Recent advances in mathematical modelling of materials behavior. (English) Zbl 0723.73043
Summary: This paper gives a short survey about some recent advances in mathematical modelling of materials behavior. The mechanical behavior of anisotropic solids requires a suitable mathematical modelling. The properties of tensor functions with several argument tensors constitute a rational basis for a consistent mathematical modelling of complex material behavior.
This paper presents principles, methods, and recent successful applications of tensor functions in solid mechanics. The rules of specifying irreducible sets of tensor invariants and tensor generators for material tensors of rank two and four are discussed.
Furthermore, it is very important to determine the scalar coefficients in constitutive equations as functions of the integrity basis and experimental data. It has been pointed out in detail that these coefficients can be determined by using tensorial interpolation methods. Some examples for practical use have been discussed.
This paper presents principles, methods, and recent successful applications of tensor functions in solid mechanics. The rules of specifying irreducible sets of tensor invariants and tensor generators for material tensors of rank two and four are discussed.
Furthermore, it is very important to determine the scalar coefficients in constitutive equations as functions of the integrity basis and experimental data. It has been pointed out in detail that these coefficients can be determined by using tensorial interpolation methods. Some examples for practical use have been discussed.
MSC:
| 74C99 | Plastic materials, materials of stress-rate and internal-variable type |
| 74A20 | Theory of constitutive functions in solid mechanics |
| 74E10 | Anisotropy in solid mechanics |
Keywords:
creep; damage; failure criteria; survey; principles; successful applications of tensor functions; irreducible sets of tensor invariants; tensor generators; material tensors of rank two and four; tensorial interpolation methodsReferences:
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