The problem of effects superposition in the case of simultaneous loadings, an important issue in mechanical structures design, have been analised. A method for the multiaxial fatigue life prediction was developed. This method was applied to fatigue life calculation in the cases of cyclical loading with: – one block of normal stress and one bloc of shear stress; – successive blocks of normal stresses, simultaneous with successive blocks of shear stresses. The influence of deterioration, of mean stress and residual stress upon the fatigue life is introduced. The theoretical results: – have been compared with experimental results reported in literature; – may be used for design, as well as for experimental data evaluation. Numerical examples show how the obtained theoretical results may be used in practical cases.

"Until now synergistic effect is considered only the case when the final effect of the simultaneous action of several loads is greater than the sum of the partial effects. But the sum refers only to linear behavior of matters. In the general case of nonlinear matter behavior the paper shows that the synergistic effect may be positive (the total effect is greater the sum of the individual effects), negative (the total effect is less the sum of the individual effects) or zero (the total effect is equal the sum of the individual effects). The synergistic effect depends on the matter behavior. Some general examples and practical examples allowed a generalization of the problem of synergistic effect."

The paper develops in the case of mixed-mode fracture: criteria of nonpropagation crack and fracture criteria, for mechanical structures, taking into account the deterioration, namely general relations for the superposition of loadings corresponding to the three fracture modes. It refers to the concepts of stress intensity factor, crack tip opening displacement and J-integral; new fracture criteria taking into account the deterioration, the rate of loading and the scattering of the material characteristics were established. The relations obtained have been compared and verified against experimental data and empirical relations reported in literature. The numerical example allows one to comprehend the practical use of the established relations.

The ability to produce motion based on man-made energy is essential to the civilization. Equally important is the most efficient use of energy to limit the consumption of natural resources as well as the resulting pollution. Consequently, it is necessary to know: - the factors that limit the energy accessibility; - the physical bases of irreversibility, as a premise of ensuring the maximum efficiency. The paper presents two new transdisciplinary principles: - the principle of energy accessibility, which introduces the concepts of degree of energy accessibility, degree of energy inaccessibility caused by natural conditions and degree of energy inaccessibility induced by technical conditions; - the principle of irreversibility which introduces the concept of degree of energy irreversibility in correlation with the physical bases of irreversibility.

"Starting from the concept of deterioration, using the principle of critical energy and considering the nonlinear, power law, behavior of the sample, or of the mechanical structure, there were proposed relations for critical stresses in the case of: – uniaxial static loading with normal stress or with shear stress, or simultaneously with normal and shear stress; – uniaxial cyclic loading with one block of normal stress or one block of shear stress, as well as simultaneous with a block of normal stress and one block of shear stress, taking into account the deterioration due to crack. Failure criteria for cracked mechanical structures, uniaxial statically or cyclically loaded, have been developed. The critical stresses calculated for cracked samples compared with experimental results reported in literature, have shown good agreement between them. "