Zero strain angle

It is important to realize that for any arrangement of more than two atoms the strain energy minimized structure does not have ideal (zero strain) distances and angles. This is demonstrated in the case of ethane (Fig. 2.2), where, due to the repulsion of the protons, the experimentally determined C-C distance in ethane of 1.532 A, which is well reproduced by empirical force field calculations, is slightly longer than the ideal C-C separation of 1.523 A used in the MM2 force field1. Further examples are presented in Table 2.1. With increasing substitution of the carbon atoms the C-C separation increases up to 1.611 A in tris(t-butyl)methane. 

Ideal (or equilibrium) bond lengths, valence angles, etc., are the distances and angles that give a zero strain energy with respect to that parameter (see force field). 

The interactions between substituents at the (formal) C=N double bond and the (allylic) substituents on C are also repulsive (1,3-allylic strain). This strain is only zero at angles of r = 120° and = -120°, where the formal C=N double bond and the C jH bond are ecliptic. Figure 9.2.4 shows at first the a//-anti-conformer with vjr = 120° and (j) = -120° and the numbering used in the conformational models. 

The relationship (Equation (26)) reveals that in a perfect liquid the phase shift angle of stress and strain is tcH. Figure 10 illustrates the phase shift 5for a viscoelastic body. It becomes obvious that zero strain amplitnde coincides with maxi-mnm of stress for a perfect liquid. In other words, in a perfect liqnid, stress and rate of strain are in phase rather than stress and strain. Strain lags behind stress by kH. It follows for the phase shift angle 5 ... 

Figure 13. Volumetric strain (angle of dilatancy is zero).

We see that cyclopropane has the largest strain energy of any cycloalkane, which is consistent with the extreme compression of its C—C—C bond angles from 109.5° to 60°. Cyclobutane and cyclopentane each have less strain, and cyclohexane, as expected, has zero strain. What is perhaps surprising is the presence of strain in rings of from 7 to 13 carbon atoms. This strain is primarily the result of torsional and steric strain caused by the fact that these rings are constrained to conformations that cannot achieve ideal bond and torsional angles. 

The reference 4 authors discuss criteria that should be applied when describing molecules with these molecular mechanics programs. Some of these are as follows (1) Check the error file for interactions not in the parameter set, because some programs will assign a force constant of zero to unrecognized atom types (2) check all interactions generating >5 kJ/mol of strain to determine, for instance, whether that bond or angle really is that strained or whether there is a parameterization or molecular structure problem and (3) check the... 

PP bead foams were subjected to oblique impacts (167), in which the material was compressed and sheared. This strain combination could occur when a cycle helmet hit a road surface. The results were compared with simple shear tests at low strain rates and to uniaxial compressive tests at impact strain rates. The observed shear hardening was greatest when there was no imposed density increase and practically zero when the angle of impact was less than 15 degrees. The shear hardening appeared to be a unique function of the main tensile extension ratio and was a polymer contribution, whereas the volumetric hardening was due to the isothermal compression of the cell gas. Eoam material models for FEA needed to be reformulated to consider the physics of the hardening mechanisms, so their... 

In search for true equilibrium shapes, a smaller system with a periodic length equal to 100 fl is used to study isolated islands. In Fig. 5, such isolated islands are examined as a function ofmisfit strain, e. All other input conditions are similar to those ofFig. 3. Whene = 0, the island becomes a semi-circle in the infinite-torque condition, whereas a lense shape with a dihedral angle of 120° should be established in the zero-torque condition. Albeit some facetting due to the discrete nature, the shapes are consistent with the Wulff construction. For 8 0, the shapes of e = 0 are used as the initial configurations. As e increases, the... 

An alternative approach to modeling the L-M-L angles is to set the force constants to zero and include nonbonded 1,3-interactions between the ligand atoms. In most force fields, 1,3-interactions are not explicitly included for any atoms, instead they are taken up in the force constants for the valence angle terms. This is an approximation because the 1,3-interactions are most often repulsive and thus the function used to calculate the strain energy arising from valence angle deformation should be asymmetric. It was shown that the nonbonded 1,3-interactions around the metal atom are in many cases a major determinant of the coordination... 

Figure 9-33a shows the predicted shear stress as a function of strain for the initial foam orientation depicted in Fig. 9-32. The stress grows continuously until at y = 1.15 a T1 reorganization occurs which brings the cell structure back to its starting state, and the stress jumps back to zero. Thereafter, the stress history repeats itself. Similar periodic stress patterns and stress jumps have been predicted for the three-dimensional tetrakaidecahedron foam model (Reinelt 1993). If the initial orientation is rotated through an angle of r/12 with respect to that shown in Fig. 9-32, the stress history also has jumps, but is aperiodic (see Fig. 9-33b). Aperiodic behavior is the norm, and periodic stress histories occur only for special initial orientations (Kraynik and Hansen 1986). These unsteady, discontinuous stress...

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