Constitutive modeling of solvent plasticization and physical aging in glassy polymers

doi:10.1007/s10483-026-3355-9

Abstract

Abstract:

Glassy polymers are widely used in biomedical applications in a solvent environment, yet their long-term performance is governed by the competing effects of physical aging and solvent-induced plasticization. Here, we develop a constitutive model that explicitly couples the solvent concentration, structural relaxation, and mechanical response. This framework is built on a multiplicative decomposition of deformation and an Eyring-type flow rule, with structural evolution described by an effective temperature. A generalized shift factor is introduced to quantify how the solvent concentration and effective temperature jointly affect the relaxation time, thereby integrating physical aging and plasticization. The model is subsequently applied to methacrylate (MA)-based copolymer networks immersed in phosphate-buffered saline for up to nine months. Simulations accurately capture key experimental features, including the strong softening of highly swellable networks, the partial recovery due to aging, and the mitigating role of hydrophobic crosslinking in reducing solvent uptake. While the current single-mode description cannot reproduce the full relaxation spectrum, it establishes an efficient framework for predicting the long-term mechanical performance under coupled environmental and mechanical loading. This study provides a constitutive description of solvent-swollen glassy polymers, offering mechanistic insight into the interplay between plasticization and aging. Beyond biomedical MA networks, this framework establishes a foundation for predicting the long-term performance of polymer glasses under coupled aqueous environmental and mechanical loading.

Key words: glassy polymer, swelling, physical aging, constitutive model

2010 MSC Number:

Xu CAO, Kerong WU, Ji LIN, Rui XIAO. Constitutive modeling of solvent plasticization and physical aging in glassy polymers. Applied Mathematics and Mechanics (English Edition), 2026, 47(3): 535-554.

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Figures/Tables 13

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Table 1

Fig. 6

Table 2

Summary of parameters and their values used in the constitutive model"

Parameter	Physical meaning	Value
Parameter	Physical meaning	29MA	36MA	50MA-DDDA
$μ 0$ /MPa	Shear modulus of equilibrium part	5	2	5
$λ L$	Stretch limit of equilibrium network	6	6	6
$μ neq$ /MPa	Non-equilibrium shear modulus	270	200	200
κ/MPa	Bulk modulus	810	600	600
$τ s 0$ /s	Basic stress relaxation time	10	2.5	2.5
$τ e 0$ /s	Basic structural relaxation time	$2 × 108$	$2 × 109$	$5 × 108$
$Q s / s y / (K ⋅ (MPa) − 1)$	Activation parameter of Eyring model	100	100	100
B₀	Activation energy factor	5 500	5 500	5 500
C₀	Heat capacity factor	1 720	1 720	1 600
T₂/K	Kauzmann temperature	275	275	275
T₀/K	Reference effective temperature	313	313	313
$κ rej 0 / (K ⋅ (MPa) − 1)$	Rejuvenation rate	0.2	0.2	0.2

Table 2

Fig. 7

Fig. 8

Fig. 9

Fig. 10

Fig. 11

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Time	29MA	36MA	50MA-DDDA
1 day	6.3	7.5	4.8
7 days	8.3	12.3	6.6
2 months	10.5	12.8	7.2
9 months	8.8	12	7.2