Abstract: Hydrogels are nowadays widely used in various biomedical applications,  and show great potential for the making of devices such as biosensors, drug delivery vectors, carriers or matrices for cell cultures in tissue engineering, etc. In these applications, due to the irregular complex surface of the human body or its organs/structures, the devices are often designed with a small thickness, and required to be flexible when attached to biological surfaces. The devices will deform as driven by human motion and under external loading. In terms of mechanical modeling, most of these devices can be abstracted as shells. In this paper, we propose a mixed Graph-FEM (finite element method) phase field approach to model the fracture of curved shells composed of hydrogels, for biomedical applications. We present herein examples for the fracture of a wearable biosensor, a membrane coated drug, and a matrix for a cell culture, each made of a hydrogel. Used in combination with experimental material testing, our method opens a new pathway to the efficient modeling of fracture in biomedical devices with surfaces of arbitrary curvature, helping in the design of devices with tunable fracture properties.

Abstract: In this paper, a data-driven approach for constructing elastoplastic constitutive law of microstructured materials is proposed by combining the insights from plasticity theory and the tools of artificial intelligence (i.e., constructing yielding function through ANN) to reduce the required amount of data for machine learning. Illustrative examples show that the constitutive laws constructed by the present approach can be used to solve the boundary value problems (BVPs) involving elastoplastic materials with microstructures under complex loading paths (e.g., cyclic/reverse loading) effectively. The limitation of the proposed approach is also discussed. 

Abstract: Direct numerical simulation based on experimental stress–strain data without explicit constitutive models is an active research topic. In this paper, a mechanistic-based, data-driven computational framework is proposed for elastoplastic materials undergoing finite strain. Harnessing the physical insights from the existing model-based plasticity theory, multiplicative decomposition of deformation gradient and the coaxial relationship between the logarithmic trial elastic strain and the true stress is employed to perform stress-update, driven by two sets of the specifically measured one dimensional (1D) stress–strain data. The proposed

approach, called MAP123-EPF, is used to solve several Boundary-Value Problems (BVPs) involving elastoplastic materials undergoing finite strains. Numerical results indicate that the proposed approach can predict the response of isotropic elastoplastic materials (characterized by the classical J2 plasticity model and the associative Drucker–Prager model) with good accuracy using numerically/experimentally generated data. The proposed approach circumvents the need for the several basic ingredients of a traditional finite strain computational plasticity model, such as an explicit yielding function, a hardening law and an appropriate objective stress rate. Demonstrative examples are shown and strengths and limitations of the proposed approach

are discussed.

Abstract：In this paper, a mechanistic-based data-driven approach, MAP123-EP, is proposed for numerical analysis of elastoplastic materials. In this method, stress-update is driven by a set of one-dimensional stress–strain data generated by numerical or physical experiments under uniaxial loading. Numerical results indicate that combined with the classical strain-driven scheme, the proposed method can predict the mechanical response of isotropic elastoplastic materials (characterized by J2 plasticity model with isotropic/kinematic hardening and associated Drucker–Prager model) accurately without resorting to the typical ingredients of classical model-based plasticity, such as decomposing the total strain into elastic and plastic parts, as well as identifying explicit functional expressions of yielding surface and hardening curve. This mechanistic-based data-driven approach has the potential of opening up a new avenue for numerical analysis of problems where complex material behaviors cannot be described in explicit function/functional forms. The applicability and limitation of the proposed approach are also discussed.

Abstract: Structural topology and loading condition have important influences on the mechanical behaviors of porous soft solids. The porous solids are usually set to be under uniaxial tension o compression. Only a few studies have considered the biaxial loads, especially the combined loads of tension and compression. In this study, porous soft solids with oblique and square lattices of circular voids under biaxial loadings were studied through integrated experiments and numerical simulations. For the soft solids with oblique lattices of circular voids, we found a new pattern transformation under biaxial compression, which has alternating elliptic voids with an inclined angle. This kind of pattern transformation is rarely reported under uniaxial compression. Introducing tensile deformation in one direction can hamper this kind of pattern transformation under biaxial loading. For the soft solids with square lattices of voids, the number of voids cannot change their deformation behaviors qualitatively, but quantitatively. In general, our present results demonstrate that void morphology and biaxial loading can be harnessed to tune the pattern transformations of porous soft solids under large deformation. This discovery offers a new avenue for designing the void morphology of soft solids for controlling their deformation patterns under a specific biaxial stress-state.

Abstract：In this work, we combine both experiments and numerical simulations to study the large deformation

mechanics of two-dimensional patterned porous silicone rubber under biaxial loading, by focusing on the combined compressive and tensile loading. Particularly, we design a loading apparatus to impose the biaxial loading and fabricate patterned porous silicone rubbers through 3D printing. Although the pattern transformation with alternating elliptic voids has been observed under uniaxial compression before, our results show that the pattern transformation can be promoted by biaxial compression, while biaxial compression/tension can delay it. When the ratio between tension and compression is larger than a critical value, a new pattern transformation has been observed. In addition, if the imposed tension in one direction is larger than the compression in the other direction, the pattern transformation with alternating elliptic voids cannot occur. Biaxial loading provides new opportunities to fabricate the tunable devices and imprint complex patterns with soft solids.

Abstract：In this paper,a direct data-driven approach for the modeling of isotropic,tension–compression asymmetric,elasto-plasticmaterials is proposed. Our approach bypasses the conventional construction of explicit mathematical function-based elasto-plastic models, and the need for parameter-fitting. In it, stress update is driven directly by a set of stress–strain data that is generated from uniaxial tension and compression experiments (physical). Particularly, for compression experiments, digital image correlation and homogenization are combined to further improve modeling accuracy. Two representative tension–compression asymmetric materials, titanium alloy TC4ELI and high-density polyethylene, are chosen to illustrate the effectiveness and accuracy of our proposed approach. Results indicate that our data-driven approach can predict the mechanical response of elasto-plastic materials that exhibit tension–compression asymmetry, within the small deformation regime. This data-driven approach provides a practical way to model such materials directly from physical experimental data. Our current implementation is limited, however, by a small reduction to computational efficiency, when compared to typical function-based approaches. Moreover, our present formulation is focused on tension–compression asymmetric elasto-plastic materials that are isotropic.