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Understanding the complex behavior of menisci is of growing interest in many fields including sports medicine, surgical simulation, and implant design. The selection of an appropriate material model and accurate model parameters contribute to identifying the degree of degeneration of the meniscus. Incorporating patient-specific material parameters could further improve the safe handling of tissue during probing in knee arthroscopy simulations, supporting more informed intraoperative decision-making. The objective of this study is to identify hyperelastic material parameters of individual human menisci based on an inverse parameter identification approach using optimization and demonstrate a real-time interactive surgical simulation using identified parameters. Mechanical tests were conducted in indentation of the anterior, mid-body, and posterior regions of five lateral and medial menisci to obtain experimental force–displacement data. An inverse parameter identification based on these tests and finite element (FE) models was employed to minimize the differences between the experimental and simulated force. The region-specific FE models considered the predominant collagen fiber orientation of the meniscus. Anisotropic hyperelastic material parameters were optimized using a particle swarm optimization algorithm. Finally, the optimized parameters were used in simulation open framework architecture (SOFA) and demonstrated a real-time probe-meniscus interaction during the arthroscopic meniscus examination. The optimized values revealed subject-specific characteristics, along with anatomical and regional variations, with high shear modulus observed in the anterior region of the medial meniscus (0.76 ± 0.28 MPa for 1 mm indentation). Additionally, an increase in shear modulus was observed with increased indentation depth (p<0.05 except for the mid-body of the medial meniscus).

Ensuring precise prediction, monitoring, and control of frictional contact temperature is imperative for the design and operation of advanced equipment. Currently, the measurement of frictional contact temperature remains a formidable challenge, while the accuracy of simulation results from conventional numerical methods remains uncertain. In this study, a PINN model that incorporates physical information, such as partial differential equation (PDE) and boundary conditions, into neural networks is proposed to solve forward and inverse problems of frictional contact temperature. Compared to the traditional numerical calculation method, the preprocessing of the PINN is more convenient. Another noteworthy characteristic of the PINN is that it can combine data to obtain a more accurate temperature field and solve inverse problems to identify some unknown parameters. The experimental results substantiate that the PINN effectively resolves the forward problems of frictional contact temperature when provided with known input conditions. Additionally, the PINN demonstrates its ability to accurately predict the friction temperature field with an unknown input parameter, which is achieved by incorporating a limited quantity of easily measurable actual temperature data. The PINN can also be employed for the inverse identification of unknown parameters. Finally, the PINN exhibits potential in solving inverse problems associated with frictional contact temperature, even when multiple input parameters are unknown.

A key challenge for the virtual characterization of components manufactured using short fiber-reinforced thermoplastics (SFRTs) is the inherent anisotropy which stems from the manufacturing process. To address this, a multi-scale approach is necessary, leveraging deep material networks (DMNs) as a micromechanical surrogate, for a one-stop solution when simulating SFRTs under highly nonlinear long-term load cases like creep and fatigue. Therefore, we extend the a priori fiber orientation tensor interpolation for quasi-static loading (Liu et al. in Intelligent multi-scale simulation based on process-guided composite database. arXiv:2003.09491 , 2020 ; Gajek et al. in Comput Methods Appl Mech Eng 384:113,952, 2021 ; Meyer et al. in Compos Part B Eng 110,380, 2022 ) using DMNs with a posteriori approach. We also use the trained DMN framework to simulate the stiffness degradation under fatigue loading with a linear fatigue-damage law for the matrix. We evaluate the effectiveness of the interpolation approach for a variety of load classes using a dedicated fully coupled plasticity and creep model for the polymer matrix. The proposed methodology is validated through comparison with composite experiments, revealing the limitations of the linear fatigue-damage law. Therefore, we introduce a new power-law fatigue-damage model for the matrix in the micro-scale, leveraging the quasi-model-free nature of the DMN, i.e., it models the microstructure independent of the material models attached to the constituents of the microstructure. The DMN framework is shown to effectively extend material models and inversely identify model parameters based on composite experiments for all possible orientation states and variety of material models.

In powder bed-based additive manufacturing (AM), complex geometries can be produced in a layer-wise approach. Results of material science experiments regarding material property identification, e.g., tensile strength, show interdependencies between the test load direction and the layer orientation. This goes hand-in-hand with the measured cutting force, changing with the relative angle between cutting direction and layer orientation in orthogonal cutting tests. However, due to the specific process characteristics, the layer orientation results in anisotropic material properties. Therefore, during machining, the material behaves depending on the buildup direction, which influences the cutting process. To predict this behavior, a simplified inverse approach is developed to determine the buildup direction-dependent parameters of a modified Johnson–Cook model for cutting simulation. To qualify these cutting models, mainly the cutting force and additionally the chip formation examined during orthogonal cuts are used. In the present paper, the influence of the laser-powder-bed-fusion (LPBF) process parameters on subtractive post-processing are shown. A good agreement between verification experiments and simulations is achieved.

