Strain gradient plasticity

On first strain-gradient theories in linear elasticity

S olutions are presented for the one- and two-dimensional Griffith crack problems in non-local elasticity. The displacements and stresses are determined in an elastic plate, weakened by a sharpedged line crack. The plate is loaded by a uniform tension perpendicular to the line of the crack at infinity. The non-local elastic solutions yield a finite hoop stress at the crack tip, thus allowing for a fracture criterion based on the maximum stress hypothesis.

Crack-tip problem in non-local elasticity

The behavior of solids can be represented by a variety of continuum theories. For example, Cosserat elasticity allows the points in the continuum to rotate as well as translate, and the continuum supports couple per unit area as well as force per unit area. We examine experimental methods for determining the six Cosserat elastic constants of an isotropic elastic solid, or the six Cosserat relaxation functions of a Cosserat viscoelastic solid. We also consider other generalized continuum theories (including micromorphic elasticity, Cowin's void theory, and nonlocal elasticity). Ways of experimentall y discriminating among various generalized continuum representations are presented. The applicability of Cosserat elasticity to cellular solids and fibrous composite materials is considered as is the application of related generalized continuum theories. I Introduction The classical theory of elasticity is presently used in engineering analyses of deformable objects at small strain. However there are other continuum theories for linear isotropic materials. Some have more freedom, and some have less freedom than classical elasticity. The various continuum theories are all mathematically self consistent. Therefore a discrimination among them is to be made by experiment. It is the purpose of this article to explore the physical consequences of various continuum theories, and how these consequences may be used in the design of experiments to discriminate among the theories. The constitutive equations for several theories are presented, and some of the salient consequences of each theory are stated and discussed. Some of the causal physical mechanisms associated with each theory are briefly discussed. Experimental methods for evaluating materials as generalized continua are presented, with emphasis on Cosserat elasticity. The treatment is restricted to linearly elastic behavior; study of Cosserat plasticity and related issues is presented elsewhere in this volume. A discussion of experimental aspects of generalized continua is considered particularly appropriate in view of the fact that most of the work done thus far in generalized continuum mechanics has been theoretical.

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Experimental methods for study of cosserat elastic solids and other generalized elastic continua

The plane strain of adhesively bonded structures which consist of two different orthotropic adherents is considered. Assuming that the thicknesses of the adherends are constant and are small in relation to the lateral dimensions of the bonded region, the adherends are treated as plates. The transverse shear effects in the adherends and the in-plane normal strain in the adhesive are taken into account. The problem is reduced to a system of differential equations for the adhesive stresses which is solved in closed form. A single lap joint and a stiffened plate under various loading conditions are considered as examples. To verify the basic trend of the solutions obtained from the plate theory a sample problem is solved by using the finite element method and by treating the adherends and the adhesive as elastic continua. The plate theory not only predicts the correct trend for the adhesive stresses but also gives rather surprisingly accurate results.

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Stresses in adhesively bonded joints - A closed-form solution

The effect of couple-stresses on the stress concentration around a crack☆

: The problem posed by the diffusion of load from an infinite edge-stiffener into a semi-infinite elastic sheet is reconsidered under two alternative refinements of the underlying stiffener model. First, the stiffener is regarded as an elastic strip of finite width and the theory of generalized plane stress is applied rigorously to the sheet and stiffener alike. Next, Melan's one-dimensional treatment of the stiffener is amended to account for its bending rigidity. The 'exact' and the intermediate approximate solution thus obtained are compared to Melan's results with particular attention to the relevant asymptotic behavior in the vicinity of the applied load and at large distances from the load. Comparative numerical results, showing the variation of the sheet stresses at the interface and the distribution of the axial stiffener force, are included. (Author)

Rokuro Muki

Papers

The effect of couple-stresses on the stress concentration around a crack☆

Transfer of Load From an Edge-Stiffener to a Sheet—A Reconsideration of Melan’s Problem

On the stress analysis of overlapping bonded elastic sheets