Boundary element analysis of 3D cracks in anisotropic thermomagnetoelectroelastic solids

Pasternak, Iaroslav; Pasternak, Roman; Pasternak, Viktoriya; Sulym, Heorhiy

doi:10.1016/j.enganabound.2016.10.009

Cited by 19 publications

(24 citation statements)

References 28 publications

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“…According to [], in a fixed Cartesian coordinate system

O x_{1} x_{2} x_{3}

the equilibrium equations, the Maxwell equations (Gauss theorem for electric and magnetic fields), and the balance equations of heat conduction in the steady‐state case can be presented in the following compact form

{\overset{σ}{true}}_{I j, j} + {\overset{f}{true}}_{I} = 0, h_{i, i} - f_{h} = 0,

where the capital index varies from 1 to 5, while the lower case index varies from 1 to 3, i.e.

I = 1, 2, \dots, 5

.…”

Section: Governing Equations Of Heat Conduction and Thermomagnetoelecmentioning

confidence: 99%

“…In the assumption of small strains and fields’ strengths the constitutive equations of linear thermomagnetoelectroelasticity in the compact notations are as follows

{\overset{σ}{true}}_{I j} = {\overset{C}{true}}_{I j K m} {\overset{u}{true}}_{K, m} - {\overset{β}{true}}_{I j} θ, h_{i} = - k_{i j} θ_{, j},

where

\begin{matrix} right {\overset{u}{true}}_{i} & = & left u_{i}, {\tilde{u}}_{4} = ϕ, {\tilde{u}}_{5} = ψ; {\tilde{f}}_{i} = f_{i}, {\tilde{f}}_{4} = - q, {\tilde{f}}_{5} = b_{m}; \\ right {\overset{σ}{true}}_{i j} & = & left σ_{i j}, {\tilde{σ}}_{4 j} = D_{j}, {\tilde{σ}}_{5 j} = B_{j}; \\ right {\overset{C}{true}}_{i j k m} & = & left C_{i j k m}, {\tilde{C}}_{i j 4 m} = e_{m i j}, {\tilde{C}}_{4 j k m} = e_{j k m}, {\tilde{C}}_{4 j 4 m} = - κ_{j m}, \\ right {\overset{C}{true}}_{i j 5 m} & = & left h_{m i j}, {\tilde{C}}_{5 j k m} = h_{j k m}, \end{matrix}

…”

Section: Governing Equations Of Heat Conduction and Thermomagnetoelecmentioning

confidence: 99%

“…According to [], the extended magnetoelectroelastic tensor

{\tilde{C}}_{I j K m}

has the following useful symmetry property

{\overset{C}{true}}_{I j K m} = {\overset{C}{true}}_{K m I j} .

Thus, the problem of linear thermomagnetoelectroelasticity is to solve partial differential Equations and under the given boundary conditions and volume loading. Since magneto‐electro‐mechanical fields do not influence temperature field in the considered problem (uncoupled thermomagnetoelectroelasticity) the first step is to solve the heat conduction equation and the second one is to determine mechanical, electric and magnetic fields acting in the solid.…”

Section: Governing Equations Of Heat Conduction and Thermomagnetoelecmentioning

confidence: 99%

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Boundary element analysis of 3D shell‐like rigid electrically conducting inclusions in anisotropic thermomagnetoelectroelastic solids

2019

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The paper presents general boundary element approach for analysis of thermomagnetoelectroelastic solids containing shell‐like electrically conducting inclusions with high magnetic permittivity. The latter are modeled with opened surfaces with certain boundary conditions on their faces. Rigid displacement and rotation, along with constant electric and magnetic potentials of inclusions are accounted for in these boundary conditions. Formulated boundary value problem is reduced to a system of singular boundary integral equations, which is solved numerically by the boundary element method. Special attention is paid to the field singularity at the front line of a shell‐like inclusion. Special shape functions are introduced, which account for this square‐root singularity and allow accurate determination of field intensity factors. Approaches for fast and accurate numerical evaluation of anisotropic thermomagnetoelectroelastic kernels are discussed, which are crucial in derivation of fast and precise boundary element approach. Numerical examples are presented.

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“…According to [], in a fixed Cartesian coordinate system

O x_{1} x_{2} x_{3}

{\overset{σ}{true}}_{I j, j} + {\overset{f}{true}}_{I} = 0, h_{i, i} - f_{h} = 0,

where the capital index varies from 1 to 5, while the lower case index varies from 1 to 3, i.e.

