The multiphysics fluid-structure interaction simulation of shock-loaded thin-walled structures requires the dynamic coupling of a shock-capturing flow solver to a solid mechanics solver for large deformations. By combining a Cartesian embedded boundary approach with dynamic mesh adaptation a generic software framework for such flow solvers has been constructed that allows easy exchange of the s...

As we mark the centenary of Albert Einstein’s seminal contribution to both quantum mechanics and special relativity, we approach another anniversary — that of Einstein’s foundation of the quantum theory of solids. But 100 years on, the same experimental measurement that puzzled Einstein and his contemporaries is forcing us to question our understanding of how quantum matter transforms at ultra-...

The author demonstrates a stable Lagrangian solid modeling method, tracking the interactions of solid mass particles rather than using a meshed grid. This numerical method avoids the problem of tensile instability often seen with smooth particle applied mechanics by having the solid particles apply stresses expected with Hooke’s law, as opposed to using a smoothing function for neighboring soli...

The design of furnaces and boilers for solid fuels is supported increasingly by powerful softwares and ever faster computers. A round-robin over the most important CFD (computational fluid mechanics) models and softwares currently available shows, however, that numerical procedures for particle/turbulence interactions are not (yet) very advanced. Particle/fluid interphase slip is considered, bu...

The author demonstrates a stable Lagrangian solid modeling method, tracking the interactions of solid mass particles, rather than using a meshed grid. This numerical method avoids the problem of tensile instability often seen with Smooth Particle Applied Mechanics by having the solid particles apply stresses expected with Hooke’s law, as opposed to using a smoothing function for neighboring sol...

This paper surveys selected recent progress in geometric mechanics, focussing on Lagrangian reduction and gives some new applications to nonholonomic systems, that is, mechanical systems with constraints typified by rolling without slipping. Reduction theory for mechanical systems with symmetry has its roots in the classical works in mechanics of Euler, Jacobi, Lagrange, Hamilton, Routh, Poinca...

The first part of this paper describes some important underlying themes in the mathematical theory of continuum mechanics that are distinct from formulating and analyzing governing equations. The main part of this paper is devoted to a survey of some concrete, conceptually simple, pretty problems that help illuminate the underlying themes. The paper concludes with a discussion of the crucial ro...

The application of the finite element method to nonlinear solid mechanics problems results in the neccessity to repeatedly solve a large nonlinear set of equations. In this paper we limit ourself to problems arising in constrained solid mechanics problems. It is common to apply some variant of Newton’s method or a Newton– Krylov method to such problems. Often, an analytic Jacobian matrix is for...

We propose a method for generating well-shaped curved unstructured meshes using a nonlinear elasticity analogy. The geometry of the domain to be meshed is represented as an elastic solid. The undeformed geometry is the initial mesh of linear triangular or tetrahedral elements. The external loading results from prescribing a boundary displacement to be that of the curved geometry, and the final ...

Edge-based data structures are used to improve computational efficiency of Inexact Newton methods for solving finite element nonlinear solid mechanics problems on unstructured meshes. Edge-based data structures are employed to store the stiffness matrix coefficients and to compute sparse matrix-vector products needed in the inner iterative driver of the Inexact Newton method. Numerical experime...