1887
banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
A micromechanics-based model for the Mullins effect
Rent:
Rent this article for
USD
10.1122/1.2206706
/content/sor/journal/jor2/50/4/10.1122/1.2206706
http://aip.metastore.ingenta.com/content/sor/journal/jor2/50/4/10.1122/1.2206706
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

(a) Experiment of Johnson and Beatty (1993) showing the Mullins effect for cycles with increasing amplitude; (b) Scheme of the prototypical model; (c) Energy density function; (d) Stress-strain diagram for a breakable chain.

Image of FIG. 2.
FIG. 2.

Regions of broken, active, and unloaded chains in the probability space . In (a) the current strain coincides with the maximum value attained in the loading history . In (b) we represent the case . Observe that for the loading paths with no new chain breaks and the behavior is elastic (ideal Mullins effect).

Image of FIG. 3.
FIG. 3.

Special distribution of broken chains, with a probability function concentrated on the straight line marked with bold line. In the figure we show the segments corresponding to active, unloaded, and broken chains. In (a) the present strain coincides with the maximum value attained in the loading history. In (b) we show the case .

Image of FIG. 4.
FIG. 4.

Mullins effect for a system with a probability (2.11) represented in (a), with , , and . We represent in (b) the elastic energy, in (c) the fracture energy, and in (d) the stress on the primary loading curve. In (f) we show the Mullins effect under the loading history represented in (e). Here, we take , , and a fraction of elastic chains with an energy density .

Image of FIG. 5.
FIG. 5.

Sketch of the experimental tests to deduce the probability function. In (a) we show the experiment needed under the simplifying assumption (2.8). In (b) we show the experiment for the general case to evaluate the average value of on a discrete grid shown in (c). In the figure .

Image of FIG. 6.
FIG. 6.

Hysteresis cycles for a system with a neo-Hookean type energy (4.1) with and . The breakable fraction of the material is assigned by a probability (4.5) with and a Gaussian probability with , , and is chosen by the normalizing condition (observe that by the incompressibility condition it follows that ). Here, .

Image of FIG. 7.
FIG. 7.

Mullins effect for azimuthal shear with under the hypothesis of a neo-Hookean energy (4.1) with , , and . The breakable material fraction is assigned by a probability (4.5) with and if and , otherwise. In (a) we show the probability function and in (b) the loading program. In (d) and (e) we show the rotation angle and the deformation on the primary loading curve as a function of for different values of the assigned moment. In (c) we show the moment-rotation relation. In (f) we represent the damage effect by plotting in a gray scale the fraction of broken chains for different values of the maximum moment.

Loading

Article metrics loading...

/content/sor/journal/jor2/50/4/10.1122/1.2206706
2006-07-01
2014-04-24
Loading

Full text loading...

This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: A micromechanics-based model for the Mullins effect
http://aip.metastore.ingenta.com/content/sor/journal/jor2/50/4/10.1122/1.2206706
10.1122/1.2206706
SEARCH_EXPAND_ITEM