The gradient theory [4] is recognized as Charles Manning Child?s most significant scientific contribution. Gradients brought together Child?s interest in development and his fascination with the origins of individuality and organization [5]. The theory grew from his studies of regeneration, which were largely based on work he conducted with invertebrates, such as planaria [6], a flat worm, and ...

The strain-induced reorientation response of cyclically stretched cells has been well characterized in uniform strain fields. In the present study, we comprehensively analyse the behaviour of human fibroblasts subjected to a highly non-uniform strain field within a polymethylsiloxane microdevice. Our results indicate that the strain gradient amplitude and direction regulate cell reorientation t...

Several beam and plate models have been recently developed in the literature to accommodate for size-dependence. These are usually obtained starting from a generalized continuum theory (such as couple-stress, strain-gradient or non-local their modifications) then deducing governing equations through Hamilton’s principle ingenuous kinematical assumptions. This approach, originated by Kirchhoff, ...

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...

The main focus of this paper is to introduce, in a thermodynamically consistent manner, an anisotropic interface energy into a phase field theory for phase transformations. Here we use a small strain formulation for simplicity, but we retain some geometric nonlinearities, which are necessary for introducing correct interface stresses. Previous theories have assumed the free energy density (i.e....