Weakly convex polyhedra which are star-shaped with respect to one of their vertices are infinitesimally rigid. This is a partial answer to the question whether every decomposable weakly convex polyhedron is infinitesimally rigid. The proof uses a recent result of Izmestiev on the geometry of convex caps.

In this work, we study a unilateral contact problem with non local friction of Coulombbetween a locking material and a rigid foundation. In the first step , we present the mathematicalmodel for a static process, we establish the variational formulation in the form of a variationalinequality and we prove the existence and uniqueness of the solution. In the second step, usingthe penalty method we...

The mechanical properties of extracellular matrix proteins strongly influence cell-induced tension in the matrix, which in turn influences cell function. Despite progress on the impact of elastic behaviour of matrix proteins on cell-matrix interactions, little is known about the influence of inelastic behaviour, especially at the large and slow deformations that characterize cell-induced matrix...

The two-year Foundation Programme was introduced in the UK as a structured way to deal with the lack of training, support and difficulties with career progression associated with the old senior house office (SHO) grade. Although it provides a clear curriculum and structure for career progression, there is growing dissatisfaction among participants about the difference between the aspirations of...

This paper deals with an optimal control problem associated to an evolution implicit quasi-variational inequality for elastic materials. Such problems describe the quasi-static process of bilateral contact with friction between an elastic body and a rigid foundation. Existence of an optimal control is proven and necessary optimality conditions are derived.

We consider dynamical and quasi-static thermoelastic contact problems in R modeling the evolution of temperature and displacement in an elastic body that may come into contact with a rigid foundation. The existence of solutions to these dynamical and quasi-static nonlinear problems and the exponential stability are investigated using a penalty method. Interior smoothing effects in the quasi-sta...

We consider a variational inequality for the Lamé system which models an elastic body in contact with a rigid foundation. We give conditions on the domain and the contact set which allow us to prove regularity of solutions to the variational inequality. In particular, we show that the gradient of the solution is a square integrable function on the boundary.

The response of back-supported buffer plates comprising a solid face sheet and foam core backing impacted by a column of high velocity particles (sand slug) is investigated via a lumped parameter model and coupled discrete/continuum simulations. The buffer plate is either resting on (unattached) or attached to a rigid stationary foundation. The lumped parameter model is used to construct maps o...

We introduce a class of polynomials, which we call subspace polynomials and show that the problem of explicitly constructing a rigid matrix can be reduced to the problem of explicitly constructing a small hitting set for this class. We prove that small-bias sets are hitting sets for the class of subspace polynomials, though their size is larger than desired. Furthermore, we give two alternative...