Chiqun Zhang Amit Acharya
The utility of the notion of generalized disclinations in materials science is discussed within the physical context of modeling interfacial and bulk line defects like defected grain and phase boundaries, dislocations and disclinations. The Burgers vector of a disclination dipole in linear elasticity is derived, clearly demonstrating the equivalence of its stress field to that of an edge dislocation. We also prove that the inverse deformation/displacement jump of a defect line is independent of the cut-surface when its g.disclination strength vanishes. An explicit formula for the displacement jump of a single localized composite defect line in terms of given g.disclination and dislocation strengths is deduced based on the Weingarten theorem for g.disclination theory at finite deformation. The Burgers vector of a g.disclination dipole at finite deformation is also derived.
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 g.disclination_theory.pdf | 4.01 MB |
For the past few months, I have been working with Daniel Kawano (Rose-Hulman Institute of Technology) and Alyssa Novelia (U. C. Berkeley) on an online educational resource for rotations:
http://rotations.berkeley.edu/
While the site is still a work in progress, we hope it is of interest to the mechanics
community. We also welcome hearing from you about interesting articles, animations, and
simulations that are related to the subject matter of rotations.
Sincerely,
Oliver O'Reilly
p.s. In addition to incorporating javascript demonstrations, we are currently working on a section on rotations in continuum mechanics and rod theories in particular.
This Technology Brief describes Abaqus/Explicit
modeling of the ballistic impact of metal projectiles on metal targets.
It will demonstrate the utility of Abaqus/Explicit as a tool for
reducing the amount of experimental testing as well as assessing the
projectile residual velocities and time-resolved kinematics.
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| simulia-ballistic-perforation-simulation-12.pdf | 2.97 MB |
(to appear in International Journal of Fracture; Proceedings of the 5th Intl. Symposium on Defect andMaterial Mechanics)
Amit Acharya and Claude Fressengeas
The duality between terminating discontinuities of fields and the incompatibilities of their gradients is used to define a coupled dynamics of the discontinuities of the elastic displacement field and its gradient. The theory goes beyond standard translational and rotational Volterra defects (dislocations and disclinations) by introducing and physically grounding the concept of generalized disclinations in solids without a fundamental rotational kinematic degree of freedom (e.g. directors). All considered incompatibilities have the geometric meaning of a density of lines carrying appropriate topological charge, and a conservation argument provides for natural physical laws for their dynamics. Thermodynamic guidance provides the driving forces conjugate to the kinematic objects characterizing the defect motions, as well as admissible constitutive relations for stress and couple stress. We show that even though 'higher-order' kinematic objects are involved in the specific free energy, couple stresses may not be required in the mechanical description in particular cases. The resulting models are capable of addressing the evolution of defect microstructures under stress with the intent of understanding dislocation plasticity in the presence of phase transformation and grain boundary dynamics.
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| small_def_PTP_accepted_IJF.pdf | 318.76 KB |
| Discontinuity_incompatibility.pdf | 454.42 KB |
I want to find a reference to learn about motion groups SE(N). Any recommendations will be appreciated. Regards, Deepak Trivedi
- To introduce the concepts of position, displacement, velocity, and acceleration.
- To study 3D particle motion.
- To investigate particle motion along a curved path using different coordinate systems.
back to MACE-11010 Engineering Mechanics