The elasto-plastic material behavior, material strength and failure modes of metals fabricated by additive manufacturing technologies are significantly determined by the underlying process-specific microstructure evolution. In this work a novel physics-based and data-supported phenomenological microstructure model for Ti-6Al-4V is proposed that is suitable for the part-scale simulation of laser powder bed fusion processes. The model predicts spatially homogenized phase fractions of the most relevant microstructural species, namely the stable β -phase, the stable α s -phase as well as the metastable Martensite α m -phase, in a physically consistent manner. In particular, the modeled microstructure evolution, in form of diffusion-based and non-diffusional transformations, is a pure consequence of energy and mobility competitions among the different species, without the need for heuristic transformation criteria as often applied in existing models. The mathematically consistent formulation of the evolution equations in rate form renders the model suitable for the practically relevant scenario of temperature- or time-dependent diffusion coefficients, arbitrary temperature profiles, and multiple coexisting phases. Due to its physically motivated foundation, the proposed model requires only a minimal number of free parameters, which are determined in an inverse identification process considering a broad experimental data basis in form of time-temperature transformation diagrams. Subsequently, the predictive ability of the model is demonstrated by means of continuous cooling transformation diagrams, showing that experimentally observed characteristics such as critical cooling rates emerge naturally from the proposed microstructure model, instead of being enforced as heuristic transformation criteria. Eventually, the proposed model is exploited to predict the microstructure evolution for a realistic selective laser melting application scenario and for the cooling/quenching process of a Ti-6Al-4V cube of practically relevant size. Numerical results confirm experimental observations that Martensite is the dominating microstructure species in regimes of high cooling rates, e.g., due to highly localized heat sources or in near-surface domains, while a proper manipulation of the temperature field, e.g., by preheating the base-plate in selective laser melting, can suppress the formation of this metastable phase.

When tailoring porous absorbers in acoustic applications, an appropriate acoustic material model, as well as the relationship between the material model parameters and the microscale geometry of the material, is indispensable. This relationship can be evaluated analytically only for few simple material geometries. Machine-learning models can close this gap for complex materials, but due to their black-box nature, the interpretability of obtained inferences is rather low. Therefore, an existing neural network model that predicts the acoustic properties of a porous material based on the microscale geometry is subject to statistics-based sensitivity analysis. This is conducted to gain insights into the relationship between the microscale geometry and the acoustic material parameters of a generic bar-lattice design porous material. Although it is a common approach in the field of explainable artificial intelligence research, this has not been widely investigated for porous materials yet. By deriving statistics-based sensitivity measures from the neural network model, the explainability and interpretability is increased and insights into the relationship of the acoustic properties and their microscale geometry of the porous specimen can be obtained. The results appear plausible and comparable to existing studies available in the literature, showing if and how the bar-lattice geometry influences the acoustic material parameters. Moreover, it could be shown that the applied global sensitivity analysis method allows us to not only derive a one-to-one parameter impact relation, but also reveals interdependencies that are important to address during a material tailoring process.

The application of porous materials is a common measure for noise mitigation and in room acoustics. The prediction of the acoustic behavior applies material models, among which most are based on the Biot-parameters. Thereby, it is expected that, if more Biot-parameters are used, a better prediction can be obtained. Nevertheless, an estimation of the Biot-parameters from the geometric design of the material is possible for simple structures only. For common porous materials, the microstructure is typically unknown and characterized by homogenized quantities. This contribution introduces a methodology that enables the design and optimization of porous materials based on the Biot-parameters and connects these to microscopic geometric quantities. Therefore, artificial porous materials were manufactured using 3D-printing technology with a prescribed geometric design and the influence of different design variables was investigated. The Biot-parameters were identified with an inverse procedure and it can be shown that different Biot-parameters can be influenced by adjusting the geometric design variables. Based on these findings, a one-parameter optimization procedure of the material is set up to maximize the absorption characteristics in the frequency range of interest.

Tube hydroforming is a versatile forming process widely used in lightweight structural applications, where accurate characterization of the hoop mechanical behavior is crucial for reliable design and simulation. The ring hoop tensile test (RHTT) provides valuable experimental data for evaluating the elastoplastic response of anisotropic tubes in the hoop direction, but frictional effects often distort the measured force–displacement response. This study proposes a deep learning-based inverse identification framework to accurately recover the true hoop stress–strain behavior from RHTT data. Convolutional and recurrent neural network architectures, including CNN, long short term memory (LSTM), gated recurrent unit (GRU), bidirectional GRU (BiGRU), bidirectional LSTM (BiLSTM) and ConvLSTM, were trained using numerically generated datasets from finite element simulations. Data augmentation and hyperparameter tuning were applied to generalization. The hybrid ConvLSTM model achieved superior performance, with a minimum mean absolute error (MAE) of 0.08 and a coefficient of determination (R2) value of approximately 0.97, providing a close match to the Hill48 yield criterion. The proposed approach demonstrates the potential of deep neural networks as an efficient and accurate alternative to traditional inverse methods for characterizing anisotropic tubular materials.

Hill’48 yield function has been widely used to describe the anisotropic behaviors of material in FE simulation of tube and sheet metal forming process. To obtain the material behaviors of small-sized H96 brass extrusion double-ridged rectangular tube (DRRT) in bending process, an inverse method combining response surface method and three-point bending was proposed to identify the parameters of Hill’48 yield function. It was found that comparing with Hill’48 yield function only considering the normal anisotropy and Mises yield function, Hill’48 yield function with the identified parameters performs the best in reproducing the material behavior of H96 brass DRRT in three-point bending process. And then Hill’48 yield function with the identified parameters was also adopted in the FE simulations of rotary draw bending of DRRT. It was observed that the prediction accuracy of cross sectional deformation of DRRT in rotary bending process was improved effectively by using Hill’48 yield function with the identified parameters. This proves that the proposed inverse method is suitable to the real forming process.

This paper concerns the experimental and numerical study of the plug-assisted thermoforming process of high impact polystyrene (HIPS). The thermomechanical properties of this polymer were characterized at different temperatures and deformation rates. To study the influence of different parameters in the real conditions of plug-assisted thermoforming process, we carried out “plug-only” tests at different temperatures and plug velocities. To model the deformation behaviour of HIPS, we proposed a thermo-elastic-viscoplastic model, which we have implemented in Abaqus software. A thermo-dependent friction model was also proposed and implemented in Abaqus software. The parameters of the proposed models were identified by the inverse analysis method in the real conditions of plug-assisted thermoforming. The proposed models were validated with “plug-only” tests and plug-assisted thermoforming of yogurt container.