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Noncommercial-Share Alike 2.0 Licence UK: England & Wales

https://creativecommons.org/licenses/by-nc-sa/2.0/uk/

Indentation using a Sliding Punch

A hodograph can be constructed for the case of a frictionless
(sliding) punch. With no friction assumed at the punch face, we can
postulate a different deformation pattern without the dead metal zone.

Indentation using a Sliding Punch

Rule 1:

Look for symmetry and reduce the geometry accordingly.

Look for symmetry and reduce the geometry accordingly.

Indentation using a Sliding Punch

Rule 2:

Label regions of the model which move relative to each other.

Label regions of the model which move relative to each other.

A particle will travel a path as shown. It is sheared
when meeting line AB to move parallel to AC, then sheared at BC to move
parallel to CD and finally sheared along BD to move parallel to DE.

Indentation using a Sliding Punch

Rule 3:

Define an origin of the hodograph, O, corresponding to a stationary component of the system.

Define an origin of the hodograph, O, corresponding to a stationary component of the system.

Indentation using a Sliding Punch

Rule 4:

Draw the velocity vector of the unknown force Q, or unit length (Oq), on the hodograph.

Draw the velocity vector of the unknown force Q, or unit length (Oq), on the hodograph.

Indentation using a Sliding Punch

Rule 5:

Draw vectors in the known directions of the moving components (Or , Os and Ot), relative to the origin O and to each other (qr, rs and st) on the hodograph.

Draw vectors in the known directions of the moving components (Or , Os and Ot), relative to the origin O and to each other (qr, rs and st) on the hodograph.

Indentation using a Sliding Punch

Rule 6:

Each vertex where these vectors intersect represents one (or more) of the labelled regions of the model.

Each vertex where these vectors intersect represents one (or more) of the labelled regions of the model.

Oq
defines motion of particles in region Q.

Indentation using a Sliding Punch

Rule 7:

Velocity vectors must be oriented parallel to slip planes due to conservation of matter.

Velocity vectors must be oriented parallel to slip planes due to conservation of matter.