Nature of displacement and the deformation tensor

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SUMMARY

The discussion centers on the relationship between displacement and the deformation tensor in the context of material deformation. It establishes that the deformation tensor is defined as the derivative of the displacement vector, specifically mapping the differential vector between two points in undeformed material to their corresponding points in the deformed state. The deformation gradient tensor plays a crucial role in this mapping, indicating that the deformation is not merely the displacement itself but a representation of how the material's configuration changes. The strain is identified as the change in length resulting from this deformation.

PREREQUISITES
  • Understanding of deformation gradient tensor
  • Familiarity with displacement vectors
  • Knowledge of strain concepts in material science
  • Basic principles of continuum mechanics
NEXT STEPS
  • Study the mathematical formulation of the deformation gradient tensor
  • Explore the relationship between strain and stress in materials
  • Learn about different types of strain measures (e.g., engineering strain, true strain)
  • Investigate applications of deformation tensors in finite element analysis
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Material scientists, mechanical engineers, and students studying continuum mechanics who seek to deepen their understanding of deformation and strain in materials.

mohammed El-Kady
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If we have two points P and Q in undeformed material and after deformation they become P' and Q'. The deformation tensor is the derivative of the displacement. What is the displacement? vector PP'? or the change from PQ to P'Q'?
is the second question is the strain "change in length".
Why the deformation is the derivative of displacement, why not the displacement itself? does it has scientific reason or just choice?
 
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mohammed El-Kady said:
If we have two points P and Q in undeformed material and after deformation they become P' and Q'. The deformation tensor is the derivative of the displacement. What is the displacement? vector PP'? or the change from PQ to P'Q'?
is the second question is the strain "change in length".
Why the deformation is the derivative of displacement, why not the displacement itself? does it has scientific reason or just choice?
The deformation gradient tensor maps the differential vector between P and Q into the differential vector between P'and Q'.
 

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