Concepts from Finsler differential geometry are applied towards a theory of deformable continua with internal structure. The general theory accounts for finite deformation, nonlinear elasticity, and various kinds of structural features in a solid body. The general kinematic structure of the theory includes macroscopic and microscopic displacement fields – i.e., a multiscale representation – whe...

The size and viscosity effects are noticeable at the micro-/nano scale. In present work, strain gradient viscoelastic solution of mode-III crack in an infinite quasi-brittle advanced material is proposed based on viscoelasticity theory using Wiener–Hopf method. solutions to gradient-dependent problem obtained directly by correspondence principle between elasticity Maxwell’s standard linear soli...

Anisotropic strain gradient elasticity theory is applied to the solution of a mode III crack in a functionally graded material. The theory possesses two material characteristic lengths, , and ,8, which describe the size scale effect resulting from the underlining microstructure, and are associated to volumetric and surface strain energy, respectively. The governing differential equation of the ...

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...

Abstract The equilibrium equations and the traction boundary conditions are evaluated on basis of condition stationarity Lagrangian for coupled strain gradient elasticity. quadratic form energy can be written as a function second displacement contains fourth-, fifth- sixth-order stiffness tensor $${\mathbb {C}}_4$$ C</...