Bounds for the dynamic modulus of unidirectional composites with bioinspired staggered distributions of platelets

Microstructure and Size Effects on the Mechanics of Two Dimensional, High Aspect Ratio Nanoparticle Assemblies

“…Understanding how Nature efficiently uses structural ordering in its composite materials has been the driving force behind countless theoretical and experimental investigations aimed at adopting its designs to engineered material systems (Zhang Z. Q. et al, 2010;Shao et al, 2012;Dutta et al, 2013;Barthelat, 2014;Ni et al, 2015;Wei et al, 2015;Qwamizadeh et al, 2017a;Henry and Pimenta, 2018). Yet, Nature consistently outperforms manufactured composites composed from stiff and aligned fibers embedded in low, or non-existent, volume fractions of compliant matrix material (Espinosa et al, 2009;Wei et al, 2012;Gu et al, 2016).…”

“…This can be accomplished by assuming the space between CG CNC fibers corresponds to the theoretical matrix material, with its mechanical properties govern by the non-bonded interactions between fibers (see Supplemental Information for details regarding the comparison of neat films to established continuum theories). Continuum theories have been successfully used to derive bounds for the initial elastic response of brick and mortar materials (Zhang Z. Q. et al, 2010;Lei et al, 2013;Qwamizadeh et al, 2017a). While short fiber CNC films qualitatively follow expected trends from relevant continuum theories (Zhang Z. Q. et al, 2010;Qwamizadeh et al, 2017a), the initial moduli of neat CNC films are consistently lower than predicted ranges (see Supplemental Information).…”

“…Continuum theories have been successfully used to derive bounds for the initial elastic response of brick and mortar materials (Zhang Z. Q. et al, 2010;Lei et al, 2013;Qwamizadeh et al, 2017a). While short fiber CNC films qualitatively follow expected trends from relevant continuum theories (Zhang Z. Q. et al, 2010;Qwamizadeh et al, 2017a), the initial moduli of neat CNC films are consistently lower than predicted ranges (see Supplemental Information). This discrepancy may be attributed to a number of factors.…”

“…However, accounting for the presence of pseudo-matrix material in the axial spaces between fibers of neat CNC films has only a negligible effect on the predicted initial moduli and, for the ranges of material parameters relevant to the films investigated herein, are not substantial enough to drive predictions outside the bounding cases. Another possible explanation for the discrepancy between the initial moduli of neat films and two phase continuum predictions is that continuum theories tend to assume the matrix material only supports shear loads (Ji and Gao, 2004;Zhang Z. Q. et al, 2010;Dutta et al, 2013;Lei et al, 2013;Ni et al, 2015;Wei et al, 2015;Pimenta, 2017, 2018;Qwamizadeh et al, 2017a;Abid et al, 2018;Kim et al, 2018). However, for neat films, substantial lateral expansion occurs during uniaxial extension due to the topological constraints of the CG bead-spring model.…”

“…It has been shown that hierarchal microstructures provide improved resiliency to stress concentrations near inclusions (Gorbatikh et al, 2010) and enhanced damage dispersion (Ritchie, 2011;Dutta and Tekalur, 2014;Mirzaeifar et al, 2015;Henry and Pimenta, 2018). These observations are part of a large and ever growing body of work establishing that staggered microstructures tend to be the most favorable architectures for simultaneously producing stiffness, strength, and toughness in thin, macroscopic materials (Espinosa et al, 2009;Zhang Z. Q. et al, 2010;Barthelat and Zhu, 2011;Dutta et al, 2013;Barthelat, 2014;Ni et al, 2015;Pro et al, 2015;Qwamizadeh et al, 2015Qwamizadeh et al, , 2017aAbid et al, 2018).…”