Background Hydrogels are soft, solvent-swollen polymer networks whose fracture behavior is governed by the interplay between polymer elasticity and fluid transport. As cracks accelerate, rate-dependent dissipation mechanisms become active, rendering the fracture energy a function of crack velocity rather than a single material constant. How energy is dissipated during dynamic crack propagation, and how different dissipation mechanisms contribute to the velocity-dependent fracture energy, remain open questions. Objective In this work, we quantitatively characterize the fracture energy of hydrogels during dynamic crack propagation and show how different processes involved in fracture, including polymer network scission, viscous dissipation, and poroelastic effects contribute to the rate dependence of the fracture energy. Methods We conduct a systematic experimental investigation of dynamic fracture in single-network polyacrylamide hydrogels. The fracture energy varying with crack speed, <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\varvec{\Gamma (v)}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="bold">Γ</mi> <mo mathvariant="bold" stretchy="false">(</mo> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>, is determined using multiple independent approaches based on fracture mechanics, including near-tip measurements and crack dynamics, over a wide range of crack velocities. Polymer concentration, the swelling state, and solvent viscosity are independently varied to isolate their respective influences on fracture energy dissipation. Results The fracture energy of all gels tested increases monotonically with crack speed. By comparing the energy dissipation across controlled variations of material properties, we disentangle distinct contributions to the total fracture energy. At low crack velocities, the rate dependence of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\varvec{\Gamma (v)}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="bold">Γ</mi> <mo mathvariant="bold" stretchy="false">(</mo> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> is governed by poroelastic dissipation associated with solvent drainage in the crack-tip process zone. At higher velocities, where solvent flow is effectively frozen, an additional viscous contribution emerges, with <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\varvec{\Gamma (v)}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="bold">Γ</mi> <mo mathvariant="bold" stretchy="false">(</mo> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> increasing approximately linearly with both crack speed and solvent viscosity, consistent with polymer chain pull-out in a viscous environment. These additive contributions combine with the bare fracture energy, set by the polymer network architecture, to quantitatively reconstruct the observed velocity dependence of <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\varvec{\Gamma (v)}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="bold">Γ</mi> <mo mathvariant="bold" stretchy="false">(</mo> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>. Conclusions Our results demonstrate that fracture energy in hydrogels is an intrinsically dynamic quantity governed by multiple dissipation mechanisms depending on crack speed and solvent mobility. The experimental framework presented here provides a quantitative basis for understanding and comparing dynamic fracture in soft, solvent-containing materials.

Rate-Dependent Fracture Energy of Soft and Brittle Hydrogels

期刊论文
发表日期：

2026年4月20日

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M. Wang,
Y. Chen,
Y. Paz,
J. Fineberg

摘要

Background

Hydrogels are soft, solvent-swollen polymer networks whose fracture behavior is governed by the interplay between polymer elasticity and fluid transport. As cracks accelerate, rate-dependent dissipation mechanisms become active, rendering the fracture energy a function of crack velocity rather than a single material constant. How energy is dissipated during dynamic crack propagation, and how different dissipation mechanisms contribute to the velocity-dependent fracture energy, remain open questions.

Objective

In this work, we quantitatively characterize the fracture energy of hydrogels during dynamic crack propagation and show how different processes involved in fracture, including polymer network scission, viscous dissipation, and poroelastic effects contribute to the rate dependence of the fracture energy.

Methods

We conduct a systematic experimental investigation of dynamic fracture in single-network polyacrylamide hydrogels. The fracture energy varying with crack speed, $\varvec{\Gamma (v)}$ $Γ (v)$ , is determined using multiple independent approaches based on fracture mechanics, including near-tip measurements and crack dynamics, over a wide range of crack velocities. Polymer concentration, the swelling state, and solvent viscosity are independently varied to isolate their respective influences on fracture energy dissipation.

Results

The fracture energy of all gels tested increases monotonically with crack speed. By comparing the energy dissipation across controlled variations of material properties, we disentangle distinct contributions to the total fracture energy. At low crack velocities, the rate dependence of $\varvec{\Gamma (v)}$ $Γ (v)$ is governed by poroelastic dissipation associated with solvent drainage in the crack-tip process zone. At higher velocities, where solvent flow is effectively frozen, an additional viscous contribution emerges, with $\varvec{\Gamma (v)}$ $Γ (v)$ increasing approximately linearly with both crack speed and solvent viscosity, consistent with polymer chain pull-out in a viscous environment. These additive contributions combine with the bare fracture energy, set by the polymer network architecture, to quantitatively reconstruct the observed velocity dependence of $\varvec{\Gamma (v)}$ $Γ (v)$ .

Conclusions

Our results demonstrate that fracture energy in hydrogels is an intrinsically dynamic quantity governed by multiple dissipation mechanisms depending on crack speed and solvent mobility. The experimental framework presented here provides a quantitative basis for understanding and comparing dynamic fracture in soft, solvent-containing materials.