plane stress vs generalized plane strain vs plane strain

Posted Jun 12, 2024, 12:54 a.m. EDT Structural Mechanics, Physics Interfaces, User Interface Version 6.0 1 Reply

Jung Tae Lee

Send Private Message Flag post as spam

Please login with a confirmed email address before reporting spam

When solving 2D plane stress problem, the results are different in generalized plane strain (GPS) and plane strain (PS) both cases with external strain node applied. Which seems quite obvious because two conditions have different geverning equations. But I would like to know what exactly the plane strain does with the external strain node applied (under each linear elastic material node). Also I would like to know why the GPS results are not consistent with the 3D midplane results.

As an example, let us look at a simple solenoid case comparing the 3D midplane results with 2D plane_PS(PS+external strain) and 2D plane_GPS(GPS+external strain). All three models have the same loading condition which results from Lorentz force by applying 200 A/mm^2 in phi-direction. For 2D models, the force in z-direction is zero so this effect was accounted for by giving the resultant strain in z-direction (-0.0001464) obtained from the 3D model.

Thre results comparison for three models are shown in the figures in the image link-> https://postimg.cc/gallery/H851c4p 3D model and 2D_PS model shows consistent results with only difference in z-direction strain. It seems that the 2D_PS model solves the problem ignoring the external stress at first then recalculate the stress in z-direction with the given external strain. But then external strain value is not reflected in the final result (just displays 0 just as default value for typical PS condition). While 2D_GPS shows about 10% of difference in strain as well as in displacement, the stress in x and y-direction are consistent with other models. But then the strain and stress in z-direction shows entirely different results! This is where my mind is blowing.

My guess for this situation for now is that there should be an additional contraint to the 2D_GPS model (maybe some kind of weak constraint). This may do some trick in reformulating the problem so that the resultant strain match the given external strain. So I searched about this and found a blog from 2017 about GPS problem: https://www.comsol.com/blogs/how-to-model-generalized-plane-strain-with-comsol-multiphysics. But this has a Singular matrix problem and cannot be solved by any means.

Does anybody have a clue on why this kind of deviation occurs in 2D_GPS model and a way to resolve?

Attachments:

Reply

1 Reply Last Post Jun 12, 2024, 2:45 a.m. EDT

Henrik Sönnerlind COMSOL Employee

Please login with a confirmed email address before reporting spam

Posted: 5 months ago

Updated: 5 months ago

Without looking at your problem in detail, the general behaviour of the 2D formulations is based on the full 3D Hooke's law, expressed as

Whatever plane conditions that are imposed, are imposed on this equation.

Please note that the blog post you mention was written before generalized plane strain was a built-in option.

A more recent blog post discussing the various 2D options:

https://www.comsol.com/blogs/what-is-the-difference-between-plane-stress-and-plane-strain

Here, the effects of an imposed out-of-plane strain (in terms of thermal expansion) is discussed in some detail.

-------------------
Henrik Sönnerlind
COMSOL

Reply

Please read the discussion forum rules before posting.

Discussion Forum Rules and Guidelines

The goal of COMSOL Access is to provide a forum for you to communicate effectively with COMSOL as well as your colleagues within the multiphysics simulation community. This involves providing you with access to technical support and downloads of the latest {:comsol} software releases, as well as the ability to share your comments and work with other users of the {:comsol} software through forums such as the blog, discussion forum, and Application Exchange. In order to make this an efficient and pleasant experience for you and other members of COMSOL Access, we ask that you follow a few rules and guidelines.

When registering for COMSOL Access, you agree to provide your complete and truthful information for all fields requested on your COMSOL Access account registration page. You also agree to maintain the accuracy of all information associated with you on your COMSOL Access account. You agree to maintain your COMSOL Access account for use solely by you, not to share your username and password with anyone else, and to take appropriate precautions to restrict access to your username and password from others. Furthermore, you agree not to submit any information relating to your employer through your COMSOL Access account without your employer’s authorization. Should you use a COMSOL Access account associated with an employer, you agree to immediately discontinue using that account upon termination of that employment.

The moderators of the forums will remove any generally objectionable material as quickly as possible. You acknowledge that all posts made to these forums express the views and opinions of the author and not the administrators, moderators, or webmaster (except for posts by these people). Hence, they will not be held liable.

