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The purpose of this paper is to propose a set of constitutive functions for dried bodies for accurate prediction of the entire deformation process of ceramic products during firing and to present relevant methods for determining their coefficients from a series of respective thermo-mechanical analysis (TMA) tests.

The function forms of the sintering-induced strain rate, viscoplastic multiplier and elastic modulus are formulated in order with reference to empirical data of relative densities. Separate TMA tests are conducted to identify their coefficients, while a stairway thermal cycle test is carried out to identify the parameters in the densification rate. Then, various finite element analyses (FEA) are performed for accuracy confirmation.

The performances of the present constitutive functions along with the identified material parameters were validated in comparison with the relevant test results. It has then been confirmed that these functions enable us to some extent to accurately estimate the non-mechanical and mechanical deformations of dried bodies during firing. Also, by performing FEA of an actual sanitary ware product, the applicability and capability of the proposed set of constitutive functions could be demonstrated.

The present methodology with the proposed constitutive functions is a simple, but reliable and practical approach for simulating the deformation process of arbitrary ceramic products subjected to firing and applicable for practical applications in various engineering fields.

The constitutive functions of the viscoplastic multiplier and elastic modulus, which enable us to properly characterize the mechanical behavior of dried bodies subjected to firing, are originally formulated in analogy with that of the sintering-induced strain.

This study aims to propose a novel viscoelastic–viscoplastic combined constitutive model for glassy amorphous polymers within the framework of thermodynamics at finite strain that is capable of capturing their rate-dependent inelastic mechanical behavior in wide ranges of deformation rate and amount.

The rheology model whose viscoelastic and viscoplastic elements are connected in series is set in accordance with the multi-mechanism theory. Then, the constitutive functions are formulated on the basis of the multiplicative decomposition of the deformation gradient implicated by the rheology model within the framework of thermodynamics. Dynamic mechanical analysis (DMA) and loading/unloading/no-load tests for polycarbonate (PC) are conducted to identify the material parameters and demonstrate the capability of the proposed model.

The performance was validated in comparison with the series of the test results with different rates and amounts of deformation before unloading together. It has been confirmed that the proposed model can accommodate various material behaviors empirically observed, such as rate-dependent elasticity, elastic hysteresis, strain softening, orientation hardening and strain recovery.

This paper presents a novel rheological constitutive model in which the viscoelastic element connected in series with the viscoplastic one exclusively represents the elastic behavior, and each material response is formulated according to the multiplicatively decomposed deformation gradients. In particular, the yield strength followed by the isotropic hardening reflects the relaxation characteristics in the viscoelastic constitutive functions so that the glass transition temperature could be variant within the wide range of deformation rate. Consequently, the model enables us to properly represent the loading process up to large deformation regime followed by unloading and no-load processes.