems.
JOURNAL OF NONLINEAR SCIENCE
(2023)
Article
Mechanics
Larisa V. Kovtanyuk, Galina L. Panchenko
Summary: This article discusses the accumulation of irreversible strains in an elastoviscoplastic material of a thick-walled cylindrical tube under small strains, considering the effects of creep and plastic flow mechanisms. The setting of creep and plastic potentials ensures the continuity in the growth of irreversible strains.
Article
Geochemistry & Geophysics
Luc Illien, Christoph Sens-Schoenfelder, Kuan-Yu Ke
Summary: Ground shaking induced by earthquakes can cause transient changes in seismic velocity, which are important for post-seismic hazard mitigation. However, these changes occur at small timescales and amplitudes that are challenging to link to laboratory experiments. This study investigates whether the estimation of relative seismic velocity changes can be improved using colocated stations according to the ergodic hypothesis.
GEOPHYSICAL JOURNAL INTERNATIONAL
(2023)
Article
Geochemistry & Geophysics
Vladimir Lyakhovsky, Ivan Panteleev, Eyal Shalev, John Browning, Thomas M. Mitchell, David Healy, Philip G. Meredith
Summary: Crustal rocks undergo repeated cycles of stress and can develop highly anisotropic crack distributions. However, the influence of variations in principal stresses on the evolution of anisotropic crack distributions is not well understood. This study presents a newly developed model that considers both anisotropic damage and porosity evolution, and demonstrates a reasonable fit to experimental data.
GEOPHYSICAL JOURNAL INTERNATIONAL
(2022)
Article
Engineering, Mechanical
Li Meng, Wufan Chen
Summary: This study proposes a thermodynamically based model for describing complex creep plasticity behaviors and clarifying the contribution of various creep mechanisms, which is verified using experimental data of Ti-6-4. The model successfully captures primary creep, steady creep, power-law breakdown, and creep cyclic plasticity interactions, demonstrating its validity.
INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES
(2022)
Article
Geochemistry & Geophysics
Guy Simpson
Summary: A dynamic two-dimensional model is used to simulate the emergence and propagation of shear fractures during earthquakes. The deformation consists of long periods of elastic deformation and short periods of localized sliding. The model also shows that most of the elastic strain energy is dissipated as plastic work during earthquakes.
Article
Materials Science, Multidisciplinary
Stefano Spigarelli, Michael Regev, Alberto Santoni, Marcello Cabibbo, Eleonora Santecchia
Summary: Friction Stir Welding (FSW) causes material microstructure variations and changes in mechanical properties. This study investigates the creep response of pure titanium after FSW, finding that FSW samples have lower creep rates and rupture strains.
Article
Geochemistry & Geophysics
Dong Liu, Nicolas Brantut
Summary: The rheology of rocks transitions from a cataclastic brittle behaviour to plastic flow with increasing pressure and temperature. This transition depends on multiple factors including confining stress, fracture toughness, plastic yield stress, and the friction coefficient on pre-existing defects. Goetze's criterion, although successfully describes the brittle-plastic transition for most silicates, may not be universal for all materials.
GEOPHYSICAL JOURNAL INTERNATIONAL
(2023)
Article
Quantum Science & Technology
Hari Krovi
Summary: We present generalized and improved quantum algorithms for inhomogeneous linear and nonlinear ordinary differential equations (ODE) over prior work. Our algorithm for linear ODEs can handle many non-diagonalizable matrices, including singular matrices, and is exponentially faster than previous bounds for certain diagonalizable matrices. We apply our linear ODE algorithm to nonlinear differential equations using Carleman linearization, resulting in an exponential improvement in error dependence and the ability to handle any sparse matrix with a negative log-norm, without the requirement of normality.
Article
Chemistry, Physical
E. K. H. Salje, S. Kustov
Summary: Domain walls and ferroelastic twin boundaries play important roles in the diffusion of chemical dopants and lattice defects. They can serve as templates for chemical structures and carry dopants when moved. However, the activation of this mechanism depends on the external force applied. This article discusses various experimental methods and approaches in this field.
PHYSICAL CHEMISTRY CHEMICAL PHYSICS
(2023)
Article
Mathematics, Applied
Alexander Mielke, Tomas Roubicek
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
(2020)
Article
Mathematics, Applied
Tomas Roubicek, Chrysoula Tsogka
Summary: The study proposes an extension of the two-step staggered time discretization method of linear elastodynamics to systems involving internal variables subjected to non-linear dissipative evolution. A three-step scheme is developed, providing enhancements for problems in continuum mechanics at small strain, including plasticity, viscoelasticity, diffusion in poroelastic media, and damage.
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS
(2021)
Article
Engineering, Multidisciplinary
Stefan Kromer, Tomas Roubicek
JOURNAL OF ELASTICITY
(2020)
Article
Materials Science, Multidisciplinary
Elisa Davoli, Tomas Roubcek, Ulisse Stefanelli
Summary: In this paper, Maxwellian-type rheological models of inelastic effects at large strains are reexamined in relation to inelastic strain gradient theories. An alternative inelastic model of creep type is proposed to prevent spurious hardening effects under large slips, by introducing higher-order energy contribution from elastic strain and plastic strain rate gradients. The combination of Kelvin-Voigt damping and Maxwellian creep results in a Jeffreys-type rheological model, and weak solutions are proven to exist through a Faedo-Galerkin approximation.
