Linear elasticity

About: Linear elasticity is a research topic. Over the lifetime, 9080 publications have been published within this topic receiving 258684 citations.

Size-dependent effective modulus of elastic composite materials: Spherical nanocavities at dilute concentrations

Abstract: The effect of surface energy on the effective elastic properties was analyzed for elastic composite materials containing spherical nanocavities at dilute concentration. Closed-form solutions of the effective shear modulus and bulk modulus were obtained, which turn out to be a function of the surface energy and size of the nanocavity. The dependence of the elastic response on size of the nanocavity in composite materials is different from the classic results obtained in the linear elasticity theory, suggesting the importance of the surface energy of the nanocavity in analyzing the deformation of nanoscale structures.

On the well-posedness of the linear peridynamic model and its convergence towards the Navier equation of linear elasticity

Abstract: The non-local peridynamic theory describes the displacement field of a continuous body by the initial-value problem for an integro-differential equation that does not include any spatial derivative. The non-locality is determined by the so-called peridynamic horizon $\delta$ which is the radius of interaction between material points taken into account. Well-posedness and structural properties of the peridynamic equation of motion are established for the linear case corresponding to small relative displacements. Moreover the limit behavior as $\delta \rightarrow 0$ is studied.

Composite and Reinforced Elements of Construction

Abstract: Part 1 Mechanics of inhomogeneous deformable solids: basic relations of continuum mechanics basic equations of thermoelasticity and electroelasticity mechanical models of composite materials. Part 2 Asymptotic homogenization of regular structures: homogenization techniques for periodic structures homogenization method for regions with a wave boundary local problems and effective coefficients. Part 3 Elasticity of regular composite structures: homogenization of the linear elasticity problem laminated composites - effective properties and fracture criteria effective characteristics of unidirectional fibre composites plane elasticity problem for a periodic composite with a crack homogenization of the geometrically nonlinear elasticity problem for a periodic composite elastic stability equatiions. Part 4 Thermoelasticity of regular composite structures: homogenization of thermoelasticity problem fibre composites - local stresses and effective properties laminated composite with prescribed thermoelastic properties composite material design. Part 5 General homogenization models for composite shells and plates with rapidly varying thickness: elasticity problem for a shell of a regularly nonhomogeneous material with wavy surfaces thermal conductivity of a curved thin shell of a regularly nonhomogeneous material with corrugated surfaces thermoelasticity of a curved shell of regularly nonhomogeneous material with corrugated surfaces geometrically nonlinear problem for a thin regularly nonhomogeneous shell with corrugated faces. Part 6 Structurally nonhomogeneous periodic shells and plates: local problem formulation for structurally nonhomogeneous shells and plates of orthotropic material an approximate method for determining the effective properties of ribbed and wafer shells effective properties of a three-layered shell with a honeycomb filler elastic moduli and local stresses in wafer type plates and shells, including the interaction between cell elements stretching of shells or plates reinforced by regular system of thin surface strips shells and plates with corrugated surfaces of regular structure. Part 7 Network and framework reinforced shells and plates with regular structure effective elastic moduli of a network reinforced shell effective thermoelastic properties of network reinforced shells heat conduction of network reinforced plates and shells constitutional equations for network reinforced plates and shells of rectangular, rhombic and triangular structure composite shells with high stiffness framework type reinforcement. Part 8 The fundamental solution of the periodic elasticity problem: the derivation of a doubly periodic fundamental solution of the three-dimensional elasticity problem transformation of the doubly periodic fundamental solution of the elasticity problem singly periodic fundamental solution of the plane elasticity. Appendices.