2.1 INTRODUCTION We consider the eecient simulationof the quasi-static deformation process of materials with memory, where the history of the deformation is described by internal variables. Here, we focus on techniques which are required for large scale computations in three space dimensions on very ne grids with more than 10 6 unknowns. This involves the combination of parallel multigrid metho...

In recent years, Lattice Boltzmann methods (LBMs) have been adapted and developed to simulate the behavior of solids. They already applied fractures as well. However, until now, our previous work has restricted stationary cracks. this work, we regard reduced 2D case anti-plane shear deformation with mode III crack opening. The wave equation is governing for problem, which solved via an LBM. mai...

We consider a new class of inclusions in Hilbert spaces for which we provide an existence and uniqueness result. The proof is based on arguments monotonicity, convexity fixed point. use this result to establish the unique solvability associated Moreau’s sweeping processes. Next, give two applications Solid Mechanics. first one concerns study time-dependent constitutive law with unilateral const...

Nowadays, inverse scattering problems in solid mechanics bear relevance to a wide range of applications such as seismic tomography and imaging, non-destructive material testing, and medical diagnosis. To help advance the state of the art on the subject, this research deals with detecting and identifying unknown scatterers i.e. obstacles (e.g. material defects, cracks, or lesions in soft tissues...