42
D. Dudin and I. Keller
3.1 Introduction
The study of coupled processes in multicomponent metal alloys including diffusive
mass transfer, viscoelastic deformation, chemical reactions, and the evolution of
microstructures is a necessary condition for successful solution of various problems
in material mechanics. For example, such studies will allow researchers to optimize
the technology of surface treatment of machine parts to increase their durability
either by exposing them to the action of high-energy particle fluxes or subjecting
them to mechanical, ultrasonic, or laser peening followed by a diffusion-chemical
stage of formation of a gradient layer. The problems of predicting the resistance
of loaded machine parts and structures to chemical corrosion also require coupled
formulations.
Elements constituting an alloy might form a microstructure. And this is itself
a very interesting subjects in modern continuum mechanics and engineering: the
development of newly (scientifically) conceived materials (“metamaterials”) with
mechanical properties that cannot be found in nature (Barchiesi et al. 2018; Del
Vescovo and Giorgio 2014). These (macroscopic) properties are mainly determined
by the microstructure or nanostructure of the considered metamaterial rather than by
the chemical and physical properties of the materials constituting it at the microscopic
level. The reader is explicitly warned here: with the prefixes “macro” or “micro” and
we do not necessarily refer to a specific absolute characteristic length. We, instead,
refer generically to the length-scale where phenomena are observed and need to
be controlled (macro) and to one or more than one length-scales used to build the
architecture of the metamaterial (micro): in particular, the prefix “micro” does not
refer to micrometers or to any other specific length.
An example of mechanical metamaterials is pantographic structures (dell’Isola
et al. 2016a, b, c, 2017, 2019a, 2019b; Placidi et al. 2016, 2017).
In order to account for multiscale mechanical interactions, which taking place
for metamaterials, higher order gradient continuum theories can be a choice (Alibert
et al. 2003; Auffray et al. 2013; dell’Isola et al. 2012, 2015, 2016a, b, c; Rahali et al.
2015; Sciarra et al. 2007).
Rather complicated processes of transformations take place in solid and powder
metal materials under intense plastic deformations (Straumal et al. 2004). In the
literature, there are few studies on this subject (Knyazeva 2003, 2004, 2005), which,
however, do not close the gaps in the problem of interpreting the qualitative behavior
of coupled processes under the action of various external factors, which, in addition,
intends to settle a number of methodological issues.
To do this, the study of wave processes can be effectively used. Stephenson (1988)
and later (Brassart et al. 2018) used, as a framework for a qualitative investigation
of rather slow (non-dynamic) coupled diffusion and rheological processes, a onedimensional model problem, in which the relaxation of small spatial perturbations
of a uniform stationary solution was studied. Within this problem, the perturbed
behavior of the fields is described only by the diffusion and rheological relations,
which makes it possible to obtain the relationships between the relaxation times of
D. Dudin and I. Keller
3.1 Introduction
The study of coupled processes in multicomponent metal alloys including diffusive
mass transfer, viscoelastic deformation, chemical reactions, and the evolution of
microstructures is a necessary condition for successful solution of various problems
in material mechanics. For example, such studies will allow researchers to optimize
the technology of surface treatment of machine parts to increase their durability
either by exposing them to the action of high-energy particle fluxes or subjecting
them to mechanical, ultrasonic, or laser peening followed by a diffusion-chemical
stage of formation of a gradient layer. The problems of predicting the resistance
of loaded machine parts and structures to chemical corrosion also require coupled
formulations.
Elements constituting an alloy might form a microstructure. And this is itself
a very interesting subjects in modern continuum mechanics and engineering: the
development of newly (scientifically) conceived materials (“metamaterials”) with
mechanical properties that cannot be found in nature (Barchiesi et al. 2018; Del
Vescovo and Giorgio 2014). These (macroscopic) properties are mainly determined
by the microstructure or nanostructure of the considered metamaterial rather than by
the chemical and physical properties of the materials constituting it at the microscopic
level. The reader is explicitly warned here: with the prefixes “macro” or “micro” and
we do not necessarily refer to a specific absolute characteristic length. We, instead,
refer generically to the length-scale where phenomena are observed and need to
be controlled (macro) and to one or more than one length-scales used to build the
architecture of the metamaterial (micro): in particular, the prefix “micro” does not
refer to micrometers or to any other specific length.
An example of mechanical metamaterials is pantographic structures (dell’Isola
et al. 2016a, b, c, 2017, 2019a, 2019b; Placidi et al. 2016, 2017).
In order to account for multiscale mechanical interactions, which taking place
for metamaterials, higher order gradient continuum theories can be a choice (Alibert
et al. 2003; Auffray et al. 2013; dell’Isola et al. 2012, 2015, 2016a, b, c; Rahali et al.
2015; Sciarra et al. 2007).
Rather complicated processes of transformations take place in solid and powder
metal materials under intense plastic deformations (Straumal et al. 2004). In the
literature, there are few studies on this subject (Knyazeva 2003, 2004, 2005), which,
however, do not close the gaps in the problem of interpreting the qualitative behavior
of coupled processes under the action of various external factors, which, in addition,
intends to settle a number of methodological issues.
To do this, the study of wave processes can be effectively used. Stephenson (1988)
and later (Brassart et al. 2018) used, as a framework for a qualitative investigation
of rather slow (non-dynamic) coupled diffusion and rheological processes, a onedimensional model problem, in which the relaxation of small spatial perturbations
of a uniform stationary solution was studied. Within this problem, the perturbed
behavior of the fields is described only by the diffusion and rheological relations,
which makes it possible to obtain the relationships between the relaxation times of