# Non-Linear Creep-Relaxation Constitutive Damage Model for Aging Concrete
## 4 Conclusions
\begin{tabular}{l l} \(\mathcal{G}_{1}\) & Isotropic age-dependent relaxation function related to the deviatoric strain; \\ \(\hat{\mathcal{G}}_{2}\) & Isotropic age-dependent relaxation function related to the dilatational strain; \\ \(G_{ijkl}\) & Components of age-independent relaxation tensor; \\ \(H_{\rm f}\) & Temporal Heaviside function; \\ \(H_{\rm e}\) & Heaviside function defined in the principal strain space; \\ \(I\) & Identity tensor; \\ \(J\) & Thermodynamic fluxes; \\ \(k_{0}\) & Experimental exponent to replace \(k_{i}^{\lambda}\), \(k_{i}^{\mu}\) and \(k_{i}^{x\bar{l}}\) for simplification; \\ \(k_{i}^{\lambda}\) & Department replacing the function \(\hat{k}_{D}\) for simplification; \\ \(k_{i}^{k}\) & Experimental exponents of the \(\lambda\) non-aging function; \\ \(k_{i}^{x\bar{l}}\) & Experimental exponents of the \(\mu\) non-aging function; \\ \(\hat{k}_{D}\) & Experimental aging hardening function; \\ \(\hat{k}_{D}\) & Rate of change in experimental aging hardening function; \\ \(\hat{k}_{f}\) & Long-term creep bulk aging function; \\ \(\hat{k}_{f}\) & Rate of change in long-term creep bulk aging function; \\ \(\mathbf{n}^{(i)D}\) & Eigenvectors of the damage tensor; \\ \(\mathbf{n}^{(i)\epsilon}\) & Eigenvectors of the strain tensor; \\ \(p\) & Hydrostatic pressure; \\ \(\mathbb{P}^{\epsilon+}\) & Positive orthogonal projection of the strain; \\ \(\mathcal{Q}^{\epsilon+}\) & Positive strain rotation tensor; \\ \(s_{ij}\) & Deviatoric stress tensor components; \\ \(\mathbf{s}\) & Deviatoric stress tensor; \\ \(t\) & Current time variable; \\ \(v\) & Degree of solidification; \\ \(V\) & Thermodynamic conjugate of the degree of solidification; \\ \(\mathbf{x}\) & Position vector; \\ \(\mathbf{X}\) & Thermodynamic forces; \\ \(Y_{EQ}\) & Equivalent energy release rate; \\ \(Y_{ij}\) & Energy release rate components; \\ \(\mathbf{Y}\) & Energy release rate associated to the damage; \\ \(\beta\) & Damage strengthening; \\ \(\hat{\beta}\) & Rate of the damage strengthening; \\ \(\delta_{ij}\) & Kronecker delta; \\ \(\varepsilon_{ij}\) & Strain tensor components; \\ \(\varepsilon\) & State of strain at any point; \\ \(\varepsilon^{ep}\) & Elastoplastic strain; \\ \(\hat{\varepsilon}_{ij}^{c}\) & Crep strain components; \\ \(\varepsilon^{c}\) & Creep strain; \\ \(\varepsilon^{v}_{ij}\) & Eigenvalues of the short-term creep strain tensor; \\ \(\varepsilon^{v}_{ij}\) & Short-term creep strain components; \\ \(\varepsilon^{v}\) & Short-term creep strain; \\ \(\varepsilon^{v\bar{v}+}_{ij}\) & Components of positive part of short-term creep strain; \\ \(\varepsilon^{v\bar{v}+}\) & Positive part of short-term creep strain; \\ \(\varepsilon^{f}_{ij}\) & Long-term creep strain components; \\ \(\hat{\varepsilon}_{ij}^{f}\) & Rate of long-term creep strain components; \\ \(\varepsilon^{v}\) & Long-term creep strain; \\ \(\varepsilon^{v\bar{v}}\) & Viscoelastic creep strain; \\ \(\varepsilon^{ep}\) & Viscoplastic creep strain; \\ \(\varepsilon^{vd}\) & Viscolamage creep strain; \\ \(\varepsilon^{0}\) & Shrinkage and thermal strain; \\ \(\hat{\eta}\) & Aging viscosity function; \\ \(\eta_{0}\) & Effective viscosity of the solidified matter; \\ \(\theta\) & Time variable for changes in mechanical properties; \\ \(\lambda\) & First Lam\(\acute{e}\) elastic constant and First Lam\(\acute{e}\) non-aging relaxation function; \\ \end{tabular}