Semi-linear Material Research Articles

Complementary energy, neutral equilibrium and buckling

The theorem of stationary complementary energy is applied to buckling problems for structures of a semi-linear material in cases of an irrotational linear prebuckling state.

Stability of a nonlinearly elastic cylinder under side pressure and axial compression

Abstract There is considered the problem of loss of stability of thick-walled cylinders subjected to inhomogeneous initial stresses. The analysis is based on the exact threedimensional equations of neutral equilibrium problems derived by superposing small on finite deformations. The law of the state is determined by a five-constant Murnaghan relationship. Cases are studied of the buckling of circular cylinders subjected to axial load and side internal and external hydrostatic pressure. Results are represented for calculations exhibiting the influence of nonlinearity on the upper critical load as a function of the geometric parameters. There exists a comparatively small number of papers in which the stability of equilibrium is investigated on the basis of the three-dimensional equations of nonlinear elasticity theory /1/. Results are obtained for bodies of simple shape (slab, rod, hollow sphere, cylindrical tube), in which most solutions rely on a simplifying hypothesis regarding the incompressibility of the material or an assumption regarding the simple form of the state function. Mainly cases of neo-Hookean and semilinear materials are studied /2,3/.

On a dual variational principle in geometrically nonlinear elasticity theory: PMM vol. 43, no. 2, 1979, pp. 321–329

A method for constructing a dual variational principle in geometrically non-linear elasticity theory is elucidated. The dual functional (a functional of Castigliano type) is evaluated in the case of an isotropic semilinear material.

A variational principle for non-linear elastodynamics and its application to the hybrid stress model

A variational principle is derived for the mixed initial-boundary value problem of non-linear elastodynamics. This principle involves stress quantities only. It is an extension of a similar one derived by Gurtin[1] for linear elastodynamics. The principle is then specialized to the class of semilinear materials, and generalized for the use in the hybrid stress model of finite element analysis. An incremental procedure for the numerical solution is described.

Nonlinear and semilinear rheology of porous solids

The nonlinear and semilinear mechanics of porous solids is developed in terms of the Cartesian definition of finite strain and a local rotation field. It is based on modern developments in irreversible thermodynamics and viscoelasticity. This particular approach provides a method of introducing an essential feature of porous solids referred to here as semilinearity. The linear behavior is represented by a linear dependence of the volume of the individual grains on stresses and pressure. The nonlinear behavior is then mainly a consequence of local geometric effects such as changes in contact areas, crack closure, etc. Under these conditions it is shown that seven physical constants describe the semilinear properties of an isotropic porous solid. Viscoelastic behavior is analyzed in the semilinear context, and a plastic flow condition is also formulated in terms of the effective stress. Nonlinear equations for the displacement field are derived in which a Cartesian representation is used. The equations are found to be relatively simple and are directly applicable to semilinear materials. It is also shown how the present Cartesian semilinear formulation leads to variational principles and Lagrangian equations that bring the theory within the more general framework of modern developments in nonlinear irreversible thermodynamics.

Approximate theory of buckling of thin plates of semilinear material in case of affine initial deformation: PMM vol. 33, n≗4, 1969, pp. 668–675

Approximate theory of buckling of thin plates of semilinear material in case of affine initial deformation: PMM vol. 33, n≗4, 1969, pp. 668–675

Theory of elasticity for a semilinear material: PMM vol.32, n≗6, 1968, pp. 1053–1069

Theory of elasticity for a semilinear material: PMM vol.32, n≗6, 1968, pp. 1053–1069