Published online by Cambridge University Press: 23 November 2009
When a continuum region consists of either a rigid strain hardening or an elastic strain hardening material, the strains and displacements of the region for a given history of loading can be determined. If, on the other hand, the continuum region is made of either a rigid perfectly plastic or an elastic perfectly plastic material the situation is quite different. A qualitative picture of the behaviour of such a material was discussed at the very start of this volume. For example, at sufficiently small loads the region can either remain rigid or experience small elastic deformations. As the loading increases parts of the continuum region can become plastic, but the region as a whole can withstand collapse due to the restraining effect of elastic regions. As the loads increase, larger regions of the continuum can experience plastic yield and eventually the continuum region can undergo ‘indefinite’ plastic deformations leading to what we term ‘collapse’ of the region. Two interesting examples that illustrate the definition of a ‘collapse’ state in the context of limit analysis are given by Drucker et al. (1952). In this process we implicitly assume that the deformations experienced by the continuum region are small enough so that changes in the geometry of the region may be neglected and that all the deformations take place in a quasi-static fashion so that any dynamic effects can be ignored.
To save this book to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Find out more about the Kindle Personal Document Service.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.