I = 1, 2, \dots, 5

.…”

Section: Governing Equations Of Heat Conduction and Thermomagnetoelecmentioning

confidence: 99%

“…In the assumption of small strains and fields’ strengths the constitutive equations of linear thermomagnetoelectroelasticity in the compact notations are as follows

{\overset{σ}{true}}_{I j} = {\overset{C}{true}}_{I j K m} {\overset{u}{true}}_{K, m} - {\overset{β}{true}}_{I j} θ, h_{i} = - k_{i j} θ_{, j},

where

\begin{matrix} right {\overset{u}{true}}_{i} & = & left u_{i}, {\tilde{u}}_{4} = ϕ, {\tilde{u}}_{5} = ψ; {\tilde{f}}_{i} = f_{i}, {\tilde{f}}_{4} = - q, {\tilde{f}}_{5} = b_{m}; \\ right {\overset{σ}{true}}_{i j} & = & left σ_{i j}, {\tilde{σ}}_{4 j} = D_{j}, {\tilde{σ}}_{5 j} = B_{j}; \\ right {\overset{C}{true}}_{i j k m} & = & left C_{i j k m}, {\tilde{C}}_{i j 4 m} = e_{m i j}, {\tilde{C}}_{4 j k m} = e_{j k m}, {\tilde{C}}_{4 j 4 m} = - κ_{j m}, \\ right {\overset{C}{true}}_{i j 5 m} & = & left h_{m i j}, {\tilde{C}}_{5 j k m} = h_{j k m}, \end{matrix}

…”

Section: Governing Equations Of Heat Conduction and Thermomagnetoelecmentioning

confidence: 99%

“…According to [], the extended magnetoelectroelastic tensor

{\tilde{C}}_{I j K m}

has the following useful symmetry property

{\overset{C}{true}}_{I j K m} = {\overset{C}{true}}_{K m I j} .

Section: Governing Equations Of Heat Conduction and Thermomagnetoelecmentioning

confidence: 99%

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Boundary element analysis of 3D shell‐like rigid electrically conducting inclusions in anisotropic thermomagnetoelectroelastic solids

2019

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“…According to Pasternak et al (2017), in a fixed Cartesian coordinate system 1 2 3 the equilibrium equations, the Maxwell equations (Gauss theorem for electric and magnetic fields), and the balance equations of heat conduction in the steady-state case can be presented in the following compact form…”

Section: Governing Equations Of Heat Conduction and Thermomagnetoelecmentioning

confidence: 99%

“…According to the philosophy of the discontinuity function approach the exterior problem of 3D TMEE is reduced to the following system of dual boundary integral equations (see Pasternak et al (2017)):…”

Section: Fig 1 Simplification Of a Thin Inclusionmentioning

confidence: 99%

Boundary Element Analysis of Anisotropic Thermomagnetoelectroelastic Solids with 3D Shell-Like Inclusions

Pasternak

Sulym

2017

Acta Mechanica Et Automatica

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Abstract:The paper presents novel boundary element technique for analysis of anisotropic thermomagnetoelectroelastic solids containing cracks and thin shell-like soft inclusions. Dual boundary integral equations of heat conduction and thermomagnetoelectroelasticity are derived, which do not contain volume integrals in the absence of distributed body heat and extended body forces. Models of 3D soft thermomagnetoelectroelastic thin inclusions are adopted. The issues on the boundary element solution of obtained equations are discussed. The efficient techniques for numerical evaluation of kernels and singular and hypersingular integrals are discussed. Nonlinear polynomial mappings are adopted for smoothing the integrand at the inclusion's front, which is advantageous for accurate evaluation of field intensity factors. Special shape functions are introduced, which account for a square-root singularity of extended stress and heat flux at the inclusion's front. Numerical example is presented.

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Boundary Element Analysis of Partially Debonded Shell-Like Rigid Inclusions in Anisotropic Medium

Sulym

Ilchuk

Pasternak

2020

Structural Integrity

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Boundary element analysis of 3D cracks in anisotropic thermomagnetoelectroelastic solids

Cited by 19 publications

References 28 publications

Boundary element analysis of 3D shell‐like rigid electrically conducting inclusions in anisotropic thermomagnetoelectroelastic solids

Boundary element analysis of 3D shell‐like rigid electrically conducting inclusions in anisotropic thermomagnetoelectroelastic solids

Boundary Element Analysis of Anisotropic Thermomagnetoelectroelastic Solids with 3D Shell-Like Inclusions

Boundary Element Analysis of Partially Debonded Shell-Like Rigid Inclusions in Anisotropic Medium

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