scholarly journals Estimation of effective elastic moduli of random structure composites by the method of fundamental solutions

2016 ◽  
Vol 62 ◽  
pp. 13-21 ◽  
Author(s):  
Valeriy A. Buryachenko
Keyword(s):  
Elastic Moduli ◽  
Fundamental Solutions ◽  
Method Of Fundamental Solutions ◽  
Random Structure ◽  
Effective Elastic Moduli

Method of Fundamental Solutions in Micromechanics of Random Structure Linear Elastic Composites

2016 ◽  
Author(s):  
Valeriy A. Buryachenko
Keyword(s):  
Integral Equation ◽  
Meshfree Method ◽  
Fundamental Solutions ◽  
Effective Field ◽  
Method Of Fundamental Solutions ◽  
Random Structure ◽  
Linear Elastic ◽  
General Integral ◽  
Homogeneous Matrix ◽  
Linear Thermoelasticity

One considers a linear elastic composite material (CM, [1]), which consists of a homogeneous matrix containing the random set of heterogeneities. An operator form of the general integral equation (GIE, [2–6]) connecting the stress and strain fields in the point being considered and the surrounding points are obtained for the random fields of inclusions in the infinite media. The new GIE is presented in a general form of perturbations introduced by the heterogeneities and defined at the inclusion interface by the unknown fields of both the displacement and traction. The method of obtaining of the GIE is based on a centering procedure of subtraction from both sides of a new initial integral equation their statistical averages obtained without any auxiliary assumptions such as the effective field hypothesis (EFH), which is implicitly exploited in the known centering methods. One proves the absolute convergence of the proposed GIEs, and some particular cases, asymptotic representations, and simplifications of proposed GIEs are presented for the particular constitutive equations of linear thermoelasticity. In particular, we use a meshfree method [7] based on fundamental solutions basis functions for a transmission problem in linear elasticity. Numerical results were obtained for 2D CMs reinforced by noncanonical inclusions.

Variational principles and generalized Hill’s bounds in micromechanics of linear peridynamic random structure composites

2019 ◽  
Vol 25 (3) ◽  
pp. 682-704 ◽  
Author(s):  
Valeriy A Buryachenko
Keyword(s):  
Elastic Moduli ◽  
Variational Principles ◽  
Virtual Work ◽  
Static Problem ◽  
Material Behavior ◽  
Reciprocal Theorem ◽  
Random Structure ◽  
Effective Elastic Moduli ◽  
Peridynamic Model ◽  
Non Local

We consider a static problem for statistically homogeneous matrix linear peridynamic composite materials (CMs). The basic feature of the peridynamic model considered is a continuum description of a material behavior as the integrated non-local force interactions between infinitesimal particles. In contrast to these classical local and non-local theories, the peridynamic equation of motion introduced by Silling ( J Mech Phys Solids 2000; 48: 175–209) is free of any spatial derivatives of displacement. Estimation of effective moduli of peridynamic CMs is performed by generalization of some methods used in locally elastic micromechanics. Namely, the admissible displacement and force fields are defined. The theorem of work and energy, Betti’s reciprocal theorem, and the theorem of virtual work are proved. Principles of minimum of both potential energy and complimentary energy are generalized. The strain energy bounds are estimated for both the displacement and force homogeneous volumetric boundary conditions. The classical representations of effective elastic moduli through the mechanical influence functions for elastic CM are generalized to the case of peridynamics, and the energetic definition of effective elastic moduli is proposed. Generalized Hill’s bounds on the effective elastic moduli of peridynamic random structure composites are obtained. In contrast to the classical Hill’s bounds, in the new bounds, comparable scales of the inclusion size and horizon are taken into account that lead to dependance of the bounds on both the size and shape of the inclusions. The numerical examples are considered for the 1D case.

Micromechanical Background of Random Structure Thermoperistatic Composites

2015 ◽  
Author(s):  
Valeriy A. Buryachenko
Keyword(s):  
Elastic Moduli ◽  
Effective Properties ◽  
Local Fields ◽  
Random Structure ◽  
Effective Elastic Moduli ◽  
Displacement Fields ◽  
General Integral ◽  
Spatial Derivatives ◽  
Effective Thermal Expansion ◽  
Derivatives Of

In contrast to the classical local and nonlocal theories, the peridynamic equation of motion introduced by Silling (J. Mech. Phys. Solids 2000; 48: 175–209) is free of any spatial derivatives of displacement. The new general integral equations (GIE) connecting the displacement fields in the point being considered and the surrounding points of random structure composite materials (CMs) is proposed. For statistically homogemneous thermoperistatic media subjected to homogeneous volumetric boundary loading, one proved that the effective behaviour of this media is governing by conventional effective constitutive equation which is intrinsic to the local thermoelasticity theory. It was made by the most exploitation of the popular tools and concepts used in conventional thermoelasticity of CMs and adapted to thermoperistatics. The general results establishing the links between the effective properties (effective elastic moduli, effective thermal expansion) and the corresponding mechanical and transformation influence functions are obtained by the use of decomposition of local fields into the load and residual fields similarly to the locally elastic CMs. This similarity opens a way for straightforward expansion of analytical micromechanics tools for locally elastic CMs to the new area of random structure peridynamic CMs. Detailed numerical examples for 1D case are considered.

Micromechanics of Random Structure Thermoperistatic Composites

2016 ◽  
Author(s):  
Valeriy A. Buryachenko
Keyword(s):  
Elastic Moduli ◽  
Effective Properties ◽  
Local Stress ◽  
Local Fields ◽  
Random Structure ◽  
Influence Functions ◽  
Effective Elastic Moduli ◽  
Displacement Fields ◽  
General Integral ◽  
Inclusion Phase

In contrast to the classical local and nonlocal theories, the peridynamic equation of motion introduced by Silling (J. Mech. Phys. Solids 2000; 48: 175–209) is free of any spatial derivatives of displacement. The new general integral equations (GIE) connecting the displacement fields in the point being considered and the surrounding points of random structure composite materials (CMs) is proposed. For statistically homogeneous thermoperistatic media subjected to homogeneous volumetric boundary loading, one proved that the effective behaviour of this media is governing by conventional effective constitutive equation which is intrinsic to the local thermoelasticity theory. It was made by the most exploitation of the popular tools and concepts used in conventional thermoelasticity of CMs and adapted to thermoperistatics. A generalization of the Hills equality to peri-static composites is proved. The classical representations of effective elastic moduli through the mechanical influence functions for elastic CMs are generalized to the case of peristatics, and the energetic definition of effective elastic moduli is proposed. The general results establishing the links between the effective properties (effective elastic moduli, effective thermal expansion) and the corresponding mechanical and transformation influence functions are obtained by the use of the decomposition of local fields into load and residual fields. Effective properties of thermoperistatic CM are expressed through the introduced local stress polarization tensor averaged over the extended inclusion phase. This similarity opens a way for straightforward expansion of analytical micromechanics tools for locally elastic CMs to the new area of random structure peri-dynamic CMs. Detailed numerical examples for 1D case are considered.

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