E lasticity is the property that enables a fluid or solid body to resist change in size and shape when an external force is applied and to return to its original size and shape when the force is removed. This concept is a major building block in seismology because it is the elastic properties of rocks which allow seismic waves to propagate through the earth. The theory of elasticity is one of t...

We analyze a thin elastic, homogeneous strip under a smooth load and several different types of boundary conditions. The strip is assumed to obey either a plane strain or a plane stress type deformation of linear theory of elasticity. We characterize the 2D solution and consider dimension reduction of arbitrary order n. Both interior and global energy estimates for the reduction error are derived.

The principle underlying cloaking theory is the transformation method whereby the material properties of the cloak are defined by a (singular) spatial transformation. For elastodynamics, Milton et al. [1] concluded that the transformed materials are described by the Willis model, involving coupling between stress and velocity, in addition to anisotropic inertia. For a restricted transformation,...

In some circumstances, elastic-plastic deformation occurs in which both components of strain are finite. Such situations fall outside the scope of classical plasticity theory which assumes either infinitesimal strains or plastic-rigid theory for large strains. The present theory modifies the kinematics to include finite elastic and plastic strain components. For situations requiring this genera...

Abstract In this contribution, a finite element implementation of the stress gradient theory is proposed. The relies on reformulation governing set partial differential equations in terms one primary tensor-valued field variable third order, so-called generalised displacement field. Whereas volumetric part closely related to classic field, deviatoric can be interpreted micro-displacements. asso...

Deflection analysis of a simply supported microbeam subjected to a concentrated load at the middle is investigated on the basis of a shear deformable beam theory and non-classical theory. Effects of shear deformation and small size are taken into consideration by hyperbolic shear deformable beam theory and modified strain gradient theory, respectively. The governing differential equations and c...