An implicit integration scheme with consistent tangent modulus for Leblond’s model of transformation-induced plasticity in steels

Thermomechanical treatments involving solid-state phase transformations play an important role for the manufacturing of functional and reliable components in many engineering applications. Accordingly, numerical investigation and optimization of such processes require considering thermoelastoplasticity under the influence of ongoing transformations and in particular the impact of transformation-induced plasticity (TRIP). While a number of elaborate plasticity models have been proposed for the description of TRIP, none of them seem to have received much prevalence in applications due to their complexity or hard to determine model parameters. Instead, the overwhelming majority of applied research either relies on simplistic formulations dating back to early phenomenological approaches or neglects TRIP altogether. In this work, we therefore provide an accessible, straightforward and easy-to-implement solution scheme for the TRIP model proposed by Leblond et al. which, despite being widely recognized, is hardly ever employed in full form. Specifically, we employ implicit backward-Euler integration and an elastic–plastic operator split approach to update the stresses in order to obtain a simple and concise algorithm for which we then derive the corresponding consistent tangent modulus. Furthermore, the work contains an application of the solution scheme to a symmetrically cooled plate and an in-depth discussion of the influence of TRIP by means of this tractable numerical example. Specifically, we highlight the discrepancies arising in transient and residual stresses and strains compared to the conventional $$J_2$$ J 2 -plasticity approach where the phase transformation is accounted for merely by adapting the yield strength of the compound.

ALE formulation for thermomechanical inelastic material models applied to tire forming and curing simulations

Forming of tires during production is a challenging process for Lagrangian solid mechanics due to large changes in the geometry and material properties of the rubber layers. This paper extends the Arbitrary Lagrangian–Eulerian (ALE) formulation to thermomechanical inelastic material models with special consideration of rubber. The ALE approach based on tracking the material and spatial meshes is used, and an operator-split is employed which splits up the solution within a time step into a mesh smoothing step, a history remapping step and a Lagrangian step. Mesh distortion is reduced in the smoothing step by solving a boundary value problem. History variables are subsequently remapped to the new mesh with a particle tracking scheme. Within the Lagrangian steps, a fully coupled thermomechanical problem is solved. An advanced two-phase rubber model is incorporated into the ALE approach, which can describe green rubber, cured rubber and the transition process. Several numerical examples demonstrate the superior behavior of the developed formulation in comparison to purely Lagrangian finite elements.

Non-LTE radiation hydrodynamics in PLUTO

Context. Modeling the dynamics of most astrophysical structures requires an adequate description of the interaction of radiation and matter. Several numerical (magneto-) hydrodynamics codes were upgraded with a radiation module to fulfill this request. However, those that used either the flux-limited diffusion (FLD) or the M1 radiation moment approaches are restricted to local thermodynamic equilibrium (LTE). This assumption may not be valid in some astrophysical cases. Aims. We present an upgraded version of the LTE radiation-hydrodynamics (RHD) module implemented in the PLUTO code, which we have extended to handle non-LTE regimes. Methods. Starting from the general frequency-integrated comoving-frame equations of RHD, we have justified all the assumptions that were made to obtain the non-LTE equations that are implemented in the module under the FLD approximation. An operator-split method with two substeps was employed: the hydrodynamics part was solved with an explicit method by the solvers that are currently available in PLUTO, and the non-LTE radiation diffusion and energy exchange part was solved with an implicit method. The module was implemented in the PLUTO environment. It uses databases of radiative quantities that can be provided independently by the user: the radiative power loss, and the Planck and Rosseland mean opacities. In our case, these quantities were determined from a collisional-radiative steady-state model, and they are tabulated as functions of temperature and density. Results. Our implementation has been validated through different tests, in particular, radiative shock tests. The agreement with the semi-analytical solutions (when available) is good, with a maximum error of 7%. Moreover, we have proved that a non-LTE approach is of paramount importance to properly model accretion shock structures. Conclusion. Our radiation FLD module represents a step toward a general non-LTE RHD modeling.

On Mindlin’s isotropic strain gradient elasticity: Green tensors, regularization, and operator-split

The theory of Mindlin’s isotropic strain gradient elasticity of form II is reviewed. Three-dimensional and two-dimensional Green tensors and their first and second derivatives are derived for an unbounded medium. Using an operator-split in Mindlin’s strain gradient elasticity, three-dimensional and two-dimensional regularization function tensors are computed, which are the three-dimensional and two-dimensional Green tensors of a tensorial Helmholtz equation. In addition, a length scale tensor is introduced, which is responsible for the characteristic material lengths of strain gradient elasticity. Moreover, based on the Green tensors of Mindlin’s strain gradient elasticity, point, line and double forces are studied.

Three-dimensional elastoplastic damage concrete model by dissipation-based arc-length method

This article presents a three-dimensional isotropic elastoplastic damage model for concrete structures. The plasticity of concrete is described by a nonassociated flow rule, using a three-parameter yield function as well as a modified Drucker–Prager-type potential. The damage of concrete is seen as a contribution work of tensile and compressive damage, with the evolution histories driven by the internal tensile and compressive variables, respectively. The iterative solution of plasticity and damage is carried out according to the concept of operator split, where a return-mapping algorithm as well as a substepping strategy is used. The consistent tangent stiffness considering the recursive relationship among substeps is derived. For the solution of global iteration, a dissipation-based arc-length method is employed. Good agreements are found in comparisons between numerical results and experimental data on both elementary and structural levels. Furthermore, the sensitivities of parameters that control strain softening are investigated.