Abstract
Due to complex mesoscopic and the distinct macroscopic evolution characteristics of ice, especially for its brittle-to-ductile transition in dynamic response, it is still a challenging task to build an accurate ice constitutive model to predict ice loads during ship-ice collision. To address this, we incorporate the conventional multi-yield-surface plasticity model with the state-based peridynamics to simulate the stress and crack formation of ice under impact. Additionally, we take into account of the effects of inhomogeneous temperature distribution, strain rate, and pressure sensitivity. By doing so, we can successfully predict material failure of isotropic freshwater ice,iceberg ice, and columnar saline ice. Particularly, the proposed ice constitutive model is validated through several benchmark tests, and proved its applicability to model ice fragmentation under impacts, including drop tower tests and ballistic problems. Our results show that the proposed approach provides good computational performance to simulate ship-ice collision.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Abbreviations
- ξ ij :
-
Bond vector in reference configuration
- η ij :
-
The relative displacement vector in current configuration
- \(\underline {\boldsymbol{Y}}<\cdot>\) :
-
State function
- \({H_{{x_i}}}\) :
-
The horizon of particle x
- \(\underline {\boldsymbol{T}} \left({{\xi _{ij}},\underline {\boldsymbol{Y}} ({\xi _{ij}})} \right)\) :
-
The force-vector state
- \({{\boldsymbol{K}}_{{x_i}}}\) :
-
The reference symmetric shape tensor of particle xi
- \({{\boldsymbol{P}}_{{x_i}}}\) :
-
The first Piola-Kirchhoff stress
- \({{\boldsymbol{F}}_{{x_i}}}\) :
-
The nonlocal deformation gradient
- L :
-
The spatial velocity gradient
- D :
-
Symmetric deformation rate tensor
- W :
-
Asymmetric rotation tensor
- d :
-
The non-rotational deformation rate tensor
- R t :
-
Orthogonal rotation tensor
- f :
-
The yield function
References
Carney KS, Benson DJ, DuBois P, Lee R (2006) A phenomenological high strain rate model with failure for ice. International Journal of Solids and Structures 43(25–26): 7820–7839
Cui P, Zhang AM, Wang S, Khoo BC (2018) Ice breaking by a collapsing bubble. Journal of Fluid Mechanics 841: 287–309
Derradji-Aouat A (2003) Multi-surface failure criterion for saline ice in the brittle regime. Cold Regions Science and Technology 36 (1–3): 47–70
Derradji-Aouat A (2000) A unified failure envelope for isotropic fresh water ice and iceberg ice. Proceedings of ETCE/OMAE Joint Conference, New Orleans
Drucker DC, Prager W (1952) Soil mechanics and plastic analysis or limit design. Quarterly of Applied Mathematics 10(2): 157–165
Fan H, Bergel GL, Li S (2016) A hybrid peridynamics-sph simulation of soil fragmentation by blast loads of buried explosive. International Journal of Impact Engineering 87: 14–27
Fan H, Li S (2017a) A peridynamics-sph modeling and simulation of blast fragmentation of soil under buried explosive loads. Computer Methods in Applied Mechanics and Engineering 318: 349–381
Fan H, Li S (2017b) Parallel peridynamics-SPH simulation of explosion induced soil fragmentation by using openmp. Computational Particle Mechanics 4(2): 199–211
Fan H, Ren B, Li S (2015) An adhesive contact mechanics formulation based on atomistically induced surface traction. Journal of Computational Physics 302: 420–438
Gold LW (1988) On the elasticity of ice plates. Canadian Journal of Civil Engineering 15(6): 1080–1084
Han R, Zhang AM, Tan S, Li S (2022) Interaction of cavitation bubbles with the interface of two immiscible fluids on multiple time scales. Journal of Fluid Mechanics 932: A8
Hu Y, Feng G, Li S, Sheng W, Zhang C (2020) Numerical modelling of ductile fracture in steel plates with non-ordinary state-based peridynamics. Engineering Fracture Mechanics 225: 106446
