Formulations of the elastodynamic equations in anisotropic and multiphasic porous media from the principle of energy conservation

Abstract Elastodynamic equations have been formulated with Newton's second law of motion, Lagrange's equation, or Hamilton's principle for over 150 years. In this work, contrary to classical continuum mechanics, a novel strategic methodology is proposed formulating general mechanical using the energy conservation. First, based on principle, equations, and elastodynamic equation motion are derived in arbitrarily anisotropic multiphasic porous elastic media, first time. Secondly, these all conservation related media. Both formulation results two kinds principles compared validated by each other. The advantages our lie that mechanics directly simple constraint without introducing variational concepts. It easy understand has clear physical meanings. Our unlocks physics essences which consequence Although linear stress–strain constitutive relation considered, can still be used nonlinear dynamical system. also paves an alternative way treating other complex continuous systems broad sense. addition, as application, continuity conditions at various medium interfaces revisited extended approach, explains reflections refractions.