Fiber plasticity and loss of ellipticity in soft composites under non-monotonic loading
Fiber plasticity and loss of ellipticity in soft composites under non-monotonic loading
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DOI：
10.1016/j.ijsolstr.2022.111628
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发表时间：
2022-05
影响因子：
3.6
通讯作者：
Fernanda F Fontenele;N. Andarawis-Puri;M. Agoras;Nikolaos Bouklas
中科院分区：
文献类型：
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作者：
Fernanda F Fontenele;N. Andarawis-Puri;M. Agoras;Nikolaos Bouklas
在这项工作中，我们将软复合材料中的纤维塑性与非单调单轴载荷下复合材料平衡控制方程的椭圆度损失联系起来。椭圆度的损失强烈表明复合材料中出现了局部化现象，让人想起肌腱中扭结不稳定性的出现，这是对肌腱“过载”的反应，不需要任何宏观压缩载荷。我们研究了软复合材料，其中纤维和基体都具有高度延展性，并且纤维相中存在塑性变形。我们首先提出了一种允许塑性变形的纤维横向各向同性本构模型，考虑到单一滑移方向，与分层组装的胶原纤维的微观结构一致。接下来，我们提出了一个简单的矩阵超弹性模型，并根据 Voigt 假设将两者结合起来。然后，我们为受到有限变形的弹塑性材料制定了一般的椭圆率损失准则。我们使用这个标准来指示在各种加载-卸载路径下，软复合材料和纤维相中椭圆度损失的临界条件。结果表明，拉伸加载过程中纤维相的塑性变形会导致弹性卸载过程中椭圆度破坏，而宏观上材料仍处于拉伸状态，这表明可能会出现不稳定。
In this work, we relate fiber plasticity in soft composites to the loss of ellipticity of the governing equations of equilibrium of a composite under non-monotonic uniaxial loading. The loss of ellipticity strongly indicates the emergence of localization phenomena in the composite, reminiscent of the emergence of kinking instabilities in tendon, which occur as a response to tendon “overload” without requiring any macroscopic compressive loading. We examine soft composites where both fibers and matrix can be highly extensible and plastic deformations are present in the fiber phase. We first propose a transversely isotropic constitutive model for the fibers allowing for plastic deformations, taking into account a single slip direction, consistent with the microstructure of hierarchically assembled collagen fibers. Following, we propose a simple hyperelastic model for the matrix and combine the two following the Voigt assumption. We then formulate a general loss of ellipticity criterion for an elastoplastic material subjected to finite deformations. We use this criterion to indicate critical conditions for loss of ellipticity in the soft composite and individually in the fiber phase, under various loading–unloading paths. Results show that plastic deformation of the fiber phase during tensile loading can lead to ellipticity breakdown during elastic unloading while, macroscopically, the material is still in tension, indicating the possible onset of an instability.