A physics-augmented neural network framework for modeling and detecting thermo-visco-plastic behavior

Abstract

Although considerable attention has been devoted to the development of models for isothermal, rate-independent plasticity, many high-consequence performance assessments involve viscoplastic processes that generate substantial heat. In addition, materials may transit from a nearly isothermal, rate-independent regime to a viscous, temperature-dependent regime during these processes, which makes modeling more challenging. In this work, we develop a physics-augmented neural network (PANN) framework for modeling general temperature-dependent, rate-dependent inelastic processes firmly based on physical principles, including the second law of thermodynamics and coordinate equivariance. These embedded properties are enabled by a number of architectural innovations in the structure and training of an input convex and potential-based neural ordinary differential equation framework. The resulting neural network models are capable of representing a wide spectrum of rate- and temperature-dependence ranging from isothermal, rate-independent elastic-plastic phenomenology to rate-dependent fully viscous inelastic behavior, as we demonstrate. We also show that the framework is capable of modeling complex microstructural inelasticity and predicting the conversion of plastic work to heating when calibrated to stress-temperature observations.

Figures (18)

• Figure 1: Schematic of dissipation potential. Gray is the elastic region with no flow of internal variables. The effect of different rectifiers, ReLU and SoftPlus, on the dissipation potential are shown in blue and cyan, respectively.
• Figure 2: Trainable rectifier $\operatorname{softplus}_a$ that smoothly approximates the ReLU ($a\to\infty$) and can represent the SoftPlus ($a=1$) exactly.
• Figure 3: The PANN framework for thermoviscoplasticity: Two potential ICNN-NODE integrated with a Heun-like scheme.
• Figure 4: Complementarity loss function diffused with p=2, nominal p=1, sharpened with power = 1/2
• Figure 5: Path sampling orbits: (a) deformation invariants $I_1 = {\operatorname{tr}} \mathbf{C}$ and $I_3 = \det \mathbf{C}$, and (b) deformation-rate invariants $I_1$ and $I_4 = {\operatorname{tr}} \mathbf{C}\dot{\mathbf{C}}$. The lower left panels show the trajectories, while the upper and right panels depict the marginal densities.

Theorems & Definitions (1)

• Remark