Nodally integrated thermomechanical RKPM: Part II—generalized thermoelasticity and hyperbolic finite-strain thermoplasticity

Michael Hillman, Kuan Chung Lin

Research output: Contribution to journalArticlepeer-review

Abstract

In this two-part paper, a stable and efficient nodally-integrated reproducing kernel particle method (RKPM) approach for solving the governing equations of generalized thermomechanical theories is developed. Part I investigated quadrature in the weak form using classical thermoelasticity as a model problem, and a stabilized and corrected nodal integration was proposed. In this sequel, these methods are developed for generalized thermoelasticity and generalized finite-strain plasticity theories of the hyperbolic type, which are more amenable to explicit time integration than the classical theories. Generalized thermomechanical models yield finite propagation of temperature, with a so-called second sound speed. Since this speed is not well characterized for common engineering materials and environments, equating the elastic wave speed with the second sound speed is investigated to obtain results close to classical thermoelasticity, which also yields a uniform critical time step. Implementation of the proposed nodally integrated RKPM for explicit analysis of finite-strain thermoplasticity is also described in detail. Several benchmark problems are solved to demonstrate the effectiveness of the proposed approach for thermomechanical analysis.

Original languageEnglish (US)
Pages (from-to)821-844
Number of pages24
JournalComputational Mechanics
Volume68
Issue number4
DOIs
StatePublished - Oct 2021

All Science Journal Classification (ASJC) codes

  • Computational Mechanics
  • Ocean Engineering
  • Mechanical Engineering
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

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