Continuum Mechanics and Thermodynamics,
Journal Year:
2024,
Volume and Issue:
36(6), P. 1413 - 1453
Published: Aug. 5, 2024
Abstract
Starting
from
the
seminal
works
of
Toupin,
Mindlin
and
Germain,
a
wide
class
generalized
elastic
models
have
been
proposed
via
principle
virtual
work,
by
postulating
expressions
energy
enriched
additional
kinematic
descriptors
or
higher
gradients
placement.
More
recently,
such
adopted
to
describe
phenomena
which
are
not
consistent
with
Cauchy-Born
continuum,
namely
size
dependence
apparent
moduli
observed
for
micro
nano-objects,
wave
dispersion,
optical
modes
band
gaps
in
dynamics
heterogeneous
media.
For
those
structures
mechanical
response
is
affected
surface
effects
predominant
respect
bulk,
scale
external
actions
interferes
characteristic
heterogeneities.
Generalized
continua
very
often
referred
as
media
microstructure
although
rigorous
deduction
lacking
between
specific
microstructural
features
constitutive
equations.
While
forward
modelling
predictions
observations
provided,
actual
at
multiple
scales
can
be
used
inversely
integrate
some
lack
information
about
model.
In
this
review
paper,
investigated
standpoint
inverse
problems,
focusing
onto
three
topics,
tightly
connected
located
border
multiscale
experimental
assessment,
namely:
(i)
parameter
identification
models,
including
asymptotic
methods
homogenization
strategies;
(ii)
design
non-conventional
tests,
possibly
integrated
full
field
measurements
advanced
modelling;
(iii)
synthesis
meta-materials,
microstructures
fit
target
behaviour
macroscale.
The
scientific
literature
on
media,
focus
gradient
fathomed
search
questions
typical
problems
theory
issues
related
estimation,
providing
hints
perspectives
future
research.
Mechanics of Advanced Materials and Structures,
Journal Year:
2025,
Volume and Issue:
unknown, P. 1 - 18
Published: Jan. 2, 2025
The
classical
multiscale
homogenization
methods
can
only
take
into
account
the
pure
microstructural
effect,
resulting
in
inability
to
accurately
capture
nonlocal
interactions
emerged
from
underlying
microstructures
of
metamaterial
structures.
This
paper
explores
interplay
mechanism
that
artificial
and
develops
a
well-posed
microstructure-emerged
method
capable
capturing
nonlocality
is
strictly
related
its
extrinsic
intrinsic
length
scales.
First,
we
propose
novel
concentrated
element
model
accounts
for
both
effect
interaction
describe
static
response
trusses.
not
considers
but
also
further
interaction,
thus
providing
more
comprehensive
description
Then,
based
on
model,
developed
trusses
with
an
accuracy
comparable
high-fidelity
numerical
methods.
Since
well-posed,
closed-form
solution
displacement
truss
obtained.
High-fidelity
finite
simulations
show
effective
moduli
different
have
significant
effects,
especially
high
porosity.
Results
indicate
provides
robust
accurate
representation
truss,
significantly
outperforming
consider
effects.
