One important advantage[1] of the MCA method is that it permits direct simulation of material fracture, including damage generation, crack propagation, fragmentation, and mass mixing.

The dynamics of the set of automata are defined by their mutual forces and rules for their relationships.

The mutual forces and rules for inter-elements relationships are defined by the function of the automaton response.

The new concept of the MCA method is based on the introducing of the state of the pair of automata (relation of interacting pairs of automata) in addition to the conventional one – the state of a separate automaton.

As a result of this, the automata have the ability to change their neighbors by switching the states (relationships) of the pairs.

The introducing of new type of states leads to new parameter to use it as criteria for switching relationships.

The initial structure is formed by setting up certain relationships among each pair of neighboring elements.

Due to finite size of movable automata the rotation effects have to be taken into account.

The equations of motion for rotation can be written as follows: Here Θij is the angle of relative rotation (it is a switching parameter like hij for translation), qij is the distance from center of automaton i to contact point of automaton j (moment arm), τij is the pair tangential interaction,

Translation of the pair automata The dimensionless deformation parameter for translation of the i j automata pair can be presented as: In this case: where Δt time step, Vnij – relative velocity.

As an example the titanium specimen under cyclic loading (tension – compression) is considered.

The loading diagram is shown in the next figure: Due to mobility of each automaton the MCA method allows to take into account directly such actions as: Using boundary conditions of different types (fixed, elastic, viscous-elastic, etc.)

It is possible to model different modes of mechanical loading (tension, compression, shear strain, etc.)