Model of the Catastrophic Stage of Wood Damage Accumulation Under Uniaxial Compression

It is known that the failure of quasi-brittle materials such as wood is accompanied by an accumulation of damage and a decrease in the effective cross-sectional area of the specimen. At a certain stage of loading the process of damage accumulation significantly accelerates and is characterized as a catastrophic process. Purpose of work: developing a model of catastrophic stage of damage accumulation under uniaxial compression of wood. Damage accumulation is characterized by a damage function. The choice of the damage function is not the only one. Two such sigmoid functions are discussed. Only one of the two functions provided the ability to quantify the rate and acceleration of catastrophic damage accumulation. It is shown that the rate of damage accumulation increases with increasing axial strain and reaches an extremum in the middle of the theoretical process duration. The theoretical dependence is not fully realized, since the failure occurs in the vicinity of the point of rate extremum, but does not reach it. Analytical and graphical estimates of the rate and acceleration of damage accumulation were obtained. The simulation results are in agreement with the data known from the literature.