One-dimensional nonlocal elastodynamics: constitutive modeling, hyperbolicity, Riemann invariants, characteristic directions

Integro-partial differential equations (45K05) Nonlinear elasticity (74B20) Singularities, blow-up, stress concentrations for dynamical problems in solid mechanics (74H35) PDEs in connection with mechanics of deformable solids (35Q74) First-order hyperbolic equations (35L02)

Cites Work

Title not available (Why is that?)
Title not available (Why is that?)
Title not available (Why is that?)
Title not available (Why is that?)
Blow-up and global existence for a general class of nonlocal nonlinear coupled wave equations
Weak solutions of a class of quasilinear hyperbolic integro-differential equations describing viscoelastic materials
The Cauchy problem for a one-dimensional nonlinear elastic peridynamic model
The Cauchy problem in one-dimensional nonlinear viscoelasticity
Fading memory
Development of singularities in the motion of materials with fading memory
Coercive estimates and existence of solutions for a model of one- dimensional viscoelasticity with a non-integrable memory function
Equilibrium of bars
Symmetry group classification for one-dimensional elastodynamics problems in nonlocal elasticity
Nonlocal elasticity in nanobeams: the stress-driven integral model
Closed form solution for a nonlocal elastic bar in tension.
On the symmetry group properties of equations of nonlocal elasticity
The regularity properties and blow-up of the solutions for nonlocal general wave equations
On the convergence of the nonlocal nonlinear model to the classical elasticity equation
Analytical solution to 1D nonlinear elastodynamics with general constitutive laws
Iterative methods for nonlocal elasticity problems
Dirichlet's principle and wellposedness of solutions for a nonlocal \(p\)-Laplacian system
On the well-posedness of the linear peridynamic model and its convergence towards the Navier equation of linear elasticity
Elasticity theory of materials with long range cohesive forces
On the thermodynamics of system with nonlocality
Nonlocal continuum mechanics
Nonlocal polar elastic continua
Linear theory of nonlocal elasticity and dispersion of plane waves
Measure solutions for non-local interaction PDEs with two species
Results on Nonlocal Boundary Value Problems
A class of integro-differential equations incorporating nonlinear and nonlocal damping with applications in nonlinear elastodynamics: Existence via time discretization
SYSTEMS OF HYPERBOLIC CONSERVATION LAWS WITH MEMORY
Global Existence and Asymptotic Stability for a Semilinear Hyperbolic Volterra Equation with Large Initial Data
Delelopment of singularities of smooth solutions of nonlinear hyperbolic volterra equations
Energy methods for nonlinear hyperbolic volterra integrodifferential equations
A model for one-dimensional, nonlinear viscoelasticity
Breakdown of smooth solutions in dissipative nonlinear hyperbolic equations
Monotonic, completely monotonic, and exponential relaxation functions in linear viscoelasticity
Measure-valued and weak solutions to the nonlinear peridynamic model in nonlocal elastodynamics
Existence results for some nonlocal problems
Global existence and blow-up for a class of nonlocal nonlinear Cauchy problems arising in elasticity
Hyperbolic Conservation Laws in Continuum Physics
Nonlocal elasticity and related variational principles
A generalized integro-differential theory of nonlocal elasticity of \(n\)-Helmholtz type. II: Boundary-value problems in the one-dimensional case
On formulation of nonlocal elasticity problems

This page was built for publication: One-dimensional nonlocal elastodynamics: constitutive modeling, hyperbolicity, Riemann invariants, characteristic directions

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6660998)