Thermodynamics of viscoelastic solids, its Eulerian formulation, and existence of weak solutions
DOI10.1007/s00033-023-02175-7arXiv2203.06080OpenAlexW4392190298MaRDI QIDQ6131411
Publication date: 5 April 2024
Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2203.06080
elastodynamicsweak solutionslarge strainsthermal couplingKelvin-Voigt viscoelasticitymultipolar continuasemi-Galerkin discretization
Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with fluid mechanics (35Q35) Nonlinear elasticity (74B20) Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) (74F10) Nonlinear waves in solid mechanics (74J30) Soil and rock mechanics (74L10) Viscoelastic fluids (76A10) Nonsimple materials (74A30) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Weak solutions to PDEs (35D30) Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics (76N10) Geophysical solid mechanics (74L05) PDEs in connection with mechanics of deformable solids (35Q74) PDEs in connection with classical thermodynamics and heat transfer (35Q79) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Diffusive and convective heat and mass transfer, heat flow (80A19) Transport equations (35Q49)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Continuum mechanics through the twentieth century. A concise historical perspective
- Incompressible bipolar and non-Newtonian viscous fluid flow
- Global solutions to repulsive Hookean elastodynamics
- The Lagrange multipliers and hyperstress constraint reactions in incompressible multipolar elasticity theory
- Global well-posedness for compressible viscoelastic fluids near equilibrium
- Relative entropy for hyperbolic-parabolic systems and application to the constitutive theory of thermoviscoelasticity
- Thermoviscoelasticity in Kelvin-Voigt rheology at large strains
- A discrete variational scheme for isentropic processes in polyconvex thermoelasticity
- Tractions, balances, and boundary conditions for nonsimple materials with application to liquid flow at small-length scales
- Nonlinear elliptic and parabolic equations involving measure data
- Global solutions for incompressible viscoelastic fluids
- Quasilinear equations for viscoelasticity of strain-rate type
- Hypertractions and hyperstresses convey the same mechanical information
- One-dimensional variational problems whose minimizers do not satisfy the Euler-Lagrange equation
- Elastic materials with couple-stresses
- Global solution to the compressible isothermal multipolar fluid
- Global solution to the incompressible viscous-multipolar material problem
- Well-posed quasi-linear second-order hyperbolic systems with applications to nonlinear elastodynamics and general relativity
- Physically unacceptable viscous stresses
- Nonlinear parabolic equations with measure data
- The Lavrentiev gap phenomenon in nonlinear elasticity
- Weak solutions for a class of nonlinear systems of viscoelasticity
- Quasilinear hyperbolic systems with involutions
- A first order hyperbolic framework for large strain computational solid dynamics. III: Thermo-elasticity
- On Hamiltonian continuum mechanics
- Visco-elastodynamics at large strains Eulerian
- Quasistatic hypoplasticity at large strains Eulerian
- Global well-posedness for a class of fourth-order nonlinear strongly damped wave equations
- Loss of regularity for the continuity equation with non-Lipschitz velocity field
- Weak-strong uniqueness of dissipative measure-valued solutions for polyconvex elastodynamics
- Dynamics of charged elastic bodies under diffusion at large strains
- Multipolar viscoelastic materials and the symmetry of the coefficients of viscosity
- On the Navier-Stokes equations with temperature-dependent transport coefficients
- Micro-structure in linear elasticity
- Thermodynamically consistent nonlinear model of elastoplastic Maxwell medium
- Some Open Problems in Elasticity
- Finite thermoelastoplasticity and creep under small elastic strains
- Convergence of a Finite Element-Based Space-Time Discretization in Elastodynamics
- Young Measure Solutions for Nonconvex Elastodynamics
- Principles of Continuum Mechanics
- Time-Space Discretization of the Nonlinear Hyperbolic Systemutt= div (\sigma(Du)+Dut)
- Mathematical Methods in Continuum Mechanics of Solids
- Young-Measure approximations for elastodynamics with non-monotone stress-strain relations
- An Approach to Nonlinear Viscoelasticity via Metric Gradient Flows
- Nonlinear partial differential equations with applications
- A variational approximation scheme for three-dimensional elastodynamics with polyconvex energy
- An Eulerian description of fluids containing viscoelastic particles
- Existence and uniqueness for a viscoelastic Kelvin–Voigt model with nonconvex stored energy
- Viscoelastodynamics of Swelling Porous Solids at Large Strains by an Eulerian Approach
