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Harmonic Decomposition, Irreducible Basis Tensors, and Minimal Representations of Material Tensors and Pseudotensors
We propose a general and efficient method to derive various minimal representations of material tensors or pseudotensors for crystals. By a minimal...
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Algebra of Higher-Order Tensors
Recall from Chap. 1 that scalars were zeroth-order tensors with only one component and vectors or first-order...
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A three-dimensional computational multiscale micromorphic analysis of porous materials in linear elasticity
We present an extension of a multiscale micromorphic theory to three-dimensional problems for porous materials, where a clear scale separation is not...
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Elementary Concepts in Elasticity
To study the applications of finite element method in structural and continuum mechanics, sufficient background in the basic principles of solid...
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Cauchy Relations in Linear Elasticity: Algebraic and Physics Aspects
The Cauchy relations distinguish between rari- and multi-constant linear elasticity theories. These relations are treated in this paper in a form...
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Eshelby tensors and effective stiffness of one-dimensional orthorhombic quasicrystal composite materials containing ellipsoidal particles
Eshelby tensors serve as the basis of micromechanics which should be explored first to study the effective mechanical behavior of heterogeneous...
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On the Averaging and Closure of Fiber Orientation Tensors in Virtual Process Chains
Fiber orientation tensors (FOT) are widely used to approximate statistical orientation distributions of fibers within fiber-reinforced polymers. The...
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Green’s Functions, Eshelby, and Related Tensors
The key tools of random structure composite materials (CMs) such as Green’s function and related tensors are considered in this chapter for the...
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Mathematical Models of the Theory of Elasticity
The theory of elasticity is a part of the continuum mechanics and the solid mechanics. The theory of elasticity deals with the determination of a...
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Internally Balanced Elasticity Tensor in Terms of Principal Stretches
A new scheme for hyperelastic material is developed based on applying the argument of calculus variation to two-factor multiplicative decomposition...
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Nonlocal and couple stress tensors in three-dimensional nonlinear dynamical stability behavior of microshells manufactured by smart materials
By taking simultaneously the nonlocal stress and couple stress tensors into account, the nonlinear three-dimensional dynamical stability of smart...
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Plane crack problems within strain gradient elasticity and mixed finite element implementation
An alternative approach is proposed and applied to solve boundary value problems within the strain gradient elasticity theory. A mixed variation...
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Ellipticity in couple-stress elasticity
We discuss ellipticity property within the linear couple-stress elasticity. In this theory, there exists a deformation energy density introduced as a...
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Phase field modeling of ferroelastic variant switching in yttria-stabilized t′zirconia with strain gradient elasticity and interface tension
The 6–8 wt% yttria-stabilized zirconia with a tetragonal structure (t′-YSZ) is extensively employed in thermal barrier coatings. The exceptional...
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A higher-order nonlocal elasticity continuum model for deterministic and stochastic particle-based materials
This paper proposes, for particle-based materials, a higher-order nonlocal elasticity continuum model that includes the Piola peridynamics and the...
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Nonlocal Strong Forms of Thin Plate, Gradient Elasticity, Magneto–Electro-Elasticity and Phase Field Fracture by Nonlocal Operator Method
In this chapter, we apply the variational principle/weighted residual method based on the nonlocal operator method for the derivation of nonlocal...
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Harmonic Tensors and Tensorial Texture Coefficients
The purpose of this chapter is to introduce the tensorial Fourier expansion of the ODF and the tensorial texture coefficients [1, 34, 132, 190, 355]...
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Data-driven analysis of spinodoid topologies: anisotropy, inverse design, and elasticity tensor distribution
Spinodoid topologies are bicontinuous porous microstructures inspired by the natural spinodal decomposition process. They offer a vast design space...
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RETRACTED ARTICLE: Nonlinear buckling mode transition analysis of axial–thermal–electrical-loaded FG piezoelectric nanopanels incorporating nonlocal and couple stress tensors
Piezoelectric nanostructures are one of the essential components in the design of electromechanical systems and devices at nanoscale. In the present...
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Quasi-3D nonlinear primary resonance of randomly oriented CNT-reinforced micro/nano-beams incorporating nonlocal and couple stress tensors
In the current research examination, the nonlinear primary resonance of softly periodic excited nanocomposite micro/nano-beams containing nanofillers...
