A numerical investigation is carried out in this work in order to evaluate the computational performance of a numerical model based on isogeometric analysis for applications on geometrically nonlinear elastodynamics. In the FEM (finite element method) practice, it is well known that the Newmark’s method is unconditionally stable for linear structural systems, but this characteristic is frequent...

The w,-(x, i) and /i(x, I) are the Cartesian components of the displacement vector u(x, t) and the body force f (x, t); x is a point of the closed region of space R occupied by the body, and t represents the time. The cim are the components of the constant elasticity tensor c and p denotes the constant mass density. This note is concerned exclusively with the displacement boundary-value problem...

In this work we study the dynamics of an elastic bar undergoing phase transitions. It is modeled by two regularizations of the equations of nonlinear elastodynamics with a non-convex energy. We estimate the difference between solutions to the two regularizations if in one of them a coupling parameter α is sent to infinity. This estimate is based on an adaptation of the relative entropy framewor...

In this paper, the theoretical foundation of a compact scalar potential method in three-dimensional classical elastodynamics is substantiated. Beginning with a derivation of two basic lemmas on the decomposition and integration of wave solutions and vector fields which are apt to be of interest to general mechanics and analysis, the treatment proceeds to a proof of the completeness of the propo...

Space-time finite element methods are developed for classical elastodynamics. The approach employs the discontinuous Galerkin method in time and incorporates stabilizing terms of least-squares type. These enable a general convergence theorem to be proved in a norm stronger than the energy norm. Optimal error estimates are predicted, and confirmed numerically, for arbitrary combinations of displ...