Numerical and analytical model of deformation of structurally heterogeneous materials
Authors: Danilov M.N., Burnysheva T.V.
Published in issue: #7(163)/2025
DOI: 10.18698/2308-6033-2025-7-2457
Category: Mechanics | Chapter: Mechanics of Deformable Solid Body
The paper presents a process of improving the mathematical apparatus to describe the stress-strain state of structures made of the structurally inhomogeneous materials and simulate processes of their deformation under loading. It applies the structural-phenomenological approach to constructing the material deformation models. The paper proposes constitutive equations in the form of a numerical-analytical model establishing relationship between the macrostrain and the macrostress tensor components. The components boundary surface (binder and inclusions) is described by a structural model of the representative material volume, the model could be constructed based on the differential geometry mathematical apparatus. The inhomogeneous stress-strain state of the material volume representative element is reproduced by numerical simulation using the finite element method in solving the boundary value problem for a system of elasticity equations. In this case, the boundary conditions are determined by the macrostrain and macrostress tensor components characterizing the stress-strain values averaged over the representative volume. The constructed numerical-analytical model explicitly takes into account the material structural heterogeneity; therefore, it could be called the structural-phenomenological model.
EDN FIXNKI
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