A discrete model for force-based elasticity and plasticity

The article presents a mathematical model that simulates the elastic and plastic behaviour of discrete systems representing isotropic materials. The systems consist of one lattice of nodes connected by edges and a second lattice with nodes placed at the centres of the existing edges. The derivation is based on the assumption that the kinematics of the second lattice is induced by the kinematics of the first, and uses stored energies in edges of both lattices to derive a edge forces in the first lattice. This leads to a non-linear system of algebraic equations describing elasticity and plasticity in lattices. A numerical solution to the non-linear system is proposed by providing a matrix formulation necessary for software implementation. An illustrative example is given to justify the formulation and demonstrate the system behaviour

The 2nd International Conference on Mathematical Modelling in Applied Sciences, ICMMAS’19, Belgorod, Russia, August 20-24, 2019 : book of abstracts

The proposed Scientific Program of the conference is including plenary lectures, contributed oral talks, poster sessions and listeners. Five suggested special sessions / mini-symposium are also considered by the scientific committe

Stability of bounded dynamical networks with symmetry

Motivated by dynamical models describing phase separation and the motion of interfaces separating phases, we study the stability of dynamical networks in planar domains formed by triple junctions. We take into account symmetry, angle-intersection conditions at the junctions and at the points at which the curves intersect with the boundary. Firstly, we focus on the case of a network where two triple junctions have all their branches unattached to the boundary and then on the case of a network of hexagons, with one of them having all its branches unattached to the boundary. For both type of networks, we introduce the evolution problem, identify the steady states and study their stability in terms of the geometry of the boundary.Science Foundation Irelan