Nonlinear wave propagation in damaged hysteretic materials using a frequency domain-based PM space formulation

Ettore Barbieri, Michele Meo, Umberto Polimeno

Research output: Contribution to journalArticlepeer-review

26 Citations (SciVal)


In this work, a new and simple numerical approach to simulate nonlinear wave propagation in purely hysteretic elastic solids is presented. Conversely to classical time discretization method, which fully integrates the nonlinear equation of motion, this method utilizes a first-order approximation of the nonlinear strain in order to separate linear and nonlinear contributions. The problem for the nonlinear displacements is then posed as a linear one in which the solid is enforced with nonlinear forces derived from the linear strain. in this manner, a frequency analysis can be easily conducted, leading directly to a well-known frequency spectrum for the nonlinear strain. A mesoscale approach known as Preisach-Mayergoyz space (PM space) is used for the chacterization of the nonlinear elastic region of the solid. A meshless element free Galerkin method is implemented for the discretized equations of motion. Nevertheless, a mesh-based method can be still used as well without loss of generality. Results are presented for bidimensional isotropic plates both in plane stress and in plane strain subjected to harmonic monotone excitation.
Original languageEnglish
Pages (from-to)165-180
Number of pages16
JournalInternational Journal of Solids and Structures
Issue number1
Publication statusPublished - 1 Jan 2009


  • Nonlinear wave propagation
  • Meshless
  • Multiscale
  • PM space


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