Fundamental Principles of Material Response

The constitutive law is fundamentally determined for each material, and it gives an empirical rule. To establish constitutive laws the following physical conditions are required  

Principle of determinism The stress is determined by the history of the motion undergone by the body. 

Principle of local action The stress at a point is not influenced by far-field motions. Principle of frame indifference The response of a material must be described under the frame indifference (see Sect. 2.2.2). 

The principle of frame indifference is sometimes called objectivity. 

Let a stress a be described as a function of a material point x in the deformed body at time t  

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