Round 1

Reviewer 1 Report

The article introduces analytical solutions for 2D model problems targeting a micromorphic approach for gradient plasticity that can be used for the validation of numerical simulations thereof. Such models address the role of grain size in plastic deformation, which is of high practical relevance also from an engineering perspective.

• write all keywords with (or without) capital letters
• line 14: space before µm is missing
• line 31: minor grammatical error, either it should be "where hardening behavior might strictly depend" or "where hardening behavior strictly depends"
• line 97: "neglecting the kinetic energy": Does this cause a noticable dependency of accuracy on the density of a material, and/or the speed of deformation? Can you comment on that, especially if there is some effect of potential practical relevance in some application fields? Regarding speed of deformation, I'm wondering if it becomes relevant in some extreme cases like in case of deformation by an explosion or a fast projectile.
• line 201: "whic" should be "which"
• line 202: "is" doesn't seem to belong there
• Out of curiosity, is this approach for nano/micrometer grain size materials applicable also to extreme cases such as single crystals (say with a gliding plane for dislocations being the imperfection)? Also I wonder if there is some connection to boundary layers in fluid mechanics? Can you comment further on the boarders of applicability of this method? It may also be an opportunity to further highlight the relevance of the presented methods and results.
• line 261: I suppose you intended to replace the "..." by specific information.

Author Response

Response to Reviewer 1 Comments

We kindly appreciate the invested time and valuable feedback given by the reviewer.

Point1: write all keywords with (or without) capital letters

Response 1: corrected.

Point 2: line 14: space before µm is missing

Response 2: corrected.

Point 3: minor grammatical error, either it should be "where hardening behavior might strictly depend" or "where hardening behavior strictly depends"

Response 3: corrected.

Point 4: line 97: "neglecting the kinetic energy": Does this cause a noticable dependency of accuracy on the density of a material, and/or the speed of deformation? Can you comment on that, especially if there is some effect of potential practical relevance in some application fields? Regarding speed of deformation, I'm wondering if it becomes relevant in some extreme cases like in case of deformation by an explosion or a fast projectile.

Response 4: Neglecting kinetic energy is a standard assumption for implicit quasistatic numeric analysis where the inertial terms are ignored in the equilibrium which brings certain ease to implementation and computation. Those terms become important for dynamic analysis where density and speed of sound in the material play an important role in the general mechanical response.

Point 5: line 201: "whic" should be "which”

Response 5: corrected.

Point 6: line 202: "is" doesn't seem to belong there

Response 5: corrected.

Point 6: Out of curiosity, is this approach for nano/micrometer grain size materials applicable also to extreme cases such as single crystals (say with a gliding plane for dislocations being the imperfection)? also I wonder if there is some connection to boundary layers in fluid mechanics? Can you comment further on the boarders of applicability of this method? It may also be an opportunity to further highlight the relevance of the presented methods and results.

Response 5: The previous work of the same authors titled as “A Large-Deformation Gradient Damage Model for Single Crystals Based on Microdamage Theory” published in Applied Mechanics with the doi number doi.org/10.3390/app10249142 deals with those issues. We kindly bring this recently published work to the attention of the reviewer where a similar thermodynamically consistent gradient theory for single crystals is presented.

• Point 6: line 261: I suppose you intended to replace the "..." by specific information.

Response 5: fixed

Author Response File: Author Response.pdf

Reviewer 2 Report

Review of the article

The article  " Analytical solutions of model problems for large-deformation micromorphic approach to gradient plasticity" is a continuation of the previous article by the authors. Analytical solutions of the previously obtained equations are obtained.

There is one note on the article.

The following sentence from the abstract «The analytical solutions are also shown to match with the numerical results obtained by implementing a user element subroutine (UEL) to the commercial finite element software Abaqus/Standard» is not clear. In any case, analytical and numerical solutions must match. Otherwise, you need to look for an error. The resulting match simply indicates that the user element subroutine (UEL) is working correctly.

Taking into account what has been said, in the abstract and in the introduction it is necessary to clarify the meaning of this statement.

Comments for author File: Comments.docx

Author Response

Response to Reviewer 2 Comments

We kindly appreciate the invested time and valuable feedback given by the reviewer.

Point1: The analytical solutions are also shown to match with the numerical results obtained by implementing a user element subroutine (UEL) to the commercial finite element software Abaqus/Standard» is not clear. In any case, analytical and numerical solutions must match. Otherwise, you need to look for an error. The resulting match simply indicates that the user element subroutine (UEL) is working correctly.

Taking into account what has been said, in the abstract and in the introduction it is necessary to clarify the meaning of this statement.

Response 1: That statement is simply put in the paper in order to encourage the readers to consider the proposed theory in their analysis since it is straightforward to implement it into a commercial finite element software. Moreover, the consistent one to one match in the analytical solutions not only shows that the UEL is working correctly but also the analytical solutions are coherent within each other.

Author Response File: Author Response.pdf