We prove a compactness and semicontinuity result that applies to minimisation problems in nonhomogeneous linear elasticity under Dirichlet boundary conditions. This generalises previous theorem we proved employed show existence of minimisers for the problem (homogeneous) Griffith energy.

A dual-reciprocity boundary element method is presented for the numerical solution of initial-boundary value problems governed by a nonlinear partial differential equation for heat conduction in nonhomogeneous anisotropic materials. To assess the validity and accuracy of the method, some specific problems are solved. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 000: 000–...

Various methods of predicting the deformation of fine-scale cloth from coarser resolutions have been explored. However, the influence of fine-scale deformation has not been considered in coarse-scale simulations. Thus, the simulation of highly nonhomogeneous detailed cloth is prone to large errors. We introduce an effective method to simulate cloth made of nonhomogeneous, anisotropic materials....

Controlling the bandstructure through local-strain engineering is an exciting avenue for tailoring optoelectronic properties of materials at the nanoscale. Atomically thin materials are particularly well-suited for this purpose because they can withstand extreme nonhomogeneous deformations before rupture. Here, we study the effect of large localized strain in the electronic bandstructure of ato...

For classical elasticity, the constitutive equations (Hooke’s law) have the same functional form for both homogeneous and nonhomogeneous materials. However, for straingradient elasticity, such is not the case. This paper shows that for strain-gradient elasticity with volumetric and surface energy (Casal’s continuum), extra terms appear in the constitutive equations which are associated with the...