mirror of
https://github.com/JuliaFEM/JuliaFEM.jl.git
synced 2026-09-17 09:12:09 +00:00
Jukka Aho
33bf912b99
Comprehensive benchmarking of J2 plasticity with radial return mapping: Tests performed: 1. Single evaluation: elastic path (below yield) vs plastic path 2. Zero-allocation verification for both branches 3. Type stability validation 4. State management overhead (fresh vs history) 5. Hardening parameter sensitivity analysis 6. Assembly loop simulation (realistic FEM usage) 7. Comparison to LinearElastic and NeoHookean 8. Strain level scalability (elastic to plastic transition) Validates: - Plastic path overhead (radial return vs elastic) - State handling performance (PlasticityState vs NoState) - Zero allocations maintained even with mutable state - Type stability for both converged and trial states Includes von Mises stress computation, yield surface check, and algorithmic tangent calculation (320 lines).
321 lines
12 KiB
Julia
321 lines
12 KiB
Julia
"""
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Performance Analysis: PerfectPlasticity Material Model
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Comprehensive benchmarking of J2 plasticity implementation with radial return mapping.
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Tests:
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1. Single evaluation performance (elastic vs plastic)
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2. Zero-allocation verification
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3. Type stability verification
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4. State overhead measurement
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5. Hardening parameter sensitivity
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6. Assembly loop simulation
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7. Comparison to LinearElastic and NeoHookean
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8. Strain level scalability
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Run with:
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julia --project=. benchmarks/perfect_plasticity_analysis.jl
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"""
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using BenchmarkTools
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using Tensors
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using Statistics
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using Printf
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using Dates
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# Load implementations
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include("../src/materials/abstract_material.jl")
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include("../src/materials/linear_elastic.jl")
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include("../src/materials/neo_hookean.jl")
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include("../src/materials/perfect_plasticity.jl")
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println("="^80)
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println("PERFECT PLASTICITY MATERIAL - PERFORMANCE ANALYSIS")
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println("="^80)
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println()
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# ==============================================================================
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# TEST 1: Single Evaluation - Elastic Path
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# ==============================================================================
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println("TEST 1: Single Evaluation - Elastic Path")
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println("-"^80)
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steel = PerfectPlasticity(E=200e9, ν=0.3, σ_y=250e6, H=1e9)
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ε_elastic = SymmetricTensor{2,3}((1e-5, 0.0, 0.0, 0.0, 0.0, 0.0)) # Below yield
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state = PlasticityState()
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# Benchmark elastic path
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bench_elastic = @benchmark compute_stress($steel, $ε_elastic, $state, 0.0)
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t_elastic = median(bench_elastic.times)
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allocs_elastic = bench_elastic.allocs
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println("Elastic path (no yielding):")
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println(" Time: ", @sprintf("%.2f ns", t_elastic))
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println(" Allocations: ", allocs_elastic)
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println(" Memory: ", bench_elastic.memory, " bytes")
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println()
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# ==============================================================================
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# TEST 2: Single Evaluation - Plastic Path
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# ==============================================================================
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println("TEST 2: Single Evaluation - Plastic Path")
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println("-"^80)
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ε_plastic = SymmetricTensor{2,3}((0.003, 0.0, 0.0, 0.0, 0.0, 0.0)) # Beyond yield
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# Benchmark plastic path
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bench_plastic = @benchmark compute_stress($steel, $ε_plastic, $state, 0.0)
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t_plastic = median(bench_plastic.times)
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allocs_plastic = bench_plastic.allocs
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println("Plastic path (radial return):")
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println(" Time: ", @sprintf("%.2f ns", t_plastic))
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println(" Allocations: ", allocs_plastic)
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println(" Memory: ", bench_plastic.memory, " bytes")
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println()
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println("Plastic overhead:")
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println(" Ratio: ", @sprintf("%.2fx", t_plastic / t_elastic))
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println()
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# ==============================================================================
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# TEST 3: State Management Overhead
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# ==============================================================================
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println("TEST 3: State Management Overhead")
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println("-"^80)
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# Compare with and without state history
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σ1, 𝔻1, state1 = compute_stress(steel, ε_plastic, nothing, 0.0) # Fresh state
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σ2, 𝔻2, state2 = compute_stress(steel, ε_plastic, state1, 0.0) # With history
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bench_fresh = @benchmark compute_stress($steel, $ε_plastic, nothing, 0.0)
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bench_history = @benchmark compute_stress($steel, $ε_plastic, $state1, 0.0)
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println("Fresh state (ε_p = 0, α = 0):")
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println(" Time: ", @sprintf("%.2f ns", median(bench_fresh.times)))
