By Bob Svendsen (auth.), Bernd Markert (eds.)
Modern computational suggestions, equivalent to the Finite point approach, have, seeing that their improvement numerous many years in the past, effectively exploited continuum theories for varied purposes in technological know-how and expertise. even supposing average continuum tools dependent upon the Cauchy-Boltzmann continuum are nonetheless of serious significance and are everyday, it more and more looks that fabric homes stemming from microstructural phenomena need to be thought of. this can be fairly real for inhomogeneous load and deformation states, the place lower-scale dimension results start to impact the macroscopic fabric reaction; whatever average continuum theories fail to account for. Following this concept, it's obtrusive that ordinary continuum mechanics needs to be augmented to seize lower-scale structural and compositional phenomena, and to make this knowledge obtainable to macroscopic numerical simulations.
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Extra info for Advances in Extended and Multifield Theories for Continua
Diebels and Steeb . 28 S. Diebels and D. Scharding To complete the theory strain measures have to be derived from the kinematic assumptions. According to the non-symmetric part of the stress tensor the strain tensor is also non-symmetric within the Cosserat theory and can be split in a symmetric and a skew-symmetric part: 3 ε¯ = grad u + E · ϕ¯ , 1 ε¯ sym = grad u + gradT u = ε , 2 3 1 ε¯ skw = grad u − gradT u + E · ϕ¯ . 2 (7) (8) (9) The Cosserat strain tensor consists of the displacement gradient and the permutation of ϕ, ¯ cf.
Cellular solids. Cambridge Solid State Science Series. : Micromorphic Media: Interpretation and homogenization. : A numerical homogenisation strategy for micromorphic continuua. : Numerical homogenisation of micromorphic continuua. : Two-scale modelling of micromorphic continua.
This issue, the consequences of second-order, and the formulation of configurational field and balance relations based on the Eshelby stress, for the case of extended or generalized crystal plasticity, all represent work in progress and will be reported on in the future. This also holds for much more sophisticated approaches that the current “mean-field” approaches for extended or generalized continua such as those based on distribution functions [e. , 3, 39, 49] or even statistical mechanics itself [e.
Advances in Extended and Multifield Theories for Continua by Bob Svendsen (auth.), Bernd Markert (eds.)