Deformation of dispersely failing unidirectional composites

An anisotropic medium is considered in which, upon loading, scattered microdamages accumulate giving rise to nonlinear and residual strains. The damage at a point of the medium is characterized by a scalar function on a unit sphere, referred to as the damage function. This function is approximated by a fourth-rank tensor used for specifying the relation between the increments of strains and stresses. The calculation dependences are presented in detail for a unidirectional composite, which is taken to be a homogeneous transversely isotropic medium. Determination of the unknown constants is illustrated by the example of an actual fiberglass plastic. Institute of Polymer Mechanics, University of Latvia, Riga, LV-1006, Latvia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 5, pp. 561–574, September–October, 1999.     

A Deformation Model of Brittle Failing Composites with Couple-Stresses and Disperse Microdamages

A mathematical model for calculating the relation between macroscopic strains and stresses in brittle failing 3D composites upon their arbitrary deformation is suggested. The model is based on the Voigt scheme in a differential form corrected for the effect of couple-stresses arising in the matrix of composites due to relative rotation of reinforcing fibers. The nonlinearity of composites is derived as a consequence of the progressive accumulation of disperse microdamages in the material under deformation, which lead to degradation of the mechanical properties of the composites. As an example, a ±/2 angle-ply structure is considered, and it is shown how the unknown constants for the materials of such a structure can be found from the uniaxial tension or compression curves.     

Constructing convex limit surfaces in material mechanics

In our previous paper [3], a method of constructing convex surfaces in 6D space of symmetric second-rank tensors by means of deforming the unit sphere S⁵ into a conoidal surface has been considered. Now we extend this method to parabolic surfaces and to the case where the shape of the surfaces depends also on the third tensor invariant. The resulting equations can be utilized for specifying the limit surfaces in the mechanics of isotropic and anisotropic solids. Some examples on approximating data on the experimental strength are presented.Institute of Polymer Mechanics, Latvian Academy of Sciences. Riga, LV-1006 Latvia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 32, No. 3, pp. 339–349, May–June, 1996.     

Description of the elastic deformation and degradation of elastic properties of dispersedly failing isotropic materials

A model is put forward for describing the elastic deformation of a quasi-homogeneous isotropic material capable of accumulating scattered microdamages during loading, which eventually leads to its total failure. The degree of damage of the material at a point is characterized by a centrosymmetric scalar function on the unit sphere, named the damage function, whose values depend on a dimensionless equivalent stress. This function is approximated by a fourth-rank tensor, which is used to construct a constitutive relation between stresses and strains in a differential form. By way of example, the elastic deformation of concrete and the degradation of its linearly elastic properties are described, and the basic three-dimensional sections of the corresponding strength surface are constructed. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 2, pp. 193–208, March–April, 2006.     

Elastic Deformation of Dispersely Failing Unidirectionally Reinforced Composites

A phenomenological model is proposed for describing the elastic deformation of a unidirectionally reinforced composite capable of accumulating scattered microdamages during its loading. The composite is considered as a homogeneous transversely isotropic solid. Its damaged state at every point is characterized by a centrally symmetric scalar function on the unit sphere (the damage function), which is used to account for variations in the elastic properties of the material during its deformation. The damage itself depends on the history of some equivalent strain, for which four simplified variants are suggested. The relation between strains and stresses is defined in a differential form. Dependences are presented for determining all unknown constants from simple mechanical experiments. As an example, an actual unidirectionally reinforced GFRP is considered, for which the main two-dimensional sections of corresponding failure surfaces are also constructed.     

A refined strut model for calculating the elastic constants of highly porous cellular plastics by the method of orientational averaging

A model is presented for calculating the linear elastic constants of high-porosity cellular plastics by orientationally averaging the rigidity tensor of a structural element consisting of an air sheath and a loadcarrying element in the form of a straight strut with a piecewise constant cross section. The load-carrying element can resist the axial and shear loads and bending moments applied to its ends. The nonuniform orientational distribution of the elements is also taken into account. The calculation results obtained are compared with some literature data.