Mechanics of deformable bodies and structures characterized by non-smooth constitutive laws

Aim of project
The aim of the project is to systematize and develop the branch of mechanics dealing with the application of nonsmooth analysis methods for the problems of strain and stress description of engineering structures made of materials of nonclassical constitutive properties. Moreover, we anticipate to work out the methods of calculation of such structures using computer systems with designed special procedures defi ning non-classical material properties.

The methods of non-smooth mechanics are indispensable for mathematical formulation of static and dynamic problems of engineering structures made of non-classical materials described by non-diff erentiable functionals or variational inequalities. The materials belonging to this group are: shape memory alloys (SMAs), locking materials, plastics and various visco- elasto- -plastic materials.

It will be proved that the benefi t of using non-smooth analysis methods is that we can formulate and analyze a large class of scientific applications in a unifi ed and sometimes easier manner. On the other hand, the description of classical non-linear problems of continuum mechanics with the use of non-smooth analysis methods, gives the possibility to generalize the formulation. Our objective is also to work out the method of computer aided calculations supported by graphical visualization of results.

Expected results
The results of the investigations may be summarized
as follows:
To work out the procedure of mathematical formulation of static and dynamic problems of materials and structures involving non-smooth constitutive properties;

To work out the methods of solving the above mentioned problems using computer systems with special procedures designed by the authors;

Presentation of examples exhibiting the application of nonsmooth mechanics methods for both civil engineering and machinery structures subjected to various types of loadings (in particular impact loadings).