By John D. Clayton

ISBN-10: 940070349X

ISBN-13: 9789400703490

ISBN-10: 9400703503

ISBN-13: 9789400703506

This booklet describes habit of crystalline solids basically through tools of contemporary continuum mechanics. Emphasis is given to geometrically nonlinear descriptions, i.e., finite deformations.

Primary subject matters contain anisotropic crystal elasticity, plasticity, and strategies for representing results of defects within the good at the material's mechanical reaction. Defects comprise crystal dislocations, element defects, twins, voids or pores, and micro-cracks. Thermoelastic, dielectric, and piezoelectric behaviors are addressed. conventional and higher-order gradient theories of mechanical habit of crystalline solids are mentioned. Differential-geometric representations of kinematics of finite deformations and lattice illness distributions are offered. Multi-scale modeling innovations are defined within the context of elastic and plastic fabric habit. consultant ingredients in the direction of which modeling strategies will be utilized are unmarried- and poly- crystalline metals and alloys, ceramics, and minerals.

This e-book is meant to be used by means of scientists and engineers occupied with complex constitutive modeling of nonlinear mechanical habit of strong crystalline fabrics. wisdom of basics of continuum mechanics and tensor calculus is a prerequisite for getting access to a lot of the textual content. This booklet can be used as supplemental fabric for graduate classes on continuum mechanics, elasticity, plasticity, micromechanics, or dislocation mechanics, for college students in a variety of disciplines of engineering, fabrics technology, utilized arithmetic, and condensed topic physics.

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**Extra resources for Nonlinear Mechanics of Crystals**

**Sample text**

AA . F = F. Aa g a ⊗ G A = At any particular time t, spatial coordinates x a occupied by the body are assumed one-to-one functions of X A and (usually) differential of class C r ( r ≥ 1 ) with respect to X A . ,aA = ∂ a (⋅) F. Aa . 5 The Deformation Gradient 39 class C r with respect to spatial coordinates x a . ,aA ) ≠ 0 . If r = 0 across certain singular surfaces within an otherwise “smooth” body, then F may be discontinuous across such surfaces. Because it is referred to (possibly) distinct coordinate systems in different configurations, F is said to be a two-point tensor or double tensor (Ericksen 1960) whose components each transform like those of a vector (upper index) or covector (lower index) under transformations of only one set of coordinates.

A .. E .. A .. E RBCD = Γ CD , B − Γ BD ,C + Γ BE Γ CD − Γ CE Γ BD = 2∂[ B Γ C.. BAE Γ C.. 34) where indices in vertical bars are excluded from the anti-symmetry operation. Order and placement of indices used in the definition of R vary among authors (Schouten 1954; Fosdick 1966; Marsden and Hughes 1983; Clayton et al. 2005); conventions adopted in this book for the RiemannChristoffel curvature tensor and quantities derived from it follow those of Schouten (1954) and Minagawa (1979). The Riemann-Christoffel curvature tensor transforms like a true tensor of order {13 } under a change of holonomic coordinates (Schouten 1954).

AA . F = F. Aa g a ⊗ G A = At any particular time t, spatial coordinates x a occupied by the body are assumed one-to-one functions of X A and (usually) differential of class C r ( r ≥ 1 ) with respect to X A . ,aA = ∂ a (⋅) F. Aa . 5 The Deformation Gradient 39 class C r with respect to spatial coordinates x a . ,aA ) ≠ 0 . If r = 0 across certain singular surfaces within an otherwise “smooth” body, then F may be discontinuous across such surfaces. Because it is referred to (possibly) distinct coordinate systems in different configurations, F is said to be a two-point tensor or double tensor (Ericksen 1960) whose components each transform like those of a vector (upper index) or covector (lower index) under transformations of only one set of coordinates.

### Nonlinear Mechanics of Crystals by John D. Clayton

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