# What are displacement field and Deformation field?

I am studying mechanics of materials while I came across these terms called the displacement fields and the deformation fields. I am not able to understand the difference between them. Can someone explain it to me.

Conventions vary. As defined on that page, the deformation field $$\boldsymbol{\chi}_\kappa$$ represents the positions of the current points/elements/particles in an object right now as a function of a reference configuration (designated configuration $$\kappa$$) that typically corresponds to where the points were earlier: $$\boldsymbol{x}=\boldsymbol{\chi}_\kappa(\boldsymbol{X})$$.

In contrast, the displacement field $$\boldsymbol{u}$$ is a comparison of where the material particles are now relative to where they were earlier: $$\boldsymbol{u}=\boldsymbol{x}-\boldsymbol{X}$$.

(Again, conventions vary. In another context, deformation may be defined as motion other than the rigid-body motion consisting of translation and rotation. Care is required to ensure that the definitions are being applied consistently.)

Does this help clarify things?

• I am not able to understand how the deformation field is not dependent on time. For us to model the deformation of the material we have to map the point in the reference configuration X to the current configuration x. How is it possible to do this without knowing at which point of time we are talking about, ie without being dependent on time? – GRANZER Feb 22 '19 at 4:24
• @GRANZER: The example provided in this answer is just a simplification. The deformation is definitely a function of time. But the governing equations (see my answer to your other question) show that time is not important unless velocities are large. Therefore, a quasistatic (time-independent) assumption is often used. – Biswajit Banerjee Feb 22 '19 at 20:01
• In my previous comment, read " unless velocities are large" as " unless velocity changes are large". – Biswajit Banerjee Feb 22 '19 at 20:36
• @BiswajitBanerjee Here: nptel.ac.in/courses/105106049/lecnotes/mainch3.html, while explaining deformation field it is stated that the deformation field is independent of time. – GRANZER Feb 25 '19 at 7:20
• @GRANZER: The content in your link to too long for me to search for that explanation. If they actually say what you claim, they are wrong. – Biswajit Banerjee Feb 25 '19 at 21:17