A machine learning-based constitutive model is proposed to capture the strain rate-dependent, nonlinear stress-strain response of soft tissues. The total stress in the general functional form of this model is additively decomposed into a volumetric, an isochoric hyperelastic, and a viscous overstress component. Each stress component can be written as a linear combination of the components of certain irreducible integrity bases. Three Gaussian process regression (GPR) surrogates are trained, one for each stress component. These surrogates discover the mapping between invariants of the right Cauchy-Green deformation tensor and its time derivative, and the corresponding response coefficients of the integrity bases. It is shown that this type of model construction imposes several physical constraints: frame-indifference, material symmetry, stress-free reference state, and the second law of thermodynamics. An additional constraint is imposed on the GPR surrogate corresponding to the viscous overstress component to ensure that dissipation under dynamic loading is strictly non-negative. This constraint is imposed during optimization of the marginal log-likelihood function of this surrogate.
Numerical tests are conducted by training the GPR surrogates using artificially generated stress-strain data in a limited range of tensile deformation and strain rates, and then predicting responses in compression and shear. It is demonstrated that the data-driven constitutive model offers accurate fitting of the training data and makes physically reasonable predictions outside the training regime. Finally, the data-driven model is applied on experimentally obtained brain tissue response under multiple deformation modes and loading rates. Both good fitting accuracy and prediction performance is observed.
