M. Jahanshahi's blog

The homogenized constitutive models that have been utilized to simulate the behavior of nanostructures are typically based on the Cauchy–Born hypothesis, which seeks the fundamental properties of material via relating atomistic information to an assumed homogeneous deformation field. It is well known that temperature has a profound effect on the validity and size-dependency of the Cauchy-Born hypothesis in finite deformations.

In this work, a new mixed finite element formulation is presented for the analysis of two-dimensional compressible solids in finite strain regime. A three-field Hu-Washizu functional, with displacement, displacement gradient and stress tensor considered as independent fields, is utilized to develop the formulation in spatial configuration. Certain constraints are imposed on displacement gradient and stress tensor so that they satisfy the required continuity conditions across the boundary of elements.

The ever-increasing growth of nano-technology has elevated the necessity for development of new computational methods that are capable of evaluating large systems at nano-scale. The existing techniques, such as the molecular dynamics, lack the ability to simulate large systems of practical size and time scales. In order to provide a realistic simulation of large models, the multi-scale methods such as coarse-graining, have therefore become very popular. The coarse-grained models have mostly been used to simulate large biomolecules, such as proteins, lipids, DNA and polymers.

In this paper, a computational hierarchical multiscale method is presented to investigate the effect of temperature on mechanical behavior of heterogeneous nanomaterials. The embedded-atom method many-body interatomic potential is employed to investigate the complex interaction between the atoms of copper–aluminum (Cu-Al) alloy at various temperature levels. The thermo-mechanical properties of Cu-Al alloy are studied at various percentages of Cu-Al. The Nose-Hoover thermostat is proposed for the molecular dynamics analysis.

The Cauchy-Born (CB) hypothesis has been widely used in multi-scale modeling of crystalline nano-structures.

Hi All,

How can we compute the derivative of metric tensor on one manifold with respect to metric tensor on another menifold?

Regards

Mohsen