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  1. Abstract

    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 employing a total Lagrangian formulation, and (ii) a three-field mixed displacement-pressure-Jacobian formulation. The novel and formulations are consistently derived and numerically implemented, providing a satisfactory agreement with respect to 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 and herein proposed.

     
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  2. Free, publicly-accessible full text available December 1, 2024
  3. Nano-indentation is a promising method to identify the constitutive parameters of soft materials, including soft tissues. Especially when materials are very small and heterogeneous, nano-indentation allows mechanical interrogation where traditional methods may fail. However, because nano-indentation does not yield a homogeneous deformation field, interpreting the resulting load–displacement curves is non-trivial and most investigators resort to simplified approaches based on the Hertzian solution. Unfortunately, for small samples and large indentation depths, these solutions are inaccurate. We set out to use machine learning to provide an alternative strategy. We first used the finite element method to create a large synthetic data set. We then used these data to train neural networks to inversely identify material parameters from load–displacement curves. To this end, we took two different approaches. First, we learned the indentation forward problem, which we then applied within an iterative framework to identify material parameters. Second, we learned the inverse problem of directly identifying material parameters. We show that both approaches are effective at identifying the parameters of the neo-Hookean and Gent models. Specifically, when applied to synthetic data, our approaches are accurate even for small sample sizes and at deep indentation. Additionally, our approaches are fast, especially compared to the inverse finite element approach. Finally, our approaches worked on unseen experimental data from thin mouse brain samples. Here, our approaches proved robust to experimental noise across over 1000 samples. By providing open access to our data and code, we hope to support others that conduct nano-indentation on soft materials. 
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    Free, publicly-accessible full text available October 1, 2024
  4. Free, publicly-accessible full text available July 1, 2024
  5. Free, publicly-accessible full text available July 1, 2024
  6. One of the most efficient and promising separation alternatives to thermal methods such as distillation is the use of polymeric membranes that separate mixtures based on molecular size or chemical affinity. Self-assembled block copolymer membranes have gained considerable attention within the membrane field due to precise control over nanoscale structure, pore size, and chemical versatility. Despite the rapid progress and excitement, a significant hurdle in using block copolymer membranes for nanometer and sub-nanometer separations such as nanofiltration and reverse osmosis is the lower limit on domain size features. Strategies such as polymer post-functionalization, self-assembly of oligomers, liquid crystals, and random copolymers, or incorporation of artificial/natural channels within block copolymer materials are future directions with the potential to overcome current limitations with respect to separation size. 
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