Abstract
AbstractThis study aimed to find a simplified micromechanical formulation of Helmholtz free energy for quasi-brittle materials by making use of a system of microelements, and to provide a thermodynamic foundation for the development of multiscale constitutive theories. The microscopic incompatible strain field and residual stress field in an uncracked matrix between frictional microcracks were reproduced with microsprings, faults, and sliders by taking the microscopic fracture strain as a random variable. The locked microscopic additional strain energy—plastic free energy—was represented in an abstract way by the locked deformation energy within the microelement system. Straightforward free-energy functions dependent on the probability distribution of microscopic fracture strain were derived, which can be used in both deterministic and stochastic constitutive modeling.
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