The theory of homogenization provides a systematic approach to the derivation of macroscale constitutive laws, obviating the need to repeatedly resolve complex microstructure. However, the unit cell problem that defines the constitutive model is typically not amenable to explicit evaluation. It is therefore of interest to learn constitutive models from data generated by the unit cell problem. Many viscoelastic and elastoviscoplastic materials are characterized by memory-dependent constitutive laws. In order to amortize the computational investment in finding such memory-dependent constitutive laws, it is desirable to learn their dependence on the material microstructure. While prior work has addressed learning memory dependence and material dependence separately, their joint learning has not been considered. This paper focuses on the joint learning problem and proposes a novel neural operator framework to address it. In order to provide firm foundations, the homogenization problem for linear Kelvin-Voigt viscoelastic materials is studied. The theoretical properties of the cell problem in this Kelvin-Voigt setting are used to motivate the proposed general neural operator framework; these theoretical properties are also used to prove a universal approximation theorem for the learned macroscale constitutive model. This formulation of learnable constitutive models is then deployed beyond the Kelvin-Voigt setting. Numerical experiments are presented showing that the resulting data-driven methodology accurately learns history- and microstructure-dependent linear viscoelastic and nonlinear elastoviscoplastic constitutive models, and numerical results also demonstrate that the resulting constitutive models can be deployed in macroscale simulation of material deformation.

To manipulate objects or dance together, humans and robots exchange energy and haptic information. While the exchange of energy in human-robot interaction has been extensively investigated, the underlying exchange of haptic information is not well understood. Here, we develop a computational model of the mechanical and sensory interactions between agents that can tune their viscoelasticity while considering their sensory and motor noise. The resulting stochastic-optimal-information-and-effort (SOIE) controller predicts how the exchange of haptic information and the performance can be improved by adjusting viscoelasticity. This controller was first implemented on a robot-robot experiment with a tracking task which showed its superior performance when compared to either stiff or compliant control. Importantly, the optimal controller also predicts how connected humans alter their muscle activation to improve haptic communication, with differentiated viscoelasticity adjustment to their own sensing noise and haptic perturbations. A human-robot experiment then illustrated the applicability of this optimal control strategy for robots, yielding improved tracking performance and effective haptic communication as the robot adjusted its viscoelasticity according to its own and the user's noise characteristics. The proposed SOIE controller may thus be used to improve haptic communication and collaboration of humans and robots.

In this study, we present a method for estimating the viscoelasticity of a leaf-spring sports prosthesis using advanced energy minimizing inverse kinematics based on the Piece-wise Constant Strain (PCS) model to reconstruct the three-dimensional dynamic behavior. Dynamic motion analysis of the athlete and prosthesis is important to clarify the effect of prosthesis characteristics on foot function. However, three-dimensional deformation calculations of the prosthesis and viscoelasticity have rarely been investigated. In this letter, we apply the PCS model to a prosthesis deformation, which can calculate flexible deformation with low computational cost and handle kinematics and dynamics. In addition, we propose an inverse kinematics calculation method that is consistent with the material properties of the prosthesis by considering the minimization of elastic energy. Furthermore, we propose a method to estimate the viscoelasticity by solving a quadratic programming based on the measured motion capture data. The calculated strains are more reasonable than the results obtained by conventional inverse kinematics calculation. From the result of the viscoelasticity estimation, we simulate the prosthetic motion by forward dynamics calculation and confirm that this result corresponds to the measured motion. These results indicate that our approach adequately models the dynamic phenomena, including the viscoelasticity of the prosthesis.

The constitutive behavior of polymeric materials is often modeled by finite linear viscoelastic (FLV) or quasi-linear viscoelastic (QLV) models. These popular models are simplifications that typically cannot accurately capture the nonlinear viscoelastic behavior of materials. For example, the success of attempts to capture strain rate-dependent behavior has been limited so far. To overcome this problem, we introduce viscoelastic Constitutive Artificial Neural Networks (vCANNs), a novel physics-informed machine learning framework for anisotropic nonlinear viscoelasticity at finite strains. vCANNs rely on the concept of generalized Maxwell models enhanced with nonlinear strain (rate)-dependent properties represented by neural networks. The flexibility of vCANNs enables them to automatically identify accurate and sparse constitutive models of a broad range of materials. To test vCANNs, we trained them on stress-strain data from Polyvinyl Butyral, the electro-active polymers VHB 4910 and 4905, and a biological tissue, the rectus abdominis muscle. Different loading conditions were considered, including relaxation tests, cyclic tension-compression tests, and blast loads. We demonstrate that vCANNs can learn to capture the behavior of all these materials accurately and computationally efficiently without human guidance.

We develop a fully data-driven model of anisotropic finite viscoelasticity using neural ordinary differential equations as building blocks. We replace the Helmholtz free energy function and the dissipation potential with data-driven functions that a priori satisfy physics-based constraints such as objectivity and the second law of thermodynamics. Our approach enables modeling viscoelastic behavior of materials under arbitrary loads in three-dimensions even with large deformations and large deviations from the thermodynamic equilibrium. The data-driven nature of the governing potentials endows the model with much needed flexibility in modeling the viscoelastic behavior of a wide class of materials. We train the model using stress-strain data from biological and synthetic materials including humain brain tissue, blood clots, natural rubber and human myocardium and show that the data-driven method outperforms traditional, closed-form models of viscoelasticity.