An inversion method for identification of elastoplastic properties for engineering materials from limited spherical indentation measurements

Figures & data

Figure 1. Geometry of the spherical indentation.

Figure 2. Stress–strain curve and its parameterization.

Figure 3. Stress–strain curves for different engineering materials.

Figure 4. The indentation curves corresponding to the data in figure 3.

Figure 5. Finite-element mesh (upper mesh) and its part under the indenter (lower mesh).

Table 1. Mesh parameters: .

Mesh1: Nx ×Ny= 50×20,	Mesh2: Nx×Ny= 50×30
αk×10^2 cm			GPa			GPa
0.129	2.112	5.117	1.067	1.990	4.823	1.058
0.229	2.706	6.549	2.543	2.645	6.408	2.527
0.50	4.156	8.117	8.288	4.182	8.142	8.236
0.80	5.435	9.282	16.735	5.480	9.321	16.520
1.10	6.560	10.198	27.155	6.544	10.185	26.368
1.40	7.553	10.942	39.071	7.460	10.875	37.631
1.70	8.434	11.563	52.191	8.288	11.463	50.328
2.00	9.191	12.070	66.400	9.075	11.994	64.191
2.30	9.891	12.522	81.607	9.788	12.457	79.062
2.60	10.552	12.933	97.761	10.531	12.921	94.880
2.90	11.160	13.301	114.708	11.193	13.320	111.545
3.20	11.839	13.700	132.392	11.860	13.711	129.040

Figure 6. The deformed profile of the indented specimen and its scaled (enlarged) part under the indenter: E=210 GPa, e₀=0.027, κ = 0.5, α =3.2×10⁻².

Figure 7. Ill-conditionedness of the inverse problem.

Figure 8. Noise free and noisy indentation curves.

Figure 9. Identification of the stress–strain curve: E=110 GPa, e₀=0.020.

Figure 10. Identification of the stress–strain curve: E=210GPa, e₀=0.027.

Figure 11. An influence of the stopping parameter ϵ_P>0 to identifiability.

Figure 12. An influence of the relaxation parameter δ_β to identifiability.