Continuum mathematical modelling of pathological growth of blood vessels

Residual stresses calculation in a thermoelastoplastic torus after cooling

“…Mathematical models of deformation of the items manufactured by the methods described above must undoubtedly take into account temperature effects. The thermoelasticity model [6][7][8][9][10][11][12][13][14][15][16][17][18]. In this work, we will consider the problem of the residual stresses calculation under conditions of toroidal symmetry.…”

Application of surface growth model for a pathological process in a blood vessel's wall

“…The derivations of some boundary conditions using thermodynamics principles or conservation laws can be found in a number of studies. [36][37][38][39][40][41][42][43][44][45][46][47][48][49][50] The principal variables of the boundary value problem for theory of surface growth for solids are the stress tensor and strain rate tensors and velocity vector. On the surface of growth, one needs to set a specific boundary condition depending on the curvature tensor of the growth surface as well as on tension and inflow rates of the incremented elements.…”

“…Equation ( 11) forms the general boundary value problem for thick-walled solids. This boundary value problem is mathematically identical to the boundary value problem of the theory of elasticity for small deformations, and the most adequate results are obtained within the framework of this version of the theory (see, e.g., previous works [45][46][47][48] ).…”

On a differential constraint in the continuum theory of growing solids

“…The additive manufacturing techniques described above basically use wellknown ideas from natural processes: accretion of space objects, the formation of avalanches and glaciers, crystal growth processes, the growth of atherosclerotic plaques [11,12]. All these phenomena are characterized by presence of PGS.…”