Thermoelastic waves without energy dissipation in an unbounded body with a spherical cavity.
Thermoelasticity of Dipolar Bodies with Internal State Variables
Thermoelasticity without energy dissipation for initially stressed bodies.
Thermomechanical constraints and constitutive formulations in thermoelasticity.
Thermo-viscoelastic Rayleigh waves under the influence of couple-stress and gravity.
Thermo-visco-elasticity with rate-independent plasticity in isotropic materials undergoing thermal expansion
We consider a viscoelastic solid in Kelvin-Voigt rheology exhibiting also plasticity with hardening and coupled with heat-transfer through dissipative heat production by viscoplastic effects and through thermal expansion and corresponding adiabatic effects. Numerical discretization of the thermodynamically consistent model is proposed by implicit time discretization, suitable regularization, and finite elements in space. Fine a-priori estimates are derived, and convergence is proved by careful successive...
Thermo-visco-elasticity with rate-independent plasticity in isotropic materials undergoing thermal expansion*
We consider a viscoelastic solid in Kelvin-Voigt rheology exhibiting also plasticity with hardening and coupled with heat-transfer through dissipative heat production by viscoplastic effects and through thermal expansion and corresponding adiabatic effects. Numerical discretization of the thermodynamically consistent model is proposed by implicit time discretization, suitable regularization, and finite elements in space. Fine a-priori estimates are derived, and convergence is proved by careful...
Thick obstacle problems with dynamic adhesive contact
In this work, we consider dynamic frictionless contact with adhesion between a viscoelastic body of the Kelvin-Voigt type and a stationary rigid obstacle, based on the Signorini's contact conditions. Including the adhesion processes modeled by the bonding field, a new version of energy function is defined. We use the energy function to derive a new form of energy balance which is supported by numerical results. Employing the time-discretization, we establish a numerical formulation and investigate...
Thin circular plate uniformly loaded over a concentric elliptic path and supported on columns.
Thin inclusions in linear elasticity: a variational approach.
Three models of non periodic fibrous materials obtained by homogenization
Three-dimensional boundary value problems of elastothermodiffusion with mixed boundary conditions.
Three-dimensional mathematical problems of thermoelasticity of anisotropic bodies. II.
Three-dimensional mathematical problems of thermoelasticity of anisotropic bodies. I.
Time domain simulation of a piano. Part 1: model description
The purpose of this study is the time domain modeling of a piano. We aim at explaining the vibratory and acoustical behavior of the piano, by taking into account the main elements that contribute to sound production. The soundboard is modeled as a bidimensional thick, orthotropic, heterogeneous, frequency dependent damped plate, using Reissner Mindlin equations. The vibroacoustics equations allow the soundboard to radiate into the surrounding air, in which we wish to compute the complete acoustical...
Time splitting for wave equations in random media
Numerical simulation of high frequency waves in highly heterogeneous media is a challenging problem. Resolving the fine structure of the wave field typically requires extremely small time steps and spatial meshes. We show that capturing macroscopic quantities of the wave field, such as the wave energy density, is achievable with much coarser discretizations. We obtain such a result using a time splitting algorithm that solves separately and successively propagation and scattering in the simplified...
Time splitting for wave equations in random media
Numerical simulation of high frequency waves in highly heterogeneous media is a challenging problem. Resolving the fine structure of the wave field typically requires extremely small time steps and spatial meshes. We show that capturing macroscopic quantities of the wave field, such as the wave energy density, is achievable with much coarser discretizations. We obtain such a result using a time splitting algorithm that solves separately and successively propagation and scattering in the...
Time-dependent invariant regions for parabolic systems related to one- dimensional nonlinear elasticity
A parabolic system arisng as a viscosity regularization of the quasilinear one-dimensional telegraph equation is considered. The existence of - a priori estimates, independent of viscosity, is shown. The results are achieved by means of generalized invariant regions.
Time-Fractional Derivatives in Relaxation Processes: A Tutorial Survey
2000 Mathematics Subject Classification: 26A33, 33E12, 33C60, 44A10, 45K05, 74D05,The aim of this tutorial survey is to revisit the basic theory of relaxation processes governed by linear differential equations of fractional order. The fractional derivatives are intended both in the Rieamann-Liouville sense and in the Caputo sense. After giving a necessary outline of the classica theory of linear viscoelasticity, we contrast these two types of fractiona derivatives in their ability to take into...
Time-periodic solutions of a quasilinear beam equation via accelerated convergence methods
The author investigates time-periodic solutions of the quasilinear beam equation with the help of accelerated convergence methods. Using the Newton iteration scheme, the problem is approximated by a sequence of linear equations solved via the Galerkin method. The derivatiove loss inherent to this kind of problems is compensated by taking advantage of smoothing operators.