High quality simulations of the dynamics of soft flexible objects can be rather costly, because the assembly of internal forces through an often nonlinear stiffness at each time step is expensive. Many standard implicit integrators introduce significant, time-step dependent artificial damping. Here we propose and demonstrate the effectiveness of an exponential Rosenbrock-Euler (ERE) method whic...

We study strain localization as an enhanced velocity weakening mechanism on earthquake faults. Fault friction is modeled using Shear Transformation Zone (STZ) Theory, a microscopic physical model for non-affine rearrangements in granular fault gouge. STZ Theory is implemented in spring slider and dynamic rupture models of faults. We compare dynamic shear localization to deformation that is unif...

A sharp interface model of crack propagation as a phase transition process is discussed. We develop a multipole expansion technique to solve this free boundary problem numerically. We obtain steady state solutions with a self-consistently selected propagation velocity and shape of the crack, provided that elastodynamic effects are taken into account. Also, we find a saturation of the steady sta...

We introduce a new way of computation of time dependent partial differential equations using hybrid method FEM in space and FDM in time domain and explicit computational scheme. The key idea is quick transformation of standard basis functions into new simple basis functions. This new way is used for better computational efficiency. We explain this way of computation on an example of elastodynam...

An incoming elastodynamic wave impinges on an elastic obstacle is embedded in infinite medium. The objective of the paper to examine subsequent fields scattered by and transmitted into obstacle. By applying a boundary-field equation method, we are able formulate nonlocal boundary problem (NBP) Laplace transformed domain, using field equations inside integral exterior Existence, uniqueness stabi...

We show, how the Riemann–Hilbert approach to elastodynamic equations, which have been suggested in our preceding papers, works half plane case. pay a special attention emergence of Rayleigh waves within scheme.

This article proposes a boundary element method for the dynamic contact between linearly elastic body and rigid obstacle. The Signorini problem is formulated as variational inequality Poincar\'{e}-Steklov operator elastodynamic equations on boundary, which solved in mixed formulation using elements time domain. We obtain an priori estimate resulting Galerkin approximations. Numerical experiment...

For the elastodynamic simulation of a geometrically exact beam, a variational integrator is derived from a PDE viewpoint. Variational integrators are symplectic and conserve discrete momentum maps and since the presented integrator is derived in the Lie group setting (unit quaternions for the representation of rotational degrees of freedom), it intrinsically preserves the group structure withou...

Standard nonlinear schemes for the the simulation of elastodynamic problems have several shortcomings when considering high-speed rotations. To tackle these problems, we use a corotational framework and a corresponding specific linearization to design new energy-conserving numerical schemes. In the two-dimensional case, an algorithm preserving also angular momentum is presented. The existence o...