A machine-learning framework for peridynamic material models with physical constraints

As a nonlocal extension of continuum mechanics, peridynamics has been widely and effectively applied in different fields where discontinuities the field variables arise from an initially continuous body. An important component constitutive model is influence function which weights contribution all interactions over region surrounding point interest. Recent work shown that solid mechanics strong relationship with heterogeneity material’s micro-structure. However, determining accurate analytically given micro-structure typically requires lengthy derivations complex mathematical models. To avoid these complexities, goal this paper to develop data-driven regression algorithm find optimal bond-based peridynamic describe macro-scale deformation linear elastic medium periodic heterogeneity. We generate training data by averaging unit cells add physical energy constraint representing homogenized modulus algorithm. demonstrate scheme for examples one- two-dimensional elastodynamics show improves accuracy resulting model.