In the interior the stress should be induced via a constitutive law of elasticity, as a response to strain. The structure’s cost being an integral of the trace of is just as debatable. Both of these ideas were inspired by the famous Michell problem [21, 45]; the latter formulation, ...
To define the local elastic moduli as a function of length scale means averaging the stress and strain over each SV of the entire microstructure and then deter- mining the unique elastic moduli tensor for that SV. This is the equivalent of Eq. (2), but done for an SV, not over the ...
Graphene has an extremely high in-plane stiffness of 340 N/m as well as Young's modulus of 0.5 TPa. The strong carbon-carbon network cannot provide efficient energy dissipation approach for applied strain and therefore prone to crack at less than 5% strain [46]. Fortunately, theoretical ...
To calculate these properties, we first determine the axial Young’s modulus (E) by calculating the slope of the more or less straight line portion of the stress–strain curve. The tangent modulus (Et) is reported as the value of E at 50% of the maximum strength, as described in Eq. ...
modulus Gris of interest also because it is related to the zero shear limit first normal stress difference function (ψ1,0) and also to the ratio of elastic toviscous forcesinsimple shear flow(Dealy, 1982). Magnitudes of therelaxation modulusGr, calculated from recoverable strain, followed the...
The calculation of Young’s modulus from the stress–strain curves is limited to the low-strain region of less than 10% strain. The washing ability of the textile was characterized by putting the textile into a water-permeable protective sack, and the whole sack was put into a household ...
The samples were stretched at 2 mm/min (Instron model 5543) over a range of 1-10% strain and repeated across 3 cycles. The Young's modulus was then computed from the instantaneous slope of the stress-strain curve over this strain range (Supplemental Figure 2b). Suppleme...
Following the stress field calculations by Inglis [51], Griffith calculated the condition for crack growth per unit plate thickness as: (9)dUda=G=πσ2aE where E is the elastic modulus and G is a crack driving force or “strain energy release rate” per crack tip. The energy expended ...
The initial strain εo can be expressed as:(15)εo=σYk1n-σYEwhere σY and E are the initial yield stress and modulus of elasticity of the composite materials. The strength coefficient, k, and strain hardening exponent, n, of the composite materials are expressed as functions of the ...
strainεpl = ε − εelas the horizontal axis, whereεis the total strain, andεel = σ/Eis the elastic strain with a modulusE = 77.5 GPa. The sample is unloaded back to zero stress right after each jump. The first jump resulting in a non-recoverable strain ...