Cellular mechanical metamaterials are a special class of materials, whose mechanical properties are primarily determined by their geometry. But capturing the nonlinear mechanical behavior of these materials, especially with complex...
Time-and temperature-dependent structural relaxation (physical aging) of poly(styrene-b-methyl methacrylate) (PS-b-PMMA) block copolymers was investigated by calorimetry. Our study reveals the interplay of the relaxation responses of the two components of the copolymer in an intermediate temperature regime. That is, when the testing temperature is closely below the glass transition temperatures of PS and PMMA, structural relaxation in these polymer phases takes place concurrently, the corresponding thermogram displays partially superposed dual endothermic peaks as a feature of physical aging in the diblock copolymers. The aging response for each component is identified from a curve fitting method and analyzed by the relaxation of enthalpy. Comparing with the homopolymer analogs, the PS and PMMA in diblock copolymers show enhanced aging rate.
The phase-field (PF) method is a physics-based computational approach for simulating interfacial morphology. It has been used to model powder melting, rapid solidification, and grain structure evolution in metal additive manufacturing (AM). However, traditional direct numerical simulation (DNS) of the PF method is computationally expensive due to sufficiently small mesh size. Here, a physics-embedded graph network (PEGN) is proposed to leverage an elegant graph representation of the grain structure and embed the classic PF theory into the graph network. By reformulating the classic PF problem as an unsupervised machine learning task on a graph network, PEGN efficiently solves temperature field, liquid/solid phase fraction, and grain orientation variables to minimize a physics-based loss/energy function. The approach is at least 50 times faster than DNS in both CPU and GPU implementation while still capturing key physical features. Hence, PEGN allows to simulate large-scale multi-layer and multi-track AM build effectively.
The dynamics of soft mechanical metamaterials provides opportunities for many exciting engineering applications. Previous studies often use discrete systems, composed of rigid elements and nonlinear springs, to model the nonlinear dynamic responses of the continuum metamaterials. Yet it remains a challenge to accurately construct such systems based on the geometry of the building blocks of the metamaterial. In this work, we propose a machine learning approach to address this challenge. A metamaterial graph network (MGN) is used to represent the discrete system, where the nodal features contain the positions and orientations the rigid elements, and the edge update functions describe the mechanics of the nonlinear springs. We use Gaussian process regression as the surrogate model to characterize the elastic energy of the nonlinear springs as a function of the relative positions and orientations of the connected rigid elements. The optimal model can be obtained by "learning" from the data generated via finite element calculation over the corresponding building block of the continuum metamaterial. Then, we deploy the optimal model to the network so that the dynamics of the metamaterial at the structural scale can be studied. We verify the accuracy of our machine learning approach against several representative numerical examples. In these examples, the proposed approach can significantly reduce the computational cost when compared to direct numerical simulation while reaching comparable accuracy. Moreover, defects and spatial inhomogeneities can be easily incorporated into our approach, which can be useful for the rational design of soft mechanical metamaterials.
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