In this paper, we investigate the behavior of strain gradient elasticity solutions around sharp edges body loaded by concentrated loads. We consider general Mindlin–Toupin (SGET) and several simplified models, including dilatation theory (DGET) couple stress (CST). framework a plane problem for an elastic wedge with prescribed tip displacement obtain analytical assessments field state apex. Inv...

Abstract The fundamental problem of dislocations in incompatible isotropic strain gradient elasticity theory Mindlin type, unsolved for more than half a century, is solved this work. Incompatible type the generalization Mindlin’s compatible including plastic fields providing way proper eigenstrain framework study defects like dislocations. Exact analytical solutions displacement fields, elastic...

Based on fundamental equations of the elasticity theory, a unified higher-order shear deformation theory is developed for bending and free vibration analysis functionally graded (FG) microplates with porosities. The modified strain gradient employed to capture size effects. Bi-directional series hybrid shape functions are used solve problems. Several important effects including thickness-to-mat...

We develop a continuum theory for equilibrium elasticity of a network of crosslinked semiflexible filaments, spanning the full range between flexible entropy-driven chains to stiff athermal rods. We choose the 3-chain constitutive model of network elasticity over several plausible candidates, and derive analytical expressions for the elastic energy at arbitrary strain, with the corresponding st...

In this paper a composite plate with similar unidirectional fibers is considered. Assuming orthotropic structure, theory of elasticity is used for investigating the stress concentration. Also, complex variable functions are utilized for solving the plane stress problems. Then the effective characteristics of this plate are studied numerically by using ANSYS software. In this research a volume e...

In this paper we derive a strain gradient plate model from the three-dimensional equations of strain gradient linearized elasticity. The deduction is based on the asymptotic analysis with respect of a small real parameter being the thickness of the elastic body we consider. The body is constituted by a second gradient isotropic linearly elastic material. The obtained model is recognized as a st...

We study the steady-state and transient responses of a second-order elastic plate by implementing an asymptotic analysis three-dimensional equations with respect to two geometric characteristics seen as parameters: thickness inner material length. Depending on their ratio, four different models arise. Conditions under which Reissner–Mindlin kinematics may appear are discussed while influence cr...

It is well known that glassy polymer nanocomposites (PNC) exhibit heterogeneous mechanical properties, with a distinct polymer/nanoparticle (NP) interfacial region. The interphase rigidity in particular can significantly influence the overall response of PNCs. Continuum theories typically describe behavior such to depend only on deformation and, thus, they discard strong internal gradients with...