MATHEMATICS AND MECHANICS OF SOLIDS
(2021)
Article
Thermodynamics
Tomas Roubicek, Giuseppe Tomassetti
Summary: This model is developed for geophysical applications, considering inelastic strains, damage, porosity, and water diffusion in the lithosphere or crust. It uses concepts of total strain rate gradient and additive splitting while excluding displacement, making it mechanically consistent and analyzable. The energetics of the model are derived to analyze the existence of global weak energy-conserving solutions.
CONTINUUM MECHANICS AND THERMODYNAMICS
(2021)
Article
Geochemistry & Geophysics
T. Roubicek
Summary: The general-purpose model combines concepts from multiple fields and describes various geological phenomena while satisfying fundamental laws such as mass conservation and energy conservation.
GEOPHYSICAL JOURNAL INTERNATIONAL
(2021)
Article
Mathematics, Applied
Tomas Roubicek
Summary: This study investigates the isothermal quasistatic hardening-free plasticity problem at large strains. The model is reformulated in terms of rates and the plastic distortion is completely eliminated. The existence and regularity of weak solutions are proved using a regularization combined with Galerkin approximation. The study also considers rate-dependent plasticity and includes the Jeffreys' viscoelastic rheology and Kelvin-Voigt rheology.
JOURNAL OF NONLINEAR SCIENCE
(2022)
Article
Mathematics, Applied
Tomas Roubicek
Summary: This article formulates isothermal visco-elastodynamics in the Kelvin-Voigt rheology using velocity and deformation gradient in spatial Eulerian coordinates. The model allows a generally nonconvex stored energy and a nonlinear 2nd-grade nonsimple viscosity for regular velocity field. The assumption of small volume variations simplifies the analysis and uses the concept of semi-compressible materials. The existence of weak solutions is proved using the Galerkin method and a suitable regularization based on smooth velocity fields.
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
(2022)
Article
Materials Science, Multidisciplinary
Tomas Roubicek
Summary: A thermodynamically consistent model for soft deformable viscoelastic magnets is proposed in this paper, formulated in actual space coordinates. The model considers the possibility of a ferro-paramagnetic-type or ferri-antiferromagnetic transition using Landau phase-transition theory, as well as mechanical melting or solidification, which is motivated and applicable to paleomagnetism in rocks in Earth's crust and to rock-magma transition.
MATHEMATICS AND MECHANICS OF SOLIDS
(2023)
Article
Mathematics, Applied
Tomas Roubicek
Summary: This article extends the classical Stefan problem by considering mechanical effects during solid-liquid phase transition. It uses the Eulerian description with convective and Zaremba-Jaumann corotational time derivatives, linearized through the additive Green-Naghdi's decomposition in objective rates. The liquid phase is modeled as a viscoelastic fluid, while the solid phase incorporates creep and rupture via the Jeffreys viscoelastic rheology and the phase-field model for slightly compressible materials. The L-1 theory is applied to the heat equation in the Stefan problem, allowing for kinetic superheating/supercooling effects. A rigorous proof of weak solution existence is provided for cases of incomplete melting using a time discretization approximation.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Tomas Roubicek
Summary: This article investigates the mechanical interaction of compressible viscoelastic fluids with viscoelastic solids in Kelvin-Voigt rheology using the concept of higher-order viscosity. The no-slip contact between fluid and solid is considered, and a monolithic formulation of the fluid-structure interaction problem is achieved using the Eulerian-frame return-mapping technique. The existence and regularity of weak solutions are proven through a Schauder fixed-point argument combined with a suitable regularization.
JOURNAL OF MATHEMATICAL FLUID MECHANICS
(2023)
Article
Mathematics, Applied
Barbora Benesova, Miroslav Frost, Lukas Kaderavek, Tomas Roubicek, Petr Sedlak
Summary: This study enhances a phenomenological model for polycrystalline NiTi shape-memory alloys with refined dissipation function by incorporating thermomechanical coupling, and rigorously analyzes it in terms of weak solution existence, numerical stability, and convergence through staggered time discretization. The model is verified through one-dimensional computational simulations and compared with real laboratory experiments on a NiTi wire, demonstrating its validity.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S
(2021)
Article
Mathematics, Applied
Tomas Roubicek
Summary: A new concept of semi-compressible fluids is introduced for slightly compressible visco-elastic fluids, with physically consistent fully Eulerian models devised to describe the characteristics of these fluids.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S
(2021)
Article
Automation & Control Systems
Tomas Roubicek
Summary: Nonconvex optimal control problems governed by evolution problems in infinite-dimensional spaces are addressed by extending the control on a convex compactification to ensure existence of solutions and simplify analysis. A compromise convex compactification is devised using classical techniques for Young measures and Choquet theory, applied to parabolic optimal control problems for existence and optimality conditions.
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
(2021)
Article
Mathematics, Applied
Tomas Roubicek
Summary: The diffusion driven by the gradient of the chemical potential in deforming continua at large strains is analyzed, considering Fick/Darcy law, capillarity, and various methods for static and dynamic situations. The presence of capillarity leads to new terms like Korteweg-like stress and analytical complexities. Other models with gradients at an actual configuration allow for similar analysis.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S
(2021)
