Issue 49

A. Akhmetov et alii, Frattura ed Integrità Strutturale, 49 (2019) 190-200; DOI: 10.3221/IGF-ESIS.49.20 195 Figure 5: Strength of the geomedium layers as a function of depth. M ATHEMATICAL MODEL he description of continuum deformation includes the set of following equations: fundamental conservation laws and constitutive relations. Fundamental conservation laws: – Mass      , 0 i i d u dt (2) – Impulse       , i ij j i u g (3) – Energy      ij ij E (4) Here ρ is the material density, u i is the i-component of the displacement vector,  ij is the stress tensor components, i g Fis the i-component of the gravity acceleration, E is the internal energy,  ij is the strain tensor component. The constitutive equations of the first group are written down in the rate form (5)–(6) in which the stress rate is proportional to elastic strain rate         e t p ij ij ij .               1 2 3 ij e e ij kk ij D Dt s (5)     • e kk P K (6) where      ( ) ij ij ij P s (7)         ij ij ik jk jk ik s s Ds s Dt (8)       , , 1 ( ) 2 ij i j j i u u (9)       , , 1 ( ) 2 ij i j j i u u (10) T