Locking treatment of penalty-based gradient-enhanced damage formulation for failure of compressible and nearly incompressible hyperelastic materials
Locking treatment of penalty-based gradient-enhanced damage formulation for failure of compressible and nearly incompressible hyperelastic materials
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DOI：
10.1007/s00466-023-02314-x
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发表时间：
2023-03
影响因子：
4.1
通讯作者：
A. Valverde-González;J. Reinoso;B. Dortdivanlioglu;M. Paggi
中科院分区：
文献类型：
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作者：
A. Valverde-González;J. Reinoso;B. Dortdivanlioglu;M. Paggi
软材料是生物力学应用的主要兴趣，因为它们的高变形性和敏感性，在不同的负载情况下的经验损坏事件。本研究关注的是在这些非线性材料的结构响应时，低阶运动插值的非线性有限元方案的背景下，容易锁定的损伤演化过程建模。出于这个原因，一对梯度增强的连续损伤计划，提出了解决机械故障问题的应用，表现出剪切和体积锁定的目的。特别是，我们提出了一致的配方和相应的性能的评估（i）一个混合的位移增强假设应变Q1 Q1 E24采用总拉格朗日公式，和（ii）一个三场混合的位移-压力-雅可比Q1 Q1 P0制定。新颖的Q1 Q1 E24和Q1 Q1 P0配方一致地推导和数值实施，提供了一个令人满意的协议，相对于处理剪切和体积锁定的治疗，分别与ABAQUS内置的元素，通过使用基于惩罚的梯度增强配方的建模损伤现象。这种性能是通过几个数值应用程序进行检查。此外，最后的例子证明了需要一个配方结合两种混合FE方法来模拟问题，包括两个锁定问题（剪切和体积锁定），这可以使用本文提出的Q1 Q1 E24和Q1 Q1 P0的组合进行。
Soft materials are of major interest for biomechanics applications due to their high deformability and susceptibility to experience damage events under different loading scenarios. The present study is concerned with modelling damage evolution processes in these nonlinear materials whose structural responses are prone to locking when low-order kinematic interpolation is employed in the context of nonlinear Finite Element schemes. For this reason, a pair of gradient-enhanced continuum damage schemes are proposed with the aim of tackling mechanical failure problems in applications that exhibit shear and volumetric locking. In particular, we present the consistent formulation and the assessment of the corresponding performance of (i) a mixed displacement-enhanced assumed strain Q1Q1E24 employing a total Lagrangian formulation, and (ii) a three-field mixed displacement-pressure-Jacobian Q1Q1P0 formulation. The novel Q1Q1E24 and Q1Q1P0 formulations are consistently derived and numerically implemented, providing a satisfactory agreement with respect to ABAQUS built-in elements handling the treatment of shear and volumetric locking, respectively, in conjunction to the modelling damage phenomena via the use of a penalty-based gradient-enhanced formulation. This performance is examined via several numerical applications. Furthermore, the final example justifies the need for a formulation combining both mixed FE approaches to simulate problems encompassing both locking issues (shear and volumetric locking), which can be performed using a combination of the Q1Q1E24 and Q1Q1P0 herein proposed.