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[资源] 【资源】An Introduction to Computational Micromechanics

An Introduction to Computational Micromechanics
Lecture Notes in Applied
and Computational Mechanics
Volume 20
Series Editors
Prof. Dr.-Ing. Friedrich Pfeiffer
Prof. Dr.-Ing. Peter Wriggers
An Introduction
to Computational
Micromechanics
Corrected Second Printing
Tarek I. Zohdi •
Peter Wriggers
A key to the success of many modern structural components is the tailored behavior
of the material. A relatively inexpensive way to obtain macroscopically desired re-
sponses is to enhance a base material’s properties by the addition of microscopic
matter, i.e. to manipulate the microstructure. Accordingly, in many modern engi-
neering designs, materials with highly complex microstructures are now in use. The
macroscopic characteristics of modiﬁed base materials are the aggregate response
of an assemblage of different “pure” components, for example several particles or
ﬁbers suspended in a binding matrix material (Fig. 1.1). Thus, microscale inhomo-
geneities are encountered in metal matrix composites, concrete, etc. In the construc-
tion of such materials, the basic philosophy is to select material combinations to
produce desired aggregate responses. For example, in structural engineering appli-
cations, the classical choice is a harder particulate phase that serves as a stiffening
agent for a ductile, easy to form, base matrix material.
If one were to attempt to perform a direct numerical simulation, for example
of the mechanical response of a macroscopic engineering structure composed of
a microheterogeneous material, incorporating all of the microscale details, an ex-
tremely ﬁne spatial discretization mesh, for example that of a ﬁnite element mesh,
would be needed to capture the effects of the microscale heterogeneities. The re-
sulting system of equations would contain literally billions of numerical unknowns.
Such problems are beyond the capacity of computing machines for the foreseeable
future. Furthermore, the exact subsurface geometry is virtually impossible to ascer-
tain throughout the structure. In addition, even if one could solve such a system,
the amount of information to process would be of such complexity that it would
be difﬁcult to extract any useful information on the desired macroscopic behavior.
It is important to realize that solutions to partial differential equations, of even lin-
ear material models, at inﬁnitesimal strains, describing the response of small bodies
containing a few heterogeneities are still open problems. In short, complete solu-
tions are virtually impossible.>>>>>>>>>>>>>

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