A 1D elastic plastic damage constitutive law for bone tissue

A thermomechanical constitutive theory for elastic composites with distributed damage—I. Theoretical development

A functional model of a memristive element (ME) with multiple internal state variables (ISV) is proposed. The dynamics of each of the ME ISV is determined by functional transformations of the ME input stimulus by the corresponding integral and differential form and time constant. ME functional model can be efficiently implemented in modern CAD systems based on a limited number of library components and allowing simple hardware emulation. Theoretical and experimental study of the proposed model with two ISVs and its hardware emulation for the mimicry of the sodium ion channel in the development of pulse neuron adaptive networks showed its adequate response to external influences, similar to the Hodgkin-Huxley model. Truncations of this model to the first order (1C1R1MOS) with one ISV exhibit the property of forward and reverse memristivity, can be applied to mimicry of potassium ion channels.

Critical state model for structured soil

The theory of a single internal variable of state is well established including the weak nonlocality and the enrichment by extra entropy flux. The theory is based on the consideration of the internal variable of state as a tool for taking into account the internal dissipation. Inertial effects are absent in this theory by definition, which leads to parabolic evolution equations for the internal variables of state. Due to the simplicity, the single internal variable theory is the necessary first step in the construction of more sophisticated material models.

Abstract. The superplastic deformation behavior and microstructure characteristics of TA32 titanium alloy were studied at different deformation temperatures (920-960°C) and initial strain rates (1×10-3-3×10-3 s-1). A unified constitutive model was developed and coupled with internal state variables. Results show that TA32 alloy featured steady flow stress and uniform plastic deformability under the dynamic equilibrium between softening and hardening effects. Increasing temperature and strain induced α→β phase transformation and α grain growth. Dislocation accumulation and grain boundary migration formed the dynamic recovery (DRV) and dynamic recrystallization (DRX) mechanisms. Using dislocation density, the proposed unified constitutive model built a quantitative relationship between superplastic flow stress and internal state variables such as grain size, with the correlation coefficient R, average absolute relative error (AARE), and root mean square error (RMSE) between the predicted and experimental stress values being 0.98, 6.91%, and 1.94, respectively. The unified constitutive model could predict well the flow stress and grain size evolution of TA32 titanium alloy during superplastic deformation.

A coupled, transversely isotropic, deformation and damage fatigue model has been implemented within the finite element method and utilized, along with a static progressive damage model, to predict the fatigue life, stiffness degradation as a function of number of cycles, and post-fatigue tension and compression response of notched, multidirectional laminates. The material parameters for the fatigue model were obtained utilizing ply-level classical lamination theory simulations and the provided [0], [90] and [±45] experimental composite laminate S–N data. Within the fatigue damage model, the transverse and shear stiffness properties of the plies were degraded with an isotropic scalar damage variable. The stiffness damage in the longitudinal (fiber) ply direction was suppressed, and instead the strength of the fiber was degraded as a function of fatigue cycles. A maximum strain criterion was used to capture the failure in each element, and once this criterion was satisfied, the longitudinal stiffness of the element was eliminated. The resulting, degraded properties were then used to calculate the new stress state. This procedure was repeated until final failure of the composite laminate was achieved or a specified number of cycles was reached. For post-fatigue tension and compression behavior, four internal state variables were used to control the damage and failure. The predictive capability of the above-mentioned approach was assessed by performing blind predictions of notched multidirectional IM7/977-3 composite laminate response under fatigue and post-fatigue tensile and compressive loading, followed by a recalibration phase. Tabulated data along with detailed results (i.e. stress–strain curves as well as damage evolution states at given number of cycles compared to experimental data) for all laminates are presented.

First, we formulate the mixed initial boundary value problem in the theory of thermoelastic microstretch bodies having certain internal state variables. Then by using some approachable computing techniques and the known Gronwall's inequality we will prove that the presence of internal state variables do not influence the uniqueness of solution of the mixed problem.

Cortical and trabecular bone adaptation to incremental load magnitudes using the mouse tibial axial compression loading model

Viscoelastic properties of wet cortical bone—I. Torsional and biaxial studies

The nonlinear transition period of broadband ultrasound attenuation as bone density varies

Using a femtosecond pulsed laser system (pulse width = 100fs, repetition rate = 1kHz, λ = 800nm), ablation threshold studies of freshly culled bovine and ovine cortical bone samples were identified using the diameter regression technique. Using the D2 technique, the ablation threshold was found to lie within a range of 0.83 - 0.96 Jcm −2 and 0.89 - 0.95 Jcm −2 for ovine and bovine cortical bone respectively indicating that laser ablation of bone is irrespective of target species. The relationship between cortical bone tissue removal and the number of applied pulses was explored. By altering the laser spot translation rate, we varied the number of pulses at each point along scribed linear cuts. Optical Coherence Tomography (OCT) and PDMS casting indicates that cut depth is linearly dependent on the number of pulses applied to the tissue, irrespective of donor species. For single pulse ablation of ovine and bovine cortical bone, we determined that the ablation rates were 0.41 - 0.75 μm per pulse and 0.28 - 0.90 μm per pulse when pulses of fluences in the range 0.52 - 2.63 Jcm −2 were applied to ovine and bovine cortical bone tissue, respectively. Structural analysis of the ablation features using environmental scanning electron microscopy and optical microscopy were utilized to assess the ablation features and identify signs of damage to surrounding tissue. We observed no structural indications of thermal shockwave cracking, molten debris deposition or charring of the tissue whilst leaving hydroxyapatite crystal structure intact.

A model of crystal plasticity containing a natural length scale

In the semi-brittle regime, the time-dependent behavior of rocksalt results from two types of inelastic deformation mechanisms, which involve dislocations motion producing hardening and microcracks propagation leading to fracturing. In constitutive models, the former type of mechanisms can be expressed from empirical functions using external variables or introduced through the use of the internal state variables (ISV). The latter type of mechanisms, on the other hand, is often neglected or expressed from usual failure criteria. However, because these two types of mechanisms act simultaneously, a ∞upled approach should be considered. In this paper, the authors present a general ISV model that is used to describe in a unified manner the semi-brittle behavior of rocksalt for a variety of loading conditions. As specific examples, constant strain rate and creep test results under triaxial compression are presented and compared to model predictions.

A thermodynamically consistent model is formulated to depict the polarization hysteresis and the rate-dependent behavior of relaxation in ferroelectric materials. On the relaxation condition, the polarization gradually changes with time while the applied electric field is kept constant. The present model introduces internal state variables to represent such irreversible dissipation processes. Based on the first and second laws of thermodynamics, the evolution laws of the internal state variables consisting of constitutive equations are then derived through the definitions of the Helmholtz free energy and a dissipation potential. To verify the applicability of the constitutive model, numerical simulations are compared with experiment in the literature.

Phenomenological model for the macroscopical material behavior of ferroelectric ceramics