A viscoelastic theory is formulated for the deformation of particles that interact with finite-ranged surface forces. The theory generalizes the static approach based upon classic continuum elasticity theory to account for time-dependent effects, and goes beyond contact theories such as Hertz and that given by Johnson, Kendall, and Roberts by including realistic surface interactions. Common dev...

In the last decade the interest in deformation theory has grown in many areas of mathematics and physics. The deformation question is completely solved by describing a ‘‘versal’’ deformation of the given object; such a deformation induces all the other deformations. This problem turns out to be hard and a general procedure for solving this was given only recently in FF2 for Lie algebras. It is ...

With the increasing complexity of photo-realistic scenes, the question of building and placing objects in three-dimensional scenes is becoming ever more di cult. While the question of placement of rigid objects has captured the attention of researchers in the past, this work presents an intuitive and interactive scheme to properly place deformable objects with the aid of free-form deformation t...

In this study, based on nonlocal differential constitutive relations of Eringen, the first order shear deformation theory of plates (FSDT) is reformulated for vibration of nano-plates considering the initial geometric imperfection. The dynamic analog of the von Kármán nonlinear strain-displacement relations is used to derive equations of motion for the nano-plate. When dealing with nonlineariti...

We provide a prorepresenting object for the noncommutative derived deformation problem of deforming module $X$ over differential graded algebra. Roughly, we show that corresponding functor is homotopy prorepresented by dual bar construction on endomorphism algebra $X$. specialise to case when one-dimensional base field, and introduce notion framed deformations, which rigidify slightly allow us ...