This study presents a comprehensive simulation of the fused deposition modeling (FFF) process of polylactic acid (PLA) using the multiphase-field method. Compared to existing works, this work aims to simulate the overall FFF process. It combines temperature evolution, viscous flow, polymer crystallization, and residual strain calculations within the microstructure with mechanical property analysis in a single study. Simulation studies were done in the case of the single layer to study the flowing effect of the filament and the distribution of temperature, viscosity, and relative crystallinity throughout the cooling process. Afterward, a system of layers with three rows and three columns was investigated. The nozzle temperature, bed temperature, viscosity, and layer height were varied, and for each case the porosity was calculated. After running mechanical loading simulations on each case, the effective Young’s modulus was calculated. The simulations show that increasing the nozzle and bed temperatures leads to a decrease in the porosity, while increasing the layer height increases the distortion in the pores’ shapes without significantly affecting the porosity. The decrease in porosity leads to an increase in the effective Young’s modulus of the structure in a linear trend within the investigated porosities. The Young’s modulus–porosity relation was validated with experimental values from the literature within an average error of 3.6 %.

The multiphase-field method is widely used to simulate the evolution of complex microstructures in computational materials science and is commonly derived via a variational approach. When coupled with heat conduction, it is desirable to derive both the multiphase-field method and the heat conduction equation from a unified, consistent framework. In the present work, this is accomplished by introducing order parameters as internal state variables and exploiting the entropy production inequality of the diffuse interface region for multiple intersecting phases. The approach represents a generalization of the method of Prahs et al. (Prahs et al. Continuum Mech. Thermodyn. 37 , 55 (2025). https://doi.org/10.1007/s00161-025-01383-y ) via a dual-interaction ansatz and its Lagrange multiplier simplification, while maintaining thermodynamical consistency. This requirement, in turn, restricts the choice of the interpolation functions. Moreover, the coupling effects in the heat conduction equation as well as connections to established evolution equations from the literature are demonstrated through an illustrative derivation.

Crystallization of semicrystalline polymers is accompanied by changes in density as well as the release of heat. These processes generate crystallization-induced eigenstrains and establish a coupling between microstructure evolution, mechanics, and heat conduction. In the present work, a thermomechanically coupled multiphase-field formulation for non-isothermal polymer crystallization is developed by combining crystallization kinetics and crystallization-induced eigenstrains with a phase-inherent generalized Maxwell-Wiechert model. The crystallization-induced eigenstrain is derived from the local crystallinity-dependent density and enters the phase-specific strain decomposition together with thermal and viscous strains. The resulting mechanical free energy contributes to the phase-field driving force, while crystallization, eigenstrain evolution, viscoelastic dissipation, and phase evolution give rise to corresponding contributions in the heat conduction equation. The model is used to investigate the non-isothermal crystallization of polyamide 6. Numerical investigations show that the mechanical contribution to the phase-field driving force depends on the stress state associated with constrained thermal and crystallization-induced eigenstrains. For the experimentally determined Poisson ratio of polyamide 6, the effect of mechanical coupling on the final crystallinity remains small, whereas the increased volumetric stresses arising when approaching incompressibility lead to a more pronounced suppression of crystallization. Investigations into the heat source terms identify the crystallinity rate contribution as the largest internal heat source under the investigated conditions, followed by the phase evolution and thermoelastic contributions. This heat release increases the temperature, slows cooling, and reduces the final crystallinity, whereas mechanically induced heat-source contributions and viscous dissipation remain secondary under the investigated conditions.

In the continuum thermodynamic approach to the phase-field method by Prahs et al. (Prahs et al. Continuum Mech. Thermodyn. 37, 55 (2025). https://doi.org/10.1007/s00161-025-01383-y), the order parameter is considered as an internal state variable and the phase-field method is interpreted as an approximation of the corresponding sharp-interface theory. The approach involves phase-specific strains and stresses within the diffuse interface region. In the present contribution, the interpolation relation for the effective strain within the diffuse interface is used to obtain an algebraic reparametrization in which the phase-specific strains and their rates are expressed by the effective strain, the effective strain rate, and the corresponding strain jump and its rate. The reparametrization defines a bijective mapping from the two phase-specific strains to the effective strain and the strain jump and therefore preserves the dimension of the mechanical state space. It modifies the thermodynamic forces conjugate to the selected rates and, consequently, the order-parameter and mechanical contributions to the diffuse-interface dissipation, while the total dissipation remains unchanged. At the same time, the heat conduction equation obtained in the original formulation remains unchanged, since the corresponding derivation already uses the phase-specific stresses and strain rates in the mechanical power contribution. The algebraic reparametrization is generalized to the multiphase-field method based on internal state variables as described by Prahs et al. (Prahs et al., Continuum Mech. Thermodyn. 38, 47 (2026), https://doi.org/10.1007/s00161-026-01470-8).

The microstructural degradation of Ni–CGO anodes in solid oxide fuel cells affects both electrochemical and mechanical properties. This study presents an automated workflow to quantify the evolution of geometrical descriptors and their influence on effective mechanical properties. Three-dimensional anode microstructures were aged up to 35,000 h using phase-field and stochastic modeling, followed by mechanical loading simulations. Aging caused microstructural coarsening as the mean pore diameter increased, while pore specific surface area and triple-phase boundary density decreased. Effective elastic moduli and the anisotropy index also decreased, indicating a mechanically weaker and less heterogeneous microstructure. The effective Hill modulus was strongly related to pore volume fraction and pore specific surface area. Average von Mises stress remained nearly constant, but the critical volume fraction increased with aging. It related with pore diameter and inversely with pore specific surface area and triple-phase boundary density.