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M. Jahanshahi's blog

A coarse-graining approach for modeling nonlinear mechanical behavior of FCC nano-crystals

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.

A hierarchical hyperelastic-based approach for multi-scale analysis of defective nano-materials

In this paper, a continuum–atomistic multi-scale method is presented in modeling the nonlinear behavior of nano-materials under large deformation. In order to identify an appropriate strain energy function for crystalline nano-structures with different percentages of spherical voids, the hyperelastic method is employed for specimen whose behavior is determined based on the molecular dynamics analyses. In the atomistic level, the EAM many-body potential is employed to model the interactions between the atoms of Al RVEs.

An atomistic-continuum multiscale method for modeling the thermomechanical behavior of heterogeneous nanostructures

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.

Validity of Cauchy-Born hypothesis in multi-scale modeling of plastic deformations

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

Multi-scale modeling of plastic deformations in nano-scale materials; Transition to plastic limit

Despite the controversial debates concerning a unified theory, the continuum plasticity has evolved during the last few decades and an uncountable number of articles has been published on the subject. The proposal of Lee to decompose the deformation gradient, F, into elastic part Fe and plastic part Fp (i.e. F=FeFp) combined with the principle of maximum plastic dissipation is used in many publications to formulate the ensuing developments.

A new integration algorithm for finite strain J2 plasticity based on midpoint rule

Midpoint and double step algorithms are interesting implicit algorithms for integrating the governing equations in plastic regime. Developing such algorithms for large deformation is complex due to the various configurations that have to be considered. In this paper a new algorithm is proposed for the integration of governig equations in large deformation plasticity which is based on midpoint rule. The time continuous model as well as algorithmic setup are discussed in details.

Nonlinear Axisymmetric Finite Element in FEAP

Hi All,

Where can I find the details of formulation (geometric and material stiffness matrices, deformation gradient, etc.) for nonlinear axisymmetric finite element in FEAP.

Best Regads


Dependence of R on C

Hi All,

I think that the problem of R (Rotation Tensor) and C (Right Cauchy-Green Tensor) dependence is interesting enough to raise it once again. I have been reading the following paper

R.T.Shield The rotation associated with large strains. 1973

Derivative of Metric Tensor

Hi All,

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



Derivative of F with Respect to C

Hi All,

The derivative of C (Right Cauchy-Green Tensor) with respect to F (Deformation Gradient) is computed very easily, but I'm not sure if there is an explicit way to compute the derivative of F with respect to C.


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