Multi‐scale modeling of heterogeneous structures with inelastic constitutive behaviour

Abstract

PurposeTo provide a computational strategy for highly accurate analyses of non‐linear inelastic behaviour for heterogeneous structures in civil and mechanical engineering applicationsDesign/methodology/approachAdapts recent developments on mathematical formulations of multi‐scale problems to the recently developed component technology based on C++ generic templates programming.FindingsProvides the understanding how theoretical hypotheses, concerning essentially the multi‐scale interface conditions, affect the computational precision of the strategy.Practical implicationsThe present approach allows a very precise modelling of multi‐scale aspects in structural mechanics problems and can play an essential tool in searching for an optimal structural design.Originality/valueProvides all the ingredients for constructing an efficient multi‐scale computational framework, from the theoretical formulation to the implementation for parallel computing. It is addressed to researchers and engineers analysing composite structures under extreme loading.

Partitioned solution to fluid–structure interaction problem in application to free-surface flows

“…We use for this work the Communication Template Library (CTL, see [57,61]) that allows to re-use existing codes in a generic way, either called as libraries on the same computer, or as remote executables through network. With the CTL, we are able to couple existing stand-alone software, in a quite straightforward way, even if they are programmed in different langages (Fortran for the structure part, C++ for the fluid part), and to conserve the inner parallelism of each component.…”

Elements of a Computational Framework for Coupled Simulations

“…For the programmer it looks and feels like an object in an object oriented language (OOL) like C++, where it was originally formulated in. In languages like the FORTRAN dialects, which lack objects, it looks like a subroutine call ( [5], [8], and [9]). To take as an example fluid structure interaction ( [1], [7], and [8]), the structure solver would be wrapped inside a component, the fluid solver as well, and may be the mesh-movement in an arbitrary Lagrangian-Eulerian formulation would be a separate component as well.…”

“…These should also be re-used. One possibility [5] is through the formulation of the coupling not in form of the equilibrium equation, but equivalently through the solvers fixed-point equation. The Poincaré-Steklov operators contain this in some sense, although from a point of numerical efficiency www.gamm-mitteilungen.org one does not have to iterate to complete convergence in the sub-problems in the early stages of the global iteration.…”

“…In the simplest setting we have two similar problems at different scales ( [5], [2]). Computation on the small scale is usually not possible/too expensive/too time-consuming.…”

Two‐scale computational homogenization of magneto‐electric composites

“…In detail, we will use the so-called FE 2 -method, which allows for the FE solution of a macroscopic boundary value problem (BVP) in consideration of the microscopic response of attached representative volume elements (RVE), see e.g. [27][28][29][30][31][32][33][34][35][36][37][38]. Recently, the method has been extended to the homogenization of coupled phenomena as for instance in the framework of thermo-and electro-mechanics [39][40][41][42][43][44][45][46].…”