Open AccessOn continuum damage mechanics
Author(s) -
Kari Santaoja
Publication year - 2019
Publication title -
rakenteiden mekaniikka
Language(s) - English
Resource type - Journals
eISSN - 1797-5301
pISSN - 0783-6104
DOI - 10.23998/rm.76025
Subject(s) - strain rate tensor , continuum mechanics , peridynamics , hooke's law , tensor (intrinsic definition) , cartesian tensor , infinitesimal strain theory , viscous stress tensor , symmetric tensor , equivalence (formal languages) , cauchy stress tensor , tensor field , damage mechanics , physics , classical mechanics , tensor density , mathematics , mathematical analysis , geometry , exact solutions in general relativity , finite element method , pure mathematics , thermodynamics
A material containing spherical microvoids with a Hookean matrix response was shown to take the appearance usually applied in continuum damage mechanics. However, the commonly used variable damage D was replaced with the void volume fraction f , which has a clear physical meaning, and the elastic strain tensor \Bold {ε}^e with the damage-elastic strain tensor \Bold {ε}^{de}. The postulate of strain equivalence with the effective stress concept was reformulated and applied to a case where the response of the matrix obeys Hooke’s law. In contrast to many other studies, in the derived relation between the effective stress tensor \Bold {\Tilde{σ}} and the stress tensor \Bold {σ}, the tensor \Bold {\Tilde{σ}} is symmetric. A uniaxial bar model was introduce for clarifying the derived results. Other candidates for damage were demonstrated by studying the effect of carbide coarsening on creep rate.