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Additional file 1: Figure S1 (a) Time course of mibefradil mediated reversal of mechanical hypersensitivity in mice with a chronic constriction injury of the sciatic nerve. Statistical analyses were performed by two-way ANOVA followed by Tukey's test. Asterisks denote a significant difference of **P < 0.01 and ***P < 0.001 when compared with the control group (n = 5–7). Hashtags denote P < 0.001 for comparison with the sham-operated group. (b) Mibefradil at 10 mg/kg inhibits pain responses in CCI operated wild type mice, but not in Cav3.2 null mice *P < 0.05 and ***P < 0.001 (n = 5–6).

Different damage models are proposed in the literature to predict the behavior of dynamic fracture of brittle materials using the peridynamic formulation. The prototype micro-brittle material proposed by Silling and Askari (Comput. Struct. 83:1526−1535, 2005), PMB, and its modified version proposed by Du et al. (J. Elast. 132:197−218, 2018), DTT, concern bond-breakage damage criteria applied to a bond-based constitutive model. These models consider only the direct interaction between material points and have, therefore, a fixed Poisson’s ratio. Lipton et al. (J. Elast. 133:129−153, 2018) propose a state-based peridynamic model, LSJ, which, in addition to the strain state field, also considers a dilatational term and is coupled with a damage criterion that considers failure not only between bonds but also collectively, among all the bonds connected to a given material point. This criterion has two unrelated damage functions, one associated with the strain state field and the other one with its dilatational part only. In this work, we modify the LSJ model to consider only bond-breakage damage, rather than interaction-breakage damage, and call it the LSJ-T model. We also implement a bond-breakage damage criterion in the two-dimensional ordinary, state-based peridynamic model presented by Le et al. (Int. J. Numer. Methods Eng. 98:547−561, 2014), which we call the LPS-T model. In both cases, when the strain state of a bond reaches a critical value, rather than breaking, it is continuously damaged until bond-breakage occurs. To study the capability of these models in simulating the formation and the propagation of cracks, we have simulated numerically the experiment of a thin glass plate with an initial semi-crack under mode I loading. All the models were able to grasp the main features of crack propagation, such as the crack propagation speed and the crack pattern. Both the DTT and the LSJ-T models have predicted symmetric crack paths and no minor branches, which indicate a stable crack propagation path. We have also considered the experiment of a notched cement-mortar plate with a hole under quasi-static mode I loading. This experiment was simulated numerically using the aforementioned damage models together with a dynamic relaxation method. We have obtained solutions of the associated numerical problems, which yield a convergent sequence of response forces in terms of displacements. In addition, crack patterns predicted by these solutions are in good agreement with crack patterns observed experimentally.

We consider the equilibrium problem, with no body force, of a cylindrically orthotropic disk subject to a prescribed displacement along its boundary. In classical linear elasticity, the solution of this problem predicts material overlapping, which is not physically realistic. One way to prevent this anomalous behavior is to consider the minimization of the total potential energy of classical linear elasticity subject to the local injectivity constraint. In the context of this constrained minimization theory, bifurcation occurs from a radially symmetric solution to a secondary solution. In this work we present analytical and computational results indicating that this secondary solution is rotationally symmetric. Initially, we assume that the solution is rotationally symmetric, solve the Euler-Lagrange equations of the corresponding minimization problem in the region where the local injectivity constraint is not active, and obtain a solution that depends on constants of integration that are determined numerically. In the region where the constraint is active, we determine a nonlinear relation between the radial and tangential displacements, which contains a constant of integration that is also determined numerically. Still assuming rotational symmetry, we use an interior penalty formulation together with a standard finite element method to obtain sequences of numerical solutions that converge to a limit function that is in very good agreement with our analytical results in the non active region. To confirm these findings, we also search for an asymmetric solution numerically. In this case, there is no a priori assumption on symmetry and we only obtain either the radially or the rotationally symmetric solution. In all the cases investigated numerically, we have to introduce a small perturbation to obtain the latter solution. The rotationally symmetric solution presents a novel behavior that is not reported in the literature. The tangential displacement is linear near the center of the disk and the corresponding angle of rotation has the value $\pi $ at this center and decreases as we move away from it. Finally, we investigate numerically the influence of both the shear modulus and the boundary condition on the existence of the rotationally symmetric solution. For a given mesh, there is a maximum value of the shear modulus above which and a minimum value of the boundary condition below which this solution is not possible. This research is of interest in the investigation of solids having stiffer response in the radial direction than in the tangential direction, such as in the case of carbon fibers with radial microstructure and certain types of wood.

The hydroalcoholic extract of Polygala altomontana (30, 100, and 300 mg/kg, i.g.) showed a dose-dependent antinociceptive action during the inflammatory phase of the formalin test. In addition, the preparation (30 and 300 mg/kg, i.g.) showed anti-hyperalgesic action when tested on a mechanical nociception model. UPLC-ESI-QTOF-MS data indicated the active extract contained phenylpropanoid sucrose esters, glycosylated quercetin derivatives, styrylpyrones, and coumarins. Some identified compounds, including styrylpyrones and coumarins, have previously demonstrated antinociceptive action. The results also show that P. altomontana shows potential for developing pain-relieving herbal remedies and drugs.

We investigate the properties of an isotropic linear elastic peridynamic material in the context of a three-dimensional state-based peridynamic theory, which considers both length and relative angle changes, and is based on a free energy function proposed in previous work that contains four material constants. To this end, we consider a class of equilibrium problems in mechanics to show that, in interior points of the body where deformations are smooth, the corresponding solutions in classical linear elasticity are also equilibrium solutions in peridynamics. More generally, we show that the equations of equilibrium are satisfied even when two of the four peridynamic constants are arbitrary. Pure torsion of a cylindrical shaft and pure bending of a cylindrical beam are particular cases of this class of problems and are used together with a correspondence argument proposed elsewhere to determine these two constants in terms of the elasticity constants of an isotropic material from the classical linear elasticity. One of the constants has a singularity in the Poisson ratio, which needs further investigation. Two additional experiments concerning bending of cylindrical beam by terminal load and anti-plane shear of a hollow cylinder, which do not belong to the previous class of problems, are used to validate these results.

Experimental observations reveal that abnormal biological tissues, such as tumors, found in the breast and prostate, tend to be stiffer than healthy biological tissues. Classical linear elasticity is then used to model the responses of these tissues under small strains. In particular, soft tissues are modeled as linearly elastic, isotropic, and incompressible materials. For a particular class of plane problems, it has been shown that if the shear elastic modulus, \(\mu \), is known at four different points in a sample, then it can be uniquely determined from the knowledge of two displacement fields obtained from two distinct experiments performed on the same sample. We use this result to propose a non-iterative numerical procedure to determine \(\mu \) in a sample of soft tissue, which is subjected to two quasi-static experiments that are possible to reproduce in laboratory and are simulated numerically using the finite element method. No a priori knowledge of the shear elastic modulus is required, but it is assumed that resultant forces are known on complementary parts of the boundary of the sample. Results for the distribution of \(\mu \) in a long cylinder of rectangular cross section containing an eccentric circular inclusion and an inclusion with a complex geometry are presented. The methodology yields numerical results that are both in very good agreement with analytical results and more accurate than numerical results obtained from another methodology presented in the literature. This work is of great interest in the detection of cancerous tumors and in the differential diagnosis of biological tissues.