Analytical solution to 1D nonlinear elastodynamics with general constitutive laws

On conservation laws in elastodynamics

The objective of this investigation is the establishment of governing balance and conservation laws in elastodynamics. The feature of the approach employed here consists in placing time on the same level as the space coordinates, as is done in the theory of relativity, i.e., pursuing a 4 · 4 formalism. Both the Lagrangian and the Eulerian descriptions of the postulated Lagrangian function are f...

Well-posed Quasi-linear Second-order Hyperbolic Systems with Applications to Nonlinear Elastodynamics and General Relativity

Isogeometric Analysis Applied to Nonlinear Elastodynamics

A numerical investigation is carried out in this work in order to evaluate the computational performance of a numerical model based on isogeometric analysis for applications on geometrically nonlinear elastodynamics. In the FEM (finite element method) practice, it is well known that the Newmark’s method is unconditionally stable for linear structural systems, but this characteristic is frequent...

On the Identification of Nonlinear Constitutive Laws from Indentation Tests

This paper addresses the identification of the parameters of a nonlinear constitutive law from indentation tests. The case of a standard generalized material without work hardening is extensively treated using the adjoint state method. This provides a general framework to perform optimization involving contact conditions and nonlinear material behaviour. A numerical identification is presented ...

Analytical-Approximate Solution for Nonlinear Volterra Integro-Differential Equations

In this work, we conduct a comparative study among the combine Laplace transform and modied Adomian decomposition method (LMADM) and two traditional methods for an analytic and approximate treatment of special type of nonlinear Volterra integro-differential equations of the second kind. The nonlinear part of integro-differential is approximated by Adomian polynomials, and the equation is reduce...