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This paper concerns anisotropic two-dimensional and planar elasticity modelswithin the frameworks of classical linear elasticity and the bond-basedperidynamic theory of solid mechanics. We begin by reviewing correspondingmodels from the classical theory of linear elasticity. This review includes anew elementary and self-contained proof that there are exactly four materialsymmetry classes of the elasticity tensor in two dimensions. We also summarizeclassical plane strain and plane stress linear elastic models and explore theirconnections to the pure two-dimensional linear elastic model, relying on thedefinitions of the engineering constants. We then provide a novel formulationfor pure two-dimensional anisotropic bond-based linear peridynamic models,which accommodates all four material symmetry classes. We further presentinnovative formulations for peridynamic plane strain and plane stress, whichare obtained using direct analogies of the classical planar elasticityassumptions, and we specialize these formulations to a variety of materialsymmetry classes. The presented anisotropic peridynamic models are constrainedby Cauchy's relations, which are an intrinsic property of bond-basedperidynamic models. The uniqueness of the presented peridynamic plane strainand plane stress formulations in this work is that we directly reducethree-dimensional models to two-dimensional formulations, as opposed tomatching two-dimensional peridynamic models to classical plane strain and planestress formulations. This results in significant computational savings, whileretaining the dynamics of the original three-dimensional bond-based peridynamicproblems under suitable assumptions.

Anisotropic Two-Dimensional, Plane Strain, and Plane Stress Models in Classical Linear Elasticity and Bond-Based Peridynamics