Peridynamic simulation of creep deformation and damage

IF 1.9 4区工程技术 Q3 MECHANICS Continuum Mechanics and Thermodynamics Pub Date : 2024-03-17 DOI:10.1007/s00161-024-01295-3

Deepak Behera, Pranesh Roy, Erdogan Madenci

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Abstract

This study presents a nonordinary state-based (NOSB) peridynamic (PD) modeling of creep deformation and damage. The force density vectors in PD equilibrium equations are derived by considering the Liu and Murakami creep model with a damage parameter. The bond-associated (BA) deformation gradient is derived by using the PD differential operator (PDDO). Traction and displacement boundary conditions are directly imposed through a novel strategy while solving for the strong form of PD equilibrium equations. The PD form of traction components enables the imposition of traction conditions in the actual “boundary layer” region without any unphysical displacement kinks near the boundaries. The approach is validated under uniaxial and 2D plane stress assumptions by considering creep deformation due to constant stress at high temperatures. The creep strain predictions are in excellent agreement with the experimental data and analytical solutions. Subsequently, creep crack growth in a compact tension (CT) specimen is simulated by using the damage variable in Liu and Murakami constitutive model.

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蠕变变形和损伤的周动态模拟

本研究提出了一种基于非平凡状态（NOSB）的蠕变变形和损伤周动力学（PD）建模方法。PD 平衡方程中的力密度向量是通过考虑带有损伤参数的 Liu 和 Murakami 蠕变模型得出的。粘结相关（BA）变形梯度是通过使用 PD 微分算子（PDDO）得出的。在求解 PD 平衡方程的强形式时，通过一种新颖的策略直接施加牵引和位移边界条件。牵引力分量的 PD 形式可以在实际的 "边界层 "区域施加牵引力条件，而不会在边界附近产生任何非物理的位移扭结。通过考虑高温下恒定应力引起的蠕变变形，在单轴和二维平面应力假设下验证了该方法。蠕变应变预测结果与实验数据和分析解法非常吻合。随后，通过使用 Liu 和 Murakami 构成模型中的损伤变量，模拟了紧凑拉伸 (CT) 试样中蠕变裂纹的生长。

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来源期刊

Continuum Mechanics and Thermodynamics 物理-力学

CiteScore

5.30

自引率

15.40%

发文量

审稿时长

>12 weeks

期刊介绍： This interdisciplinary journal provides a forum for presenting new ideas in continuum and quasi-continuum modeling of systems with a large number of degrees of freedom and sufficient complexity to require thermodynamic closure. Major emphasis is placed on papers attempting to bridge the gap between discrete and continuum approaches as well as micro- and macro-scales, by means of homogenization, statistical averaging and other mathematical tools aimed at the judicial elimination of small time and length scales. The journal is particularly interested in contributions focusing on a simultaneous description of complex systems at several disparate scales. Papers presenting and explaining new experimental findings are highly encouraged. The journal welcomes numerical studies aimed at understanding the physical nature of the phenomena. Potential subjects range from boiling and turbulence to plasticity and earthquakes. Studies of fluids and solids with nonlinear and non-local interactions, multiple fields and multi-scale responses, nontrivial dissipative properties and complex dynamics are expected to have a strong presence in the pages of the journal. An incomplete list of featured topics includes: active solids and liquids, nano-scale effects and molecular structure of materials, singularities in fluid and solid mechanics, polymers, elastomers and liquid crystals, rheology, cavitation and fracture, hysteresis and friction, mechanics of solid and liquid phase transformations, composite, porous and granular media, scaling in statics and dynamics, large scale processes and geomechanics, stochastic aspects of mechanics. The journal would also like to attract papers addressing the very foundations of thermodynamics and kinetics of continuum processes. Of special interest are contributions to the emerging areas of biophysics and biomechanics of cells, bones and tissues leading to new continuum and thermodynamical models.