A Deformation Model for Dispersely Failing Elastoplastic Unidirectionally Reinforced Composites

A calculation model is proposed for unidirectionally reinforced elastoplastic composites capable of gradually accumulating disperse microdamages under loading. The composite is assumed to be a homogeneous transversely isotropic solid. To describe its elastoplastic behavior, an incremental plasticity theory with a nonlinear combined hardening mechanism is invoked. At each point of the solid, its damage is characterized by a centrally symmetric scalar function on a unit sphere. This function is approximated by a fourth-rank tensor, which is used for describing the degradation of the elastic properties of the solid due to the accumulation of disperse microdamages. It is shown how to determine, using the known experimental data, all material constants appearing in the theoretical relations suggested.     

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.     

有限变形弹性圆杆中的孤波

在同时引入横向惯性和横向剪切应变的情况下,导出了有限变形弹性圆杆的非线性纵向波动方程,方程中包含了二次和三次的非线性项以及由横向剪切与横向惯性导致的两种几何弥散效应．借助Mathematica软件,利用双曲正割函数的有限展开法,对该方程和对应的截断的非线性方程进行求解,得到了非线性波动方程的孤波解,同时给出了这些解存在的必要条件．     

Micromechanical Analysis of Inelastic Deformation of Unidirectional Fibrous Composites under Multiaxial and Shear Loadings

An algorithm is proposed for numerically solving nonlinear 3D problems of micromechanics of a unidirectionally reinforced composite with a regular structure. For the matrix, equations of the deformation theory of plasticity and relations of reduced rigidity in its failure zones are used, whereas the fibers are elastic and indestructible. According to the method of local approximation, fields of microstresses and microstrains are determined in a structural fragment containing nine periodic cells. Boundary conditions of the fragment correspond to an arbitrary combination of longitudinal, transverse, and shear microstresses occurring in the central part of the fragment. The solution to the nonlinear 3D problem is sought by the method of superposition with an iterational refinement based on the successive solution of an antiplane problem and a problem on a generalized plain strain state of the structural segment. Special features of the iteration procedure are considered. The calculated deformation diagrams and ultimate strengths of a unidirectional glass-epoxy composite are presented for several loading trajectories.     

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.