Viscoelastic-plastic model of polylactide for analyzing deformation of bone lattice scaffolds at different structural levels

Ilya E. Keller, Nataliya V. Elenskaya, Anatoliy A. Adamov, Ilya V. Vindokurov, Mikhail A. Tashkinov

Author details

Ilya E. Keller
Perm National Research Polytechnic University, Perm, Russian Federation
Nataliya V. Elenskaya
Perm National Research Polytechnic University, Perm, Russian Federation
Anatoliy A. Adamov
Institute of Continuous Media Mechanics of the Ural Branch of Russian Academy of Science, Perm, Russian Federation
Ilya V. Vindokurov
Perm National Research Polytechnic University, Perm, Russian Federation
Mikhail A. Tashkinov
Perm National Research Polytechnic University, Perm, Russian Federation

https://doi.org/10.15593/perm.mech/2025.4.08

Lattice structures made from biodegradable polymers are widely used in biomedical applications to replace damaged bone tissue. To accurately capture the associated deformation and biological processes in such micro-heterogeneous materials, it is essential to employ an appropriate viscoelastic-plastic material model. To this end, an experimental investigation of polylactide was conducted, encompassing the following loading protocols: (a) multiple cycles of uniaxial confined compression at various strain rates; (b) uniaxial free compression at different strain rates; (c) uniaxial free compression with cyclic loading-unloading sequences including holds and stepwise increases in stress amplitude; and (d) uniaxial free compression under triangular zero-based cyclic loading at varying stress amplitudes. For the numerical study of spatial heterogeneity in strain and stress distributions during compression of the polylactide scaffold, dependent on strain rate, a viscoplasticity model incorporating the Johnson-Cook hardening law was employed, with model constants derived experimentally from tests (a) and (b). Results showed that as compressive strain increased from 2.7 % to 10.7 %, the spatial distribution of equivalent stresses and strain rates exhibited a clear dependence on the applied compression strain rate within the range of 1.11·10-4 to 1.11·10-1 s-1. This underscores the critical importance of accounting for strain-rate sensitivity in polylactide’s viscoelastic-plastic behavior to accurately describe the localization of plastic deformation and stress concentrations, which govern the micromechanics of various physico-chemical and mechanical processes in scaffolds during use. Furthermore, the employed viscoplasticity model qualitatively captured the key features of bulk polylactide behavior under uniaxial loading, including stress relaxation during hold phases when stress exceeds the yield limit, as well as the accumulation of viscoplastic strains in cyclic loading (ratcheting). These phenomena are especially relevant for modeling the deformation of polylactide scaffolds subjected to zero-based cyclic loading with holds at amplitude levels representative of human gait.

Keywords

Polyalctidebone scaffoldsFDM printingviscoelastic-plasticity modelratchetingstrain rate dependenceJohnson–Cook hardening lawnumerical simulationexperimentmicromechanics

МОДЕЛЬ УПРУГОВЯЗКОПЛАСТИЧНОСТИ ПОЛИЛАКТИДА ДЛЯ АНАЛИЗА ДЕФОРМИРОВАНИЯ КОСТНЫХ РЕШЕТЧАТЫХ СКАФФОЛДОВ НА РАЗНЫХ СТРУКТУРНЫХ УРОВНЯХ

Решетчатые структуры из биоразлагаемых полимеров (скаффолды) используются в биомедицинских приложениях для замещения поврежденной костной ткани. Для понимания связанных деформационных и биологических процессов, происходящих в микронеоднородном материале, необходимо использование адекватной модели упруговязкопластичности материала. С этой целью предпринято экспериментальное исследование полилактида, включающего следующие программы нагружения: (а) несколько циклов одноосного стесненного сжатия с различными скоростями деформирования, (б) одноосное свободное сжатие с различными скоростями деформирования, (в) одноосное свободное сжатие по программе нагружения с циклами нагружения и разгрузки с выдержками со ступенчатыми повышением максимального напряжения, а также (г) одноосное свободное сжатие по треугольным отнулевым циклам нагружения при различных значениях максимального напряжения. Для численного исследования особенностей неоднородного распределения деформаций и напряжений при деформировании решетчатого скаффолда из полилактида сжатием в зависимости от скорости деформирования использована модель упругопластичности с законом упрочнения Джонсона – Кука, константы которой были определены экспериментально по данным испытаний (а)–(б). Обнаружено, что с увеличением деформаций сжатия образца скаффолда от 2,7 до 10,7 % начинает заметно проявляться зависимость пространственного распределения эквивалентных напряжений и скоростей деформаций от скорости деформации сжатия, приложенной к образцу, в диапазоне изменения от 1,11‧10-4 до 1,11‧10-1 с-1. Это показывает важность учета зависимости упруговязкопластических свойств полилактида от скорости деформации для корректного описания локализации пластической деформации и концентрации напряжений, влияющих на микромеханику различных физико-химических и механических процессов в скаффолдах в условиях эксплуатации. Также установлено, что использованная для описания одноосного нагружения модель упругопластичности качественно описывает поведение сплошных образцов полилактида при их нагружении: релаксацию напряжений на этапах выдержки при превышении напряжения текучести, а также накопление вязкопластических деформаций в циклах (рэтчетинг). Данные эффекты представляются важными для описания деформирования скаффолдов из полилактида в процессах отнулевого циклического нагружения с выдержками при максимальных значениях, повторяющих ходьбу человека.

Ключевые слова

полилактидкостные скаффолдыFDM-печатьмодель упруговязкопластичностирэтчетингзависимость от скорости деформацийзакон упрочнения Джонсона – Кукачисленный расчетэкспериментмикромеханика

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Article information

Published: 8 December 2025
Issue date: 8 December 2025
Issue: No. 4 (2025)