You agree not to post or link to any material that is abusive, obscene, vulgar, slanderous, hateful, threatening, sexually oriented, or that infringes upon or violates any third-party rights or any other material that may violate any applicable laws. You agree that you will not otherwise use your COMSOL Access account to violate or to assist anyone in violating any law. Engaging in any activity in violation of these COMSOL Access rules and guidelines may lead to you being immediately and permanently banned from COMSOL Access. The IP address of all posts is recorded to aid in enforcing these conditions. You agree that the webmaster, administrator, and moderators of the forums have the right to remove, move, or close any topic at any time as they see fit. As a user of COMSOL Access, you agree to any information you have entered into any of the forums being stored in a database.

You agree that you will not use your COMSOL Access account in violation of any applicable export control laws. You represent and warrant that you are not subject to any comprehensive sanction or embargo by the U.S. or any other country, nor are you identified on any list maintained by the U.S. government that identifies persons for which the U.S. maintains restrictions. Further, you represent and warrant that you are not subject to any restriction on the receipt of technology or products under the export control laws of the U.S. or any other country.

Basic Rules

Flaming: Do not post any messages that harass, insult, belittle, threaten, or flame another member or guest. Debates are fine, but argue with the point, not the person.
Trolling: Do not post with the purpose of starting a dispute. Note that a person disagreeing with your opinion is not considered trolling; keep it civil, even if you are sure that the other person is wrong. Anything seen as trolling will result in you being banned.
Spamming: Posts without content or containing nonsense waste space and everyone's time. Spam will be removed from the forum.
Offensive Posts, Links or Images: Do not use profanity, racial, ethnic, religious, or other slurs or any other offensive material.
Advertising: Posting of advertisements for products or services, links to auctions, affiliate links, links to promote websites, and so forth is not allowed.
Disclosure of Personal Information: Do not disclose any other member's email, real name, address, phone number, IP address, or other personal information. This includes posting contents of emails and private messages without the sender's consent. Do not bring personal disputes into the forums. Bans and warnings issued to other users are considered personal information.
Misleading Titles: The subject line of the post should be as informative as possible about the content of the post. This also reduces the amount of duplicate posts.
Thread Hijacking: Taking a thread off-topic to pursue one's own agenda is not permitted.
Piracy: Do not upload, post, email, transmit, or otherwise make available any content that infringes upon any patent, trademark, trade secret, copyright, or other proprietary rights ("Rights") of any party. This includes COMSOL model files created by a forged or illegitimate license.
Honesty: Users must provide truthful information in creating their COMSOL Access account.

These rules are subject to change. The moderators reserve the right to remove, edit, or move posts at their discretion. The COMSOL Access administrators will reserve the right to permanently remove a user account without notice if any of the rules are not followed. Particular services accessible with your COMSOL Access account may be subject to additional rules. You agree to comply with all rules applicable to each service you access through your COMSOL Access account.

Posting Guidelines

When posting, understand that you are trying to communicate with other people. Although many COMSOL Access members are not fluent in English, the official language of this forum is English.

Here are some important guidelines of language:

Write in English.
If you are familiar with LaTeX, please use this to write mathematical equations.
Always do a quick check for spelling/grammar mistakes.
Format your post in a legible manner. Use the Preview button often.
Be concise and articulate as much as possible.
Use the Enter key to create paragraphs.
Capitalize correctly. It is difficult to read posts that are written entirely in uppercase or lowercase.
Use correct punctuation. Avoid run-on sentences.
Try to avoid using “text speak”, “net speak”, or slang. The purpose of language is to be understood.
Never invent acronyms and use as few acronyms as possible. For example, write "COMSOL Multiphysics" and not "CMP".
Review your post before publishing it. Try to catch typos.
Please check to see if a topic has already been posted. Do not post multiple threads on the same topic.

Disclaimer

By submitting content to the forums, you hereby grant COMSOL a nonexclusive, royalty-free, perpetual, worldwide, and unrestricted license to reproduce, publicly display, publicly distribute, and prepare derivative works of the content. COMSOL hereby grants you a license to copy and/or use content from the forums solely for your own internal purposes. COMSOL provides the forum service for the benefit of our users to share content with the community. All content is provided "as is" without warranty of any kind, express or implied, including without limitation, warranties of merchantability, noninfringement, design, operation, and fitness for a particular purpose, and the entire risk as to the quality and performance of the programs is with you.

Neither COMSOL, the authors, nor the copyright owners of submitted materials warrant that the programs will be error-free, uninterrupted, virus-free, secure, and suitable for your needs, produce specific results, or that errors or failures will be corrected. Comments on supplied content should be sent to the author or copyright owner through the tools provided in the forums.

Please log in to post a reply.

Discussion Forum