Strength Analysis in Geomechanics





Preface

The solution of complex problems of strength in many branches of industry

and science is impossible without a knowledge of fracture processes. Last 50

years demonstrated a great interest to these problems that was stimulated

by their immense practical importance. Exact methods of solution aimed at

finding fields of stresses and strains based on theories of elasticity, plasticity,

creep, etc. and a rough appreciation of strength provide different results

and this discrepancy can be explained by the fact that the fracture is a complex

problem at the intersection of physics of solids, mechanics of media and

material sciences. Real materials contain many defects of different form and

dimensions beginning from submicroscopic ones to big pores and main cracks.

Because of that the use of physical theories for a quantitative appreciation of

real structures can be considered by us as of little perspective. For technical

applications the concept of fracture in terms of methods of continuum mechanics

plays an important role. We shall distinguish between the strength of

a material (considered as an element of it – a cube, for example) and that of

structures, which include also samples (of a material) of a different kind. We

shall also distinguish between various types of fracture: ductile (plastic at big

residual strains), brittle (at small changes of a bodies’ dimensions) and due

to a development of main cracks (splits).



Here we will not use the usual approach to strength computation when the

distribution of stresses are found by methods of continuum mechanics and then

hypotheses of strength are applied to the most dangerous points. Instead, we

consider the fracture as a process developing in time according to constitutive

equations taking into account large strains of unsteady creep and damage

(development of internal defects). Any stage of the structures’ deformation

can be supposed as a dangerous one and hence the condition of maximum

allowable strains can be used. But more convenient is the application of a

criterion of an infinite strain rate at the moment of beginning of unstable

deformation. This approach gives critical strains and the time in a natural

way. When the influence of the latter is small, ultimate loads may be also


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