Dear all,

    I have a question about the eigenvalue of the incompressible elasticity problem. Assume that we have a incompressible elasticity continuum body whose constitutive response holds normality. Obviously, we can treat the incompressiblity limit as a Lagrangian constraint and express the governing equation via the Lagrange-Multiplier method. If mixed finite element method is used, one can use Courant-Fischer theorem to show that the tangential stiffness matrix of  constrained variational form would have its maximum eigenvalue larger than its unconstrained counterpart and its minimum eigenvalue smaller than its uncsontrained counterpart.

Dear mechanicans,

    Can anyone explain to me what is Lavrentiev phenomenon? Thanks for your help.

WaiChing Sun

Dear mechanicans,

        For non-local continuum, is there a proper approach to determine the size of the REV in experiment? For the classical linear elastic continuum, one can measure the homogeneized stress and strain (or local averaged stress/strain)  and compute a homogeneized elastic constitutive tensor. However, I am not sure how to do it for non-local continuum, since the constitutive response is now sensititve to the gradient term. Any comment/suggestion is appreciated. 

Regards,

 WaiChing Sun

Dear all,

     Many numerical implementation of plasticity model uses spectral decomposition to represent the Cauchy stress, elastic strain,  such that stress update algorithm is written in the principal directions. As a result, I wonder what makes it benefical to write the stress update algorithm in spectral form? 

 Thanks,

WaiChing Sun

Many granular materials encountered in engineering practice are of irregular shapes that are not essentially smooth or rounded. However, in DEM, grains are idealized as spheres and ellipsoids and their surface are assumed to be sufficiently smooth. As a result, I wonder why there is no model of  irregular shapes and what is the difficulty on implementing such a model? Is there any recent work aimed to simulate grains of irregular shape? Thanks a lot. 

Does anyone knows where I can find any paper discuss the existence of potential functinoal for materials that violate the maximum plastic dissipation principle (due to non-convex yield function and/or non-associately fluw rule)?

Does anyone know if it is possible for diffuse and localized bifurcation to happen simontanously in a incompressible slab? If so, which one is more likely to occur first?

Hello, does anyone know where I can find more information about the infinite finite element or way to couple BEM/FEM to solve the problem in infinite 3D domain? Moreover, what is the difference between using a very long/large finite element and an infinite element?  Many thanks...