Localized versus Diffuse Damage in Amorphous Materials

Abstract

Based on a Griffith approach, we study the behavior of disordered media constituted at the microscale by distributions of elastic and breakable links with variable activation and fracture thresholds. Depending on the microscopic distribution properties, the material may be characterized by an unstable strain domain, which gives the possibilities of having homogeneous or localized damage. Our simple model delivers a theoretical scheme to describe main experimental effects observed at the microstructure and macroscopic scale in disordered materials undergoing damage and relates them to the inhomogeneity properties of the material.

An energetic model for macromolecules unfolding in stretching experiments

“…We refer the reader to [29] for the technical details of the variational approach, whereas we here resume the loading -unloading behaviour of the deduced continuum damage model. Based on our irreversibility assumption (no refolding), we may observe that also in the continuum damage model the memory of the loading history depends on the only value L max of the maximum end-to-end length attained in the past that assigns n u .…”

“…Based on our irreversibility assumption (no refolding), we may observe that also in the continuum damage model the memory of the loading history depends on the only value L max of the maximum end-to-end length attained in the past that assigns n u . Indeed (see again [29] for technical details), during loading (L ¼ L max ) to determine the global minimum of the energy (6.3), we minimize both with respect to L and n u . Minimization with respect to L (i.e.…”

“…Similar considerations can be extended to the next elastic and dissipative steps, so that the total dissipation is Q ¼ P Q i ¼ P [jFj] i . Based on previous considerations and inspired by the model in [2,29], where the authors describe the hysteresis of filled polymers and spider silks, here we propose an energetic approach and describe the unfolding macromolecule as a two-state material. Similarly, a two-state energetic approach was proposed in [30] to describe the helix !…”

Thermo-mechanical response of rigid plastic laminates for greenhouse covering

“…Indeed this material exhibits a uniform temperature change field revealing a uniform damage and a monotone stress-strain curve without a horizontal plateau up to failure. These two possible damage behaviours have been theoretically predicted in the microstructure inspired N o n c o m m e r c i a l u s e o n l y damage model (De Tommasi et al, 2008) that obtain a homogeneous versus inhomogeneous damage behaviour according to the microstructure properties of the rubberlike material. Within the theoretical approach above recalled, the homogeneous damage behaviour of PMMA up to failure corresponds to a material with a diffuse damage characterised by a (still damage dependent) convex-type energy for which the energetic minima are not two-phase solutions ( Figure 7A, from Figure 3A by De Tommasi et al, 2008).…”

“…This phenomenon has been the subject of study and research giving rise to expressions (De Tommasi et al, 2008) about the thermoelastic and thermoplastic behaviour of materials based on a Griffith-like approach for dissipation effects observed in these materials. Now, based on this model, we attempt to give a qualitative interpretation of the different behaviours exhibited by the polymers here analysed.…”