Numerical Modeling of Tribological Characteristics of Fibrous Polymer Composite Materials

The paper presents a numerical simulation of the contact interaction of fibrous polymer composite materials in a finite element ANSYS package and studies the friction coefficients for cells with wear of 0%, 25%, 50% and 75%. To predict the coefficient of friction of composites it was proposed to use the method of mechanics of composite materials – the method of local approximation. With the help of numerical simulation, the fields of distribution of normal stresses and contact stresses in the contact zone were obtained and the corresponding conclusions were drawn

Introduction to Macroscopic Optimal Design in the Mechanics of Composite Materials and Structures

The main goal of building composite materials and structures is to provide appropriate a priori controlled physico-chemical properties. For this purpose, a strengthening is introduced that can bear loads higher than those borne by isotropic materials, improve creep resistance, etc. Composite materials can be designed in a different fashion to meet specific properties requirements.Nevertheless, it is necessary to be careful about the orientation, placement and sizes of different types of reinforcement. These issues should be solved by optimization, which, however, requires the construction of appropriate models. In the present paper we intend to discuss formulations of kinematic and constitutive relations and the possible application of homogenization methods. Then, 2D relations for multilayered composite plates and cylindrical shells are derived with the use of the Euler–Lagrange equations, through the application of the symbolic package Mathematica. The introduced form of the First-Ply-Failure criteria demonstrates the non-uniqueness in solutions and complications in searching for the global macroscopic optimal solutions. The information presented to readers is enriched by adding selected review papers, surveys and monographs in the area of composite structures.

On the behavior of functionally graded shape memory polymer composites under thermal coupling

Shape memory polymer composites (SMPC), which are a type of stimuli-responsive material, show better mechanical properties than pure shape memory polymers. However, different engineering applications have different requirements for the fiber content of SMPC. For example, some parts of the structure require more fibers to enhance strength, while other parts require fewer fibers to maintain deformability. In order to solve this problem, a functionally graded shape memory polymer composite (FG-SMPC) is proposed in this work. The contents of the fibers for the FG-SMPC can be changed along the geometric dimension of the material, enabling different performance requirements to be met in different parts of the structure. Based on the constitutive model of the SMP and the mechanics of composite materials, the mechanical behaviors of the FG-SMPC under thermal loading are discussed. The results show that such materials exhibit gradient behaviors for both the intensity and shape memory effect with different gradient distributions.

Stable mixed finite elements for linear elasticity with thin inclusions

We consider mechanics of composite materials in which thin inclusions are modeled by lower-dimensional manifolds. By successively applying the dimensional reduction to junctions and intersections within the material, a geometry of hierarchically connected manifolds is formed which we refer to as mixed-dimensional. The governing equations with respect to linear elasticity are then defined on this mixed-dimensional geometry. The resulting system of partial differential equations is also referred to as mixed-dimensional, since functions defined on domains of multiple dimensionalities are considered in a fully coupled manner. With the use of a semi-discrete differential operator, we obtain the variational formulation of this system in terms of both displacements and stresses. The system is then analyzed and shown to be well-posed with respect to appropriately weighted norms. Numerical discretization schemes are proposed using well-known mixed finite elements in all dimensions. The schemes conserve linear momentum locally while relaxing the symmetry condition on the stress tensor. Stability and convergence are shown using a priori error estimates and confirmed numerically.

ЧИСЕЛЬНЕ ВИЗНАЧЕННЯ ЕФЕКТИВНИХ ПРУЖНИХ ХАРАКТЕРИСТИК ТРИВИМІРНОАРМОВАНОГО ВОЛОКНИСТОГО КОМПОЗИЦІЙНОГО МАТЕРІАЛУ

The processes occurring in composite materials are determined by differential equations in partial derivatives with variable coefficients. Most composite materials have a periodic structure, so the coefficients in the equations are rapidly oscillatory periodic functions. The most effective method for studying the stress and deformation field in structures made of composite materials is the method of finite elements, where a nonhomogeneous composite material is replaced by an equivalent homogeneous anisotropic material. To determine averaged characteristics of a composite material with a periodic structure requires a verified methodology allowing to do this. Therefore, the fundamental goal of the mechanics of composite materials is to calculate the effective elastic characteristics of the material. The paper considers the urgent issue of determining effective elastic characteristics of three-dimensional reinforced composite materials based on known elastic properties of fibers and matrix and distribution of reinforcing fibers by volume of composite material.The paper presents the mathematical modeling of the minimum three-dimensional representative volume element based on the specified reinforcement scheme and geometrical dimensions of components. Numerical experiments are performed with the ANSYS software package. A series of numerical experiments simulate six deformation cases: uniaxial tension in the X, Y, Z directions, and shear in the XY, YZ, and XZ planes. Numerical studies of the stress and strain state of the representative volume element of composite material determine the effective elastic constants of equivalent homogeneous material. Two series of calculations are performed with specifying appropriate symmetry and periodicity conditions.The results of the experimental study allow for the verification of the proposed methodology for determining the effective elastic characteristics of three-dimensional reinforced fiber composite materials. The developed numerical methodology enables us to solve the issues of the mechanics of composite materials with the help of modern software packages in the mathematical framework of which the finite element method is used.