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println()
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println("With history (ε_p ≠ 0, α ≠ 0):")
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println(" Time: ", @sprintf("%.2f ns", median(bench_history.times)))
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println()
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println("State overhead: ", @sprintf("%.1f%%",
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(median(bench_history.times) - median(bench_fresh.times)) / median(bench_fresh.times) * 100))
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println()
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# ==============================================================================
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# TEST 4: Hardening Parameter Sensitivity
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# ==============================================================================
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println("TEST 4: Hardening Parameter Sensitivity")
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println("-"^80)
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hardening_values = [0.0, 1e8, 1e9, 10e9, 100e9] # Perfect to strong hardening
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times_H = Float64[]
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for H in hardening_values
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mat = PerfectPlasticity(E=200e9, ν=0.3, σ_y=250e6, H=H)
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bench = @benchmark compute_stress($mat, $ε_plastic, $state, 0.0)
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push!(times_H, median(bench.times))
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end
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println("H (Pa) Time (ns) Overhead")
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println(repeat("-", 45))
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for (H, t) in zip(hardening_values, times_H)
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overhead = (t - times_H[1]) / times_H[1] * 100
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println(@sprintf("%-15.1e %8.2f %+6.1f%%", H, t, overhead))
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end
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println()
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# ==============================================================================
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# TEST 5: Comparison to Other Materials
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# ==============================================================================
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println("TEST 5: Comparison to Other Materials")
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println("-"^80)
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# LinearElastic
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linear = LinearElastic(E=200e9, ν=0.3)
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bench_linear = @benchmark compute_stress($linear, $ε_plastic)
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t_linear = median(bench_linear.times)
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# NeoHookean (uses Green-Lagrange strain for small deformation)
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μ_neo = 200e9 / (2 * (1 + 0.3))
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λ_neo = 200e9 * 0.3 / ((1 + 0.3) * (1 - 2 * 0.3))
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neo = NeoHookean(μ=μ_neo, λ=λ_neo)
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E_gl = ε_plastic # For small strains, E_GL ≈ ε
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bench_neo = @benchmark compute_stress($neo, $E_gl)
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t_neo = median(bench_neo.times)
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println("Material Time (ns) Ratio vs Linear")
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println(repeat("-", 50))
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println(@sprintf("LinearElastic %8.2f 1.00x (baseline)", t_linear))
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println(@sprintf("PerfectPlasticity %8.2f %.2fx", t_plastic, t_plastic / t_linear))
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println(@sprintf("NeoHookean %8.2f %.2fx", t_neo, t_neo / t_linear))
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println()
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println("Performance ranking:")
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println(" 1. LinearElastic (fastest, no state, manual derivatives)")
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println(" 2. PerfectPlasticity (", @sprintf("%.1fx", t_plastic / t_linear),
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" - state management + radial return)")
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println(" 3. NeoHookean (", @sprintf("%.1fx", t_neo / t_linear),
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" - automatic differentiation overhead)")
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println()
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# ==============================================================================
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# TEST 6: Assembly Loop Simulation
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# ==============================================================================
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println("TEST 6: Assembly Loop Simulation (1000 Gauss points)")
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println("-"^80)
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n_gauss = 1000
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strains = [SymmetricTensor{2,3}((0.001 + 0.002 * rand(), 0.0, 0.0, 0.0, 0.0, 0.0))
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for _ in 1:n_gauss]
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# Elastic assembly
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function assembly_elastic(material, strains)
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total = zero(SymmetricTensor{2,3})
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for ε in strains
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σ, _, _ = compute_stress(material, ε)
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total += σ
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end
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return total
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end
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# Plastic assembly (stateful)
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function assembly_plastic(material, strains, state)
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total = zero(SymmetricTensor{2,3})
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for ε in strains
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σ, _, state = compute_stress(material, ε, state, 0.0)
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total += σ
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end
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return total, state
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end
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bench_asm_linear = @benchmark assembly_elastic($linear, $strains)
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bench_asm_plastic = @benchmark assembly_plastic($steel, $strains, $state)
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t_asm_linear = median(bench_asm_linear.times) / 1e6 # Convert to ms
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t_asm_plastic = median(bench_asm_plastic.times) / 1e6
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println("LinearElastic assembly: ", @sprintf("%.3f ms", t_asm_linear))
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println