Numerical
modeling of interface mechanical problems at the microscopical level
Alberto
Carpinteri, Marco Paggi, Giorgio Zavarise*
Department of Structural and Geotechnical
Engineering, Politecnico di Torino,
Corso Duca degli Abruzzi 24, 10129 Torino, Italy
* Tel.: (+39)0115644818; Fax: (+39)0115644899;
e-mail: giorgio.zavarise@polito.it
Interface mechanical problems in
heterogeneous materials require different physical interpretations depending on
the bonding conditions of the interface and on the type of loading. For
instance, cohesive formulations are usually adopted when studying decohesion
phenomena occurring at the interfaces between two constituent materials bonded
together. On the other hand, normal contact problems and frictional phenomena
involving rough disbonded surfaces require the use of microscopical contact
constitutive laws in order to achieve a high accuracy of the mechanical
predictions [1]. Hence, in order to fully characterize damage initiation and
progress into heterogeneous materials and their size-scale dependence [2,3],
more sophisticate numerical formulations have to be invoked.
With this objective
in mind, nonlinear models pertaining to Fracture and Contact Mechanics are
profitably accounted for to formulate a unified interface constitutive law [4].
Zero-thickness interfaces are then modeled as special contact elements in the
FEAP code and a local constitutive law is established both in tension and in
compression. The weak form for this new formulation is developed and the
consistent linearization is carried out.
Moreover, it has to
be pointed out that the correct use of such generalized constitutive laws
requires a detailed geometrical formulation, to obtain the same degree of accuracy
for both the constitutive laws and the interface geometrical discretization. In
fact, if an oversimplified contact geometry is combined with nonlinear
constitutive laws, the results obtained can be unreliable. Therefore, a
particular attention is paid to the interface discretization. To achieve a high
accuracy of the predictions, numerical methods usually require a high mesh
density with a mesh refinement which involves not only the interface, but also
the discretization of the continuum. To overcome this major shortcoming of
standard methods, the virtual node technique [5] is employed in order to
decouple the discretization of the interface from that of the continuum, saving
both computational time and memory. Several examples showing the evolution of
damage in fiber-reinforced metal matrix composites under both monotonic and
cyclic loading conditions are proposed to demonstrate the effectiveness of this
approach.
[1]
Zavarise G.,
Borri-Brunetto M., Paggi M.: On the reliability of microscopical contact
models, Wear, Vol. 257, pp. 229-245 (2004).
[2]
Carpinteri A.: Cusp catastrophe
interpretation of fracture instability, J. Mech. Phys. Solids, Vol. 37, pp. 567-582 (1989).
[3]
Wriggers P.,
Zavarise G., Zohdi T.I.: A computational study of interfacial debonding damage
in fibrous composite materials, Comp. Mat. Sci., Vol. 12, pp. 39-56 (1998).
[4]
Paggi M.: Interface Mechanical Problems in
Heterogeneous Materials, Ph.D. Thesis,
Politecnico di Torino (2005).
[5]
Zavarise G.,
Boso D., Schrefler B.A.: A contact formulation for electrical and mechanical
resistance, Proc. CMIS, III Contact Mechanics International Symposium, pp.
211-218, Praja de Consolacao, Portugal, 2001.