---
_id: '64187'
abstract:
- lang: eng
text: Carbon fiber-reinforced plastics (CFRPs) have become increasingly
significant in recent decades due to their remarkable mechanical properties and
lightweight nature. This study aims to advance the understanding and simulation
of CFRP behavior through the development of a hyperelastic-plastic-damage homogenization
method combined with mean-field theory. The material responses of both the fiber
and matrix are modeled using strain energy functions that account for damage evolution,
while a complete linearization of the homogenization process is derived to ensure
the consistent implementation of the Newton–Raphson iteration scheme in large
deformation simulations. The innovative aspect of this work lies in the constitutive
linearization for the hyperelastic-plastic-damage formulation within a mean-field
homogenization framework, providing an efficient Newton algorithm for modeling
the nonlinear behavior of CFRP. A failure criterion for the hyperelastic model
of fibers is introduced, along with a damage saturation variable in rate form
for the matrix, effectively capturing damage evolution. Through discrete formulations
for the homogenization, the proposed model’s capability is demonstrated via three
numerical examples and validated against experimental investigations, proving
its effectiveness and reliability in simulating CFRP damage.
article_number: '10812865261420809'
author:
- first_name: Yingjie
full_name: Zhan, Yingjie
id: '93591'
last_name: Zhan
- first_name: Ismail
full_name: Caylak, Ismail
last_name: Caylak
- first_name: Richard
full_name: Ostwald, Richard
id: '106876'
last_name: Ostwald
orcid: 0000-0003-2147-8444
- first_name: Rolf
full_name: Mahnken, Rolf
id: '335'
last_name: Mahnken
- first_name: Enrico
full_name: Barth, Enrico
last_name: Barth
- first_name: Eckart
full_name: Uhlmann, Eckart
last_name: Uhlmann
citation:
ama: Zhan Y, Caylak I, Ostwald R, Mahnken R, Barth E, Uhlmann E. A fully implicit
mean-field damage formulation with consistent linearization at large deformations.
Mathematics and Mechanics of Solids. Published online 2026. doi:10.1177/10812865261420809
apa: Zhan, Y., Caylak, I., Ostwald, R., Mahnken, R., Barth, E., & Uhlmann, E.
(2026). A fully implicit mean-field damage formulation with consistent linearization
at large deformations. Mathematics and Mechanics of Solids, Article 10812865261420808.
https://doi.org/10.1177/10812865261420809
bibtex: '@article{Zhan_Caylak_Ostwald_Mahnken_Barth_Uhlmann_2026, title={A fully
implicit mean-field damage formulation with consistent linearization at large
deformations}, DOI={10.1177/10812865261420809},
number={10812865261420808}, journal={Mathematics and Mechanics of Solids}, publisher={SAGE
Publications}, author={Zhan, Yingjie and Caylak, Ismail and Ostwald, Richard and
Mahnken, Rolf and Barth, Enrico and Uhlmann, Eckart}, year={2026} }'
chicago: Zhan, Yingjie, Ismail Caylak, Richard Ostwald, Rolf Mahnken, Enrico Barth,
and Eckart Uhlmann. “A Fully Implicit Mean-Field Damage Formulation with Consistent
Linearization at Large Deformations.” Mathematics and Mechanics of Solids,
2026. https://doi.org/10.1177/10812865261420809.
ieee: 'Y. Zhan, I. Caylak, R. Ostwald, R. Mahnken, E. Barth, and E. Uhlmann, “A
fully implicit mean-field damage formulation with consistent linearization at
large deformations,” Mathematics and Mechanics of Solids, Art. no. 10812865261420808,
2026, doi: 10.1177/10812865261420809.'
mla: Zhan, Yingjie, et al. “A Fully Implicit Mean-Field Damage Formulation with
Consistent Linearization at Large Deformations.” Mathematics and Mechanics
of Solids, 10812865261420808, SAGE Publications, 2026, doi:10.1177/10812865261420809.
short: Y. Zhan, I. Caylak, R. Ostwald, R. Mahnken, E. Barth, E. Uhlmann, Mathematics
and Mechanics of Solids (2026).
date_created: 2026-02-17T11:21:00Z
date_updated: 2026-02-17T11:22:49Z
department:
- _id: '9'
- _id: '952'
- _id: '321'
doi: 10.1177/10812865261420809
language:
- iso: eng
publication: Mathematics and Mechanics of Solids
publication_identifier:
issn:
- 1081-2865
- 1741-3028
publication_status: published
publisher: SAGE Publications
quality_controlled: '1'
status: public
title: A fully implicit mean-field damage formulation with consistent linearization
at large deformations
type: journal_article
user_id: '85414'
year: '2026'
...
