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Main Authors: Mu, Tong, Linghu, Changhong, Liu, Yanju, Leng, Jinsong, Gao, Huajian, Hsia, K. Jimmy
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2506.11461
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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