This paper addresses a classical and largely unsolved problem: given a structural
component constructed of a heterogeneous elastic material that is in equilibrium under the …

A theory of a posteriori estimation of modeling errors in local quantities of interest in the
analysis of heterogeneous elastic solids is presented. These quantities may, for example …

In this paper, we develop a theory and methodology for obtaining approximate solutions to
boundary value problems describing the deformation of highly heterogeneous linearly …

In this paper, a methodology is introduced for the development of adaptive methods for
hierarchical modeling of elastic heterogeneous bodies. The approach is based on the idea …

This paper addresses the general problem of modeling local features of the response of
highly heterogeneous elastic materials with random distributions of the material constituents …

Predictability of the response of structural components to the action of external forces hinges
on the selection of an appropriate mathematical and computational model of the governing …

We develop computational models and adaptive modeling strategies for obtaining an
approximate solution to a boundary value problem describing the finite deformation plasticity …

This manuscript presents the results of a detailed research investigation on a fundamental
problem in wave mechanics: the propagation of stress waves in heterogeneous elastic …

We consider combined material model and FE-mesh adaptivity in the context of
computational meso–macro-scale modeling (CMM), whereby the coupling between different …

The discovery of efficient and accurate descriptions for the macroscopic behavior of
materials with complex microstructure is an outstanding challenge in mechanics of …