This paper focuses on the experimental investigation and modelling of the crosslinking reaction of photopolymers used in additive manufacturing processes such as digital light processing and stereolithography. Starting with general mathematical concepts for the description of the material behaviour of polymeric materials, the importance of modelling the crosslinking reaction is emphasized. In order to characterise the crosslinking reaction experimentally, photocalorimetric measurements with varying isothermal temperature and light intensity are shown. From the exothermic heat flows measured during the crosslinking reaction, the degree of cure can be determined for each experimental scenario as a function of time. It is shown that the test temperature and light intensity have a significant influence on the crosslinking reaction. A modelling approach for the description of the crosslinking reaction incorporating temperature and light intensity is presented. Moreover, parameter identification and a comparison of the proposed model with the experiments are conducted. The indentified model has an excellent match with experimental data, resulting in a least square error smaller than 3 %. The proposed model and identification method opens up several extensions for the modelling of the material behaviour.

In the present paper, the degree of cure-dependent viscoelastic properties of a commercial photopolymer resin (Loctite$$^{\textregistered }$$ ® 3D 3830) used in digital light processing (DLP) 3D printing are investigated experimentally and described by suitable model equations. To do this, tests are carried out both on the liquid resin and printed specimens under various conditions. The experimental methods include photo-DSC, UV rheometry, and dynamic mechanical analysis. A commercial digital light processing (DLP) printer (Loctite$$^{\textregistered }$$ ® EQ PR10.1) is used for the printing of the samples. Model equations are proposed to describe the behavior of the material during and after the printing process. For the representation of the degree of cure depending on temperature and light intensity, the one-dimensional differential equation proposed in a previous paper is extended to capture a temperature-dependent threshold value. The change of the viscoelastic properties during crosslinking is captured macroscopically by time-temperature and time-cure superposition principles. The parameters of the model equations are identified using nonlinear optimization algorithms. A good representation of the experimental data is achieved by the proposed model equations. The findings of this paper help users in additive manufacturing of photopolymers to predict the material properties depending on the degree of cure and temperature of printed components.

This paper proposes an experimental investigation of a commercial photopolymer resin followed by material modelling and manufacturing system characterization. We focus on the effect of the degree of cure and temperature on the material properties of the photopolymer materials. UV curing properties of the liquid resin are assessed with the thickness measurement by optical tomography. Besides, the specific heat capacity is determined for the almost completely cured and uncured samples with DSC measurements. Photo-DSC experiments are performed to investigate the curing reaction and modelling of the evolution of the degree of cure depending on the light intensity and temperature. In addition, chemical shrinkage behaviour is captured as function of the degree of cure by the high-precision balance setup. As a result of our experimental studies, model equations are proposed to describe the material behaviour.

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Besides large nonlinear deformations, polyurethane adhesives exhibit elastic and viscous material behaviour simultaneously. Although the concept of rheological elements is a quite simple method to describe rate effects, the identification of model parameters is a challenging task. Dynamic mechanical analysis provides the experimental database. By using time-temperature superposition, the experimental frequency range can be extended in order to identify the relaxation times and dimensionless stiffnesses of the rheological network. The simulation results are in good agreement with stress-strain curves from tests with different strain rates.The thick polyurethane adhesive layer with a thickness of 5 mm is modelled by a three-dimensional finite viscoelasticity model with respect to the reference configuration. Due to its nearly incompressibility, the second PIOLA-KIRCHHOFF stress is split into a volumetric and isochoric part additively over time t, whereby the volumetric part exhibits no viscous effects, see [1].In the isochoric part, the generalised MAXWELL solid consisting of N parallel chains with springs and dashpots is used with relaxation times τ 1 , . . . , τ N and dimensionless stiffnesses γ 1 , . . . , γ N , respectively. For quasi-static processes, the isochoric model response is governed by the dimensionless equilibrium stiffness γ ∞ only. The purely elastic bulk behaviour is described by a model proposed by MIEHE (see [2]) depending on the Jacobian J and bulk modulus K, whereas the instantaneous, isochoric response is defined by the MOONEY-RIVLIN model which has two model parameters C 10 and C 01 as well as depends on the first and second invariant of the unimodular right CAUCHY-GREEN tensorC = J −2/3 C (see [4], p. 100).Thus, the proposed model has 2N + 4 parameters in total. The push-forward operations for the CAUCHY stress and the spatial tangent modulus in terms of the deformation gradient F provide the required expressions for the implementation into the commercial finite element program LS-DYNA.The dimensionless stiffnesses and relaxation times are assumed to be constant through the deformation process. Hence, the identification of parameters for the viscous behaviour is carried out in the domain of small deformations as proposed in [3]. Parameter identificationThe identification of the model parameters is split into two consecutive steps: at first, the relaxation times τ 1 , . . . , τ N and dimensionless stiffnesses γ ∞ , γ 1 , . . . , γ N of the generalised MAXWELL solid are identified simultaneously by means of test data from dynamic mechanical analysis . For this purpose, the mastercurve of the storage modulus E ′ is created at room temperature. The viscoelastic modelling of the rectangular adhesive bar clamped at both ends and loaded by harmonic excitation u (t) =û sin (ωt) with varying angular frequency ω and small displacement amplitudeû = 40 µm leads to the analytical relation between storage modulus and spring stiffnesses E ∞ , E 1 , . . . , E N as well as relaxation times of the generalise...