Every day we experiment motion and shape change of continuum media, assembly of different space dimension structures, fluids, solids which exhibit numerous evolutions either particular or general: large deformations, incompressibility, cavitation, contact, surface tension, defects, dislocations,... Stretch and rotation are a common feature of these motions and phenomenons. We base a continuum mechanics predictive theory on stretch and rotation quantified by matrices. In this Chapter the implications of the second principle which requires that the dissipation is positive, as seen in simple experiments, are examined. The constitutive laws are relationships between the internal forces which are abstract quantities, and the state quantities and the quantities which describe the evolution which may be experimented. The derivation of these relationships is simplified by the introduction of potentials: the free energy depending on the state quantities and the pseudo-potential of dissipation depending on the quantities which describe the evolution. The potentials are convex functions due to the monotonicity of the constitutive laws: the greater the action, the greater the effect. Objectivity of the equations established by two different engineers looking at the motion from different frames is satisfied.

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The Constitutive Laws of the System. The Dissipative and Non Dissipative Properties

  • Michel Frémond

摘要

Every day we experiment motion and shape change of continuum media, assembly of different space dimension structures, fluids, solids which exhibit numerous evolutions either particular or general: large deformations, incompressibility, cavitation, contact, surface tension, defects, dislocations,... Stretch and rotation are a common feature of these motions and phenomenons. We base a continuum mechanics predictive theory on stretch and rotation quantified by matrices. In this Chapter the implications of the second principle which requires that the dissipation is positive, as seen in simple experiments, are examined. The constitutive laws are relationships between the internal forces which are abstract quantities, and the state quantities and the quantities which describe the evolution which may be experimented. The derivation of these relationships is simplified by the introduction of potentials: the free energy depending on the state quantities and the pseudo-potential of dissipation depending on the quantities which describe the evolution. The potentials are convex functions due to the monotonicity of the constitutive laws: the greater the action, the greater the effect. Objectivity of the equations established by two different engineers looking at the motion from different frames is satisfied.