---
_id: '61138'
article_number: '434'
author:
- first_name: Yingjie
full_name: Zhan, Yingjie
id: '93591'
last_name: Zhan
- first_name: Ismail
full_name: Caylak, Ismail
id: '75'
last_name: Caylak
- first_name: Richard
full_name: Ostwald, Richard
id: '106876'
last_name: Ostwald
orcid: 0000-0003-2147-8444
- first_name: Enrico
full_name: Barth, Enrico
last_name: Barth
- first_name: Eckart
full_name: Uhlmann, Eckart
last_name: Uhlmann
citation:
ama: 'Zhan Y, Caylak I, Ostwald R, Barth E, Uhlmann E. Damage-incorporated four-step
mean-field method for simulating CFRP machining: a novel algorithmic approach.
Multiscale and Multidisciplinary Modeling, Experiments and Design. 2025;8(10).
doi:10.1007/s41939-025-01026-4'
apa: 'Zhan, Y., Caylak, I., Ostwald, R., Barth, E., & Uhlmann, E. (2025). Damage-incorporated
four-step mean-field method for simulating CFRP machining: a novel algorithmic
approach. Multiscale and Multidisciplinary Modeling, Experiments and Design,
8(10), Article 434. https://doi.org/10.1007/s41939-025-01026-4'
bibtex: '@article{Zhan_Caylak_Ostwald_Barth_Uhlmann_2025, title={Damage-incorporated
four-step mean-field method for simulating CFRP machining: a novel algorithmic
approach}, volume={8}, DOI={10.1007/s41939-025-01026-4},
number={10434}, journal={Multiscale and Multidisciplinary Modeling, Experiments
and Design}, publisher={Springer Science and Business Media LLC}, author={Zhan,
Yingjie and Caylak, Ismail and Ostwald, Richard and Barth, Enrico and Uhlmann,
Eckart}, year={2025} }'
chicago: 'Zhan, Yingjie, Ismail Caylak, Richard Ostwald, Enrico Barth, and Eckart
Uhlmann. “Damage-Incorporated Four-Step Mean-Field Method for Simulating CFRP
Machining: A Novel Algorithmic Approach.” Multiscale and Multidisciplinary
Modeling, Experiments and Design 8, no. 10 (2025). https://doi.org/10.1007/s41939-025-01026-4.'
ieee: 'Y. Zhan, I. Caylak, R. Ostwald, E. Barth, and E. Uhlmann, “Damage-incorporated
four-step mean-field method for simulating CFRP machining: a novel algorithmic
approach,” Multiscale and Multidisciplinary Modeling, Experiments and Design,
vol. 8, no. 10, Art. no. 434, 2025, doi: 10.1007/s41939-025-01026-4.'
mla: 'Zhan, Yingjie, et al. “Damage-Incorporated Four-Step Mean-Field Method for
Simulating CFRP Machining: A Novel Algorithmic Approach.” Multiscale and Multidisciplinary
Modeling, Experiments and Design, vol. 8, no. 10, 434, Springer Science and
Business Media LLC, 2025, doi:10.1007/s41939-025-01026-4.'
short: Y. Zhan, I. Caylak, R. Ostwald, E. Barth, E. Uhlmann, Multiscale and Multidisciplinary
Modeling, Experiments and Design 8 (2025).
date_created: 2025-09-05T07:40:31Z
date_updated: 2025-10-20T12:05:57Z
department:
- _id: '9'
- _id: '952'
- _id: '321'
doi: 10.1007/s41939-025-01026-4
intvolume: ' 8'
issue: '10'
language:
- iso: eng
publication: Multiscale and Multidisciplinary Modeling, Experiments and Design
publication_identifier:
issn:
- 2520-8160
- 2520-8179
publication_status: published
publisher: Springer Science and Business Media LLC
quality_controlled: '1'
status: public
title: 'Damage-incorporated four-step mean-field method for simulating CFRP machining:
a novel algorithmic approach'
type: journal_article
user_id: '85414'
volume: 8
year: '2025'
...