Inverse identification of constitutive parameters from heat source fields: A local approach applied to hyperelasticity

In this paper, a new inverse identification method of constitutive parameters is developed from full kinematic and thermal field measurements. It consists in reconstructing the heat source field from two different approaches by using the heat diffusion equation. The first one requires the temperature field measurement and the value of the thermophysical parameters. The second one is based on the kinematic field measurement and the choice of a thermo-hyperelastic model that contains the parameters to be identified. The identification is carried out at the local scale, ie, at any point of the heat source field, without using the boundary conditions. In the present work, the method is applied to the challenging case of hyperelasticity from a heterogeneous test. Due to large deformations undergone by the rubber specimen tested, a motion compensation technique is developed to plot the kinematic and the thermal fields at the same points before reconstructing the heterogeneous heat source field. In the present case, the constitutive parameter of the Neo-Hookean model has been identified, and its distribution has been characterized with respect to the strain state at the surface of a cross-shaped specimen.     

Hyperelastic,Robust, Fire-Safe Multifunctional MXene Aerogels with Unprecedented Electromagnetic Interference Shielding Efficiency

MXene aerogels have shown great potential for many important functional applications, in particular electromagnetic interference (EMI) shielding. However, it has been a grand challenge to create mechanically hyperelastic, air-stable, and durable MXene aerogels for enabling effective EMI protection at low concentrations due to the difficulties in achieving tailorable porous structures, excellent mechanical elasticity, and desired antioxidation capabilities of MXene in air. Here, a facile strategy for fabricating MXene composite aerogels by co-assembling MXene and cellulose nanofibers during freeze-drying followed by surface encapsulation with fire-retardant thermoplastic polyurethane (TPU) is reported. Because of the maximum utilization of pore structures of MXene, and conductive loss enhanced by multiple internal reflections, as-prepared aerogel with 3.14 wt% of MXene exhibits an exceptionally high EMI shielding effectiveness of 93.5 dB, and an ultra-high MXene utilization efficiency of 2977.71 dB g g⁻¹, tripling the values in previous works. Owing to the presence of multiple hydrogen bonding and the TPU elastomer, the aerogel exhibits a hyperelastic feature with additional strength, excellent stability, superior durability, and high fire safety. This study provides a facile strategy for creating multifunctional aerogels with great potential for applications in EMI protection, wearable devices, thermal management, pressure sensing, and intelligent fire monitoring.     

On solving large strain hyperelastic problems with the natural element method

In this paper, an extension of the natural element method (NEM) is presented to solve finite deformation problems. Since NEM is a meshless method, its implementation does not require an explicit connectivity definition. Consequently, it is quite adequate to simulate large strain problems with important mesh distortions, reducing the need for remeshing and projection of results (extremely important in three‐dimensional problems). NEM has important advantages over other meshless methods, such as the interpolant character of its shape functions and the ability of exactly reproducing essential boundary conditions along convex boundaries. The α‐NEM extension generalizes this behaviour to non‐convex boundaries. A total Lagrangian formulation has been employed to solve different problems with large strains, considering hyperelastic behaviour. Several examples are presented in two and three dimensions, comparing the results with the ones of the finite element method. NEM performs better showing its important capabilities in this kind of applications. Copyright © 2004 John Wiley & Sons, Ltd.     

On the numerical implementation of variational arbitrary Lagrangian–Eulerian (VALE) formulations

This paper is concerned with the implementation of variational arbitrary Lagrangian–Eulerian formulations, also known as variational r‐adaption methods. These methods seek to minimize the energy function with respect to the finite‐element mesh over the reference configuration of the body. We propose a solution strategy based on a viscous regularization of the configurational forces. This procedure eliminates the ill‐posedness of the problem without changing its solutions, i.e. the minimizers of the regularized problems are also minimizers of the original functional. We also develop strategies for optimizing the triangulation, or mesh connectivity, and for allowing nodes to migrate in and out of the boundary of the domain. Selected numerical examples demonstrate the robustness of the solution procedures and their ability to produce highly anisotropic mesh refinement in regions of high energy density. Copyright © 2006 John Wiley & Sons, Ltd.     

