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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.11461 |
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| _version_ | 1866915840711983104 |
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| author | Mu, Tong Linghu, Changhong Liu, Yanju Leng, Jinsong Gao, Huajian Hsia, K. Jimmy |
| author_facet | Mu, Tong Linghu, Changhong Liu, Yanju Leng, Jinsong Gao, Huajian Hsia, K. Jimmy |
| contents | Deep indentation of soft materials is ubiquitous across scales in nature and engineering, yet accurate predictions of contact behaviors under extreme deformations ($δ/R > 1$) remain elusive due to geometric and material nonlinearities. Here, we investigate the indentation of rigid spheres into soft elastic substrates, resolving the highly nonlinear regime where the sphere becomes fully submerged. A universal geometric mapping approach reveals Hertz-type pressure distributions in the deformed configuration, validated by FEA. Closed-form solutions for contact force and radius agree with simulations up to $δ/R = 2.5$. Experiments spanning soft polymers (Ecoflex, PDMS), food substrates (tofu), and biological tissues (octopus) validate the derived scaling law for hyperelastic materials. Our results establish a universal framework for extreme mechanical interactions, with applications in soft robotics, bioengineered systems, and tissue mechanics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_11461 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Universal Scaling Laws for Deep Indentation Beyond the Hertzian Regime Mu, Tong Linghu, Changhong Liu, Yanju Leng, Jinsong Gao, Huajian Hsia, K. Jimmy Soft Condensed Matter Deep indentation of soft materials is ubiquitous across scales in nature and engineering, yet accurate predictions of contact behaviors under extreme deformations ($δ/R > 1$) remain elusive due to geometric and material nonlinearities. Here, we investigate the indentation of rigid spheres into soft elastic substrates, resolving the highly nonlinear regime where the sphere becomes fully submerged. A universal geometric mapping approach reveals Hertz-type pressure distributions in the deformed configuration, validated by FEA. Closed-form solutions for contact force and radius agree with simulations up to $δ/R = 2.5$. Experiments spanning soft polymers (Ecoflex, PDMS), food substrates (tofu), and biological tissues (octopus) validate the derived scaling law for hyperelastic materials. Our results establish a universal framework for extreme mechanical interactions, with applications in soft robotics, bioengineered systems, and tissue mechanics. |
| title | Universal Scaling Laws for Deep Indentation Beyond the Hertzian Regime |
| topic | Soft Condensed Matter |
| url | https://arxiv.org/abs/2506.11461 |