# Renewal of basic laws and principles for polar continuum theories (VI) — Conservation laws of mass and inertia

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## Abstract

The purpose is to reestablish the coupled conservation laws, the local conservation equations and the jump conditions of mass and inertia for polar continuum theories. In this connection the new material derivatives of the deformation gradient, the line element, the surface element and the volume element were derived and the generalized Reynolds transport theorem was presented. Combining, these conservation laws of mass and inertia with the balance laws of momentum, angular momentum and energy derived in our previous papers of this series, a rather complete system of coupled basic laws and principles for polar continuum theories is constituted on the whole. From this system the coupled nonlocal balance equations of mass, inertia, momentum, angular momentum and energy may be obtained by the usual localization.

## Key Words

polar continua coupled transport theorem conservation law of mass and inertia## Chinese Library Classification number

O33## 2000 Mathematics Subject Classification

74A35 74A60## Preview

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## References

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