隔振橡胶本构建模研究

提出适合描述隔振橡胶在宽频振动时力学行为的本构模型。本构模型包含超弹性和粘弹性两个部分，超弹性部分表征橡胶材料的静态特性；非线性粘弹性部分描述橡胶材料在振动、冲击载荷下的动态响应。基于该本构模型，对橡胶材料在宽应变率范围内进行试验，九个材料参数通过高、低应变率下的试验数据拟合确定。模型预测结果与试验结果是相当吻合的。     

Optimization of hyperelastic materials with isotropic damage

In many practical problems, engineering structures under repeated loading exhibit softening material behaviour. The complex micromechanical processes yielding the observed loss of stiffness are often described phenomenologically on the macroscopic level by damage mechanics. A finite strain elastic constitutive model incorporating an isotropic damage mechanism was developed by Simo (1987). The additional theoretical and computational enhancements for utilizing this damage model and the associated finite element formulation for optimization purposes are outlined in this paper.?The structural response and its sensitivity expressions at a given time and position depend on the response and the response sensitivities of all previous locations and times. The expressions for variational design sensitivity analysis within damage mechanics are fully stated and related to prior work on history dependent material behaviour such as Prandtl-Reuss elastoplasticity, see Barthold and Wiechmann (1997) and Wiechmann et al. (1997). The theoretical details and the corresponding finite element formulation were described in the paper by Firuziaan (1998).?New problem functions based on the internal variables are shown to be adequate for controlling and optimizing the damage process.?Numerical experiments illustrate the method proposed and the efficiency of the overall optimization procedure. Received April 29, 1999     

Full Eulerian deformable solid-fluid interaction scheme based on building-cube method for large-scale parallel computing

We propose a full Eulerian incompressible solid-fluid interaction scheme capable of achieving high parallel efficiency and easily generating meshes for complex solid geometries. While good scalability of a full Eulerian solid-fluid interaction formulation has been reported by Sugiyama et al, their analysis was carried out using uniform Cartesian mesh and an artificial compressibility method. Typically, it is more challenging to achieve good scalability for hierarchical Cartesian meshes and a fully incompressible formulation. In addition, the conventional full Eulerian methods require a large computational cost to resolve complex solid geometries due to the usage of uniform Cartesian meshes. In an attempt to overcome the aforementioned issues, we employ the building-cube method, where the computational domain is divided into cubic regions called cubes. Each cube is divided at equal intervals, the same number of cubes is assigned to each core, and the spatial loop processing is executed for each cube. The numerical method is verified by computing five numerical examples. In the weak scaling test, the parallel efficiency at 32768 cores with 32 cores as a reference is 93.6%. In the strong scaling test, the parallel efficiency at 32768 cores with 128 cores as a reference is 70.2%.     

A neural network constitutive model for hyperelasticity based on molecular dynamics simulations

Numerical analysis of the hyperelastic behavior of polymer materials has drawn significant interest from within the field of mechanical engineering. Currently, hyperelastic models based on the energy density function, such as the Neo-Hookean, Mooney-Rivlin, and Ogden models, are used to investigate the hyperelastic responses of materials. Conventionally, constants relating to materials were determined from experimental data by using global least-squares fitting. However, formulating a constitutive equation to capture the complex behavior of hyperelastic materials was difficult owing to the limitations of the analytical model and experimental data. This study addresses these limitations by using a system of neural networks (NNs) to design a data-driven surrogate model without a specific function formula, and employs molecular dynamics (MD) simulations to calculate the massive amount of combined loading data of hyperelastic materials. Thus, MD simulations were used to propose an NN constitutive model for hyperelasticity to derive the constitutive equation to model the complex hyperelastic response. In addition, the probability distributions of the numerical solutions of hyperelasticity are used to characterize the uncertainty of the MD models. These statistical finite element results not only present numerical results with reliability ranges but also scattered distributions of the solution obtained from the MD-based probability distributions.     

含孔橡胶矩形板的单向压缩

在船舶和海洋工程领域,以橡胶材料为代表的超弹性材料应用越来越广泛,故研究橡胶材料的损伤和破坏的力学机理是一个非常现实的重大课题.该文力求通过研究橡胶材料的空穴萌生和增长来了解超弹性材料的损伤和破坏的力学机理.利用高玉臣给出的一类应变能函数分析了含单个微孔橡胶矩形板在受单向压缩作用下生长的有限变形问题.利用不可压缩条件确定了矩形板的变形模式,此变形模式含有2个物理意义完全不一样的参数,其中一个参数可由远场的变形状态确定,另一个参数可用最小势能原理导出变分近似解.进而给出了反映微孔变形的参数与外载间的关系,以及孔边应力分布的解析解.结果显示,高玉臣给出的应变能函数能较好地描述橡胶材料的有限变形特性,含有单个圆柱微孔的三维橡胶矩形板受压与受拉时的力学特性相差较大.