Hughes T, Winget J (1980) Finite rotation effects in numerical integration of rate constitutive equations arising in large deformation analysis. International Journal for Numerical Methods in Engineering 15(12): 1862–1867
Jia B, Ju L, Wang Q (2019) Numerical simulation of dynamic interaction between ice and wide vertical structure based on peridynamics. Computer Modeling in Engineering & Sciences 121(2): 501–522
Johnson GR, Holmquist TJ (1994) An improved computational constitutive model for brittle materials. AIP Conference Proceedings, 309: 981–984
Jones SJ (1982) The confined compressive strength of polycrystalline ice. Journal of Glaciology 28(98): 171–178
Jones SJ (1997) High strain-rate compression tests on ice. The Journal of Physical Chemistry B 101(32): 6099–6101
Kolsky H (1949) An investigation of the mechanical properties of materials at very high rates of loading. Proceedings of the Physical Society, Section B 62(11): 676
Lai X, Liu L, Li S, Zeleke M, Liu Q, Wang Z (2018) A non-ordinary state-based peridynamics modeling of fractures in quasi-brittle materials. International Journal of Impact Engineering 111: 130–146
Li T, Zhang AM, Wang SP, Li S, Liu WT (2019) Bubble interactions and bursting behaviors near a free surface. Physics of Fluids 31(4): 042104
Liu M, Wang Q, Lu W (2017) Peridynamic simulation of brittle-ice crushed by a vertical structure. International Journal of Naval Architecture and Ocean Engineering 9(2): 209–218
Liu NN, Zhang AM, Cui P, Wang SP, Li S (2021) Interaction of two out-of-phase underwater explosion bubbles. Physics of Fluids 33(10): 106103
Lu W, Li M, Vazic B, Oterkus S, Oterkus E, Wang Q (2020) Peridynamic modelling of fracture in polycrystalline ice. Journal of Mechanics 36(2): 223–234
Madenci E, Oterkus E (2014) Peridynamic theory. In: Peridynamic theory and its applications, 19–43
Mellor M, Cole DM (1982) Deformation and failure of ice under constant stress or constant strain-rate. Cold Regions Science and Technology 5(3): 201–219
Palmer A, Dempsey J, Masterson D (2009) A revised ice pressure-area curve and a fracture mechanics explanation. Cold Regions Science and Technology 56(2–3): 73–76
Pernas-Sánchez J, Artero-Guerrero JA, Varas D, López-Puente J (2015) Analysis of ice impact process at high velocity. Experimental Mechanics 55(9): 1669–1679
Pernas-Sánchez J, Pedroche DA, Varas D, López-Puente J, Zaera R (2012) Numerical modeling of ice behavior under high velocity impacts. International Journal of Solids and Structures 49(14): 1919–1927
Riska K, Frederking R (1987) Ice load penetration modelling. Proceedings of the Ninth Port and Ocean Engineering Under Arctic Conditions Conference, Fairbanks, 1: 317–327
Rubinstein R, Atluri S (1983) Objectivity of incremental constitutive relations over finite time steps in computational finite deformation analyses. Computer Methods in Applied Mechanics and Engineering 36(3): 277–290
Sain T, Narasimhan R (2011) Constitutive modeling of ice in the high strain rate regime. International Journal of Solids and Structures 48(5): 817–827
Schulson E, Buck S (1995) The ductile-to-brittle transition and ductile failure envelopes of orthotropic ice under biaxial compression. Acta Metallurgica et Materialia 43(10): 3661–3668
Schulson EM (2001) Brittle failure of ice. Engineering Fracture Mechanics 68(17–18): 1839–1887
Silling SA (2000) Reformulation of elasticity theory for discontinuities and long-range forces. Journal of the Mechanics and Physics of Solids 48(1): 175–209
Snyder SA, Schulson EM, Renshaw CE (2016) Effects of prestrain on the ductile-to-brittle transition of ice. Acta Materialia 108: 110–127
Sun PN, Colagrossi A, Zhang AM (2018) Numerical simulation of the self-propulsive motion of a fishlike swimming foil using the d+-SPH model. Theoretical and Applied Mechanics Letters 8(2): 115–125
