hi Nanshu Lu,
i'm savita jain. i have project some what related to your topic. can i have results of your final coparision of slip line and FEM solutions.please let me know about any progress in your work.
I work with AVI in my research so I have included a MATLAB implementation of AVI for the 1-D harmonic oscillator. The code will solve the equation a + gamma * v + (k1 + k2 + k3) x = 0 with any initial conditions x(0) and v(0). Here the spring constant has been artifically split into three spring constants to simulate multiple potentials. If there is only one potential AVI simplifies to the usual Velocity Verlet integrator. The friction term is absorbed into the k1 term in the implementation. The main idea in the implementation is to construct the propagation matrix for the system (x,v) for the different potentials.
Given the growing interest in poroelasticity within this forum, I thought I would post the link to "Poronet" -- the poromechanics internet resources network. In particular, there is a nice long pdf chapter on the fundamentals of poroelasticity from Detournay and Cheng, 1993, which has become one of the standard references in the field.
In between stress and strain, which one is the more fundamental physical quantity? Or is it the case that each is defined independent of the other and so nothing can be said about their order? Is this the case?
I recently used focused ion beam to fabricate some small structures, such as free-standing micro-beams, in LIGA Ni thin films and applied cyclic loads to those small micro-beams. In such a way, dynamics of fatigue crack initiation and growth can be revealed. Part of my results has been attached with this post.
A recent string of papers originated from Persson's paper in the physics literature contain a number of interesting new ideas, but compare, of the many theories for randomly rough surfaces, only Persson's and Bush et al, BGT. These papers often assume the original Greenwood and Williamson (GW) theory [1] to be inaccurate, but unfortunately do not test it, assuming BGT to be its better version. The original GW however is, I will show below, still the best paper and method today (not surprisingly, as not many papers have the level of 1300 citations), containing generally less assumptions than any other model, including the constitutive equation which does not need to be elastic! I just submitted this Letter to the Editor: On "Contact mechanics of real vs. randomly rough surfaces: A Green's function molecular dynamics study" by C. Campaña and M. H. Müser, EPL, 77 (2007) 38005. C. Campaña and M. H. Müser also make several questionable statements, including a dubious interpretation of their own results, and do not even cite the original GW paper; hence, we find useful to make some comments.
Experimentally, loading to a mechanical system can be applied either through the displacement control or the force control.
However, the responses of the system can only be measured in displacements, and hence strains.
Determination of Strain Gradient Elasticity Constants for Various Metals, Semiconductors, Silica, Polymers and the (Ir) relevance for Nanotechnologies
Strain gradient elasticity is often considered to be a suitable alternative to size-independent classical elasticity to, at least partially, capture elastic size-effects at the nanoscale. In the attached pre-print, borrowing methods from statistical mechanics, we present mathematical derivations that relate the strain-gradient material constants to atomic displacement correlations in a molecular dynamics computational ensemble. Using the developed relations and numerical atomistic calculations, the dynamic strain gradient constants have been explicitly determined for some representative semiconductor, metallic, amorphous and polymeric materials. This method has the distinct advantage that amorphous materials can be tackled in a straightforward manner. For crystalline materials we also employ and compare results from both empirical and ab-initio based lattice dynamics. Apart from carrying out a systematic tabulation of the relevant material parameters for various materials, we also discuss certain subtleties of strain gradient elasticity, including: the paradox associated with the sign of the strain-gradient constants, physical reasons for low or high characteristic lengths scales associated with the strain-gradient constants, and finally the relevance (or the lack thereof) of strain-gradient elasticity for nanotechnologies.