Sun PN, Le Touze D, Oger G, Zhang AM (2021) An accurate FSI-SPH modeling of challenging fluid-structure interaction problems in two and three dimensions. Ocean Engineering 221, 108552
Sun PN, Luo M, Le Touzé D, Zhang AM (2019) The suction effect during freak wave slamming on a fixed platform deck: Smoothed particle hydrodynamics simulation and experimental study. Physics of Fluids 31(11): 117108
Vazic B, Oterkus E, Oterkus S (2020) In-plane and out-of plane failure of an ice sheet using peridynamics. Journal of Mechanics 36(2): 265–271
Wang G, Ji SY, Lv HX, Yue QJ (2006) Drucker-prager yield criteria in viscoelastic-plastic constitutive model for the study of sea ice dynamics. Journal of Hydrodynamics 18(6): 714–722
Wang Q, Wang Y, Zan Y, Lu W, Bai X, Guo J (2018) Peridynamics simulation of the fragmentation of ice cover by blast loads of an underwater explosion. Journal of Marine Science and Technology 23(1): 52–66
Xie Y, Li S (2021a) A stress-driven computational homogenization method based on complementary potential energy variational principle for elastic composites. Computational Mechanics 67: 637–652
Xie Y, Li S (2021b) Finite temperature atomistic-informed crystal plasticity finite element modeling of single crystal tantalum (a-ta) at micron scale. International Journal for Numerical Methods in Engineering 122(17): 4660–4697
Xie Y, Li S, Hu X, Bishara D (2022b) An adhesive gurtin-murdoch surface hydrodynamics theory of moving contact line and modeling of droplet wettability on soft substrates. Journal of Computational Physics 456: 111074
Xie Y, Li S, Wu C, Lyu D, Wang C, Zeng D (2022a) A generalized bayesian regularization network approach on characterization of geometric defects in lattice structures for topology optimization in preliminary design of 3D printing. Computational Mechanics 69(5): 1191–1212
Xu Y, Kujala P, Hu ZQ, Li F, Chen G (2020) Numerical simulation of level ice impact on landing craft bow considering the transverse isotropy of Baltic Sea ice based on XFEM. Marine Structures 71: 102735
Zhang AM, Li SM, Cui P, Li S, Liu YL (2023) A unified theory for bubble dynamics. Physics of Fluids 35(3): 033323
Zhang AM, Sun PN, Ming FR, Colagrossi A (2017) Smoothed particle hydrodynamics and its applications in fluid-structure interactions. Journal of Hydrodynamics, Ser. B 29(2): 187–216
Zhang LW, Xie Y, Lyu D, Li S (2019) Multiscale modeling of dislocation patterns and simulation of nanoscale plasticity in body-centered cubic (BCC) single crystals. Journal of the Mechanics and Physics of Solids 130:297–319
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Competing interest The authors have no competing interests to declare that are relevant to the content of this article.
Additional information
Article Highlights
• Compared with the traditional ice constitutive model, we can successfully predict material failure of isotropic freshwater ice, iceberg ice, and columnar saline ice.
• The proposed ice constitutive model can capture the ice failure process by taking into account of the effects of inhomogeneous temperature distribution, strain rate, and pressure sensitivity.
• We successfully applied the proposed peridynamics model simulating structural failure of ice in engineering settings.
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author (s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Song, Y., Zhang, L., Li, S. et al. A Multi-Yield-Surface Plasticity State-Based Peridynamics Model and its Applications to Simulations of Ice-Structure Interactions. J. Marine. Sci. Appl. 22, 395–410 (2023). https://doi.org/10.1007/s11804-023-00344-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11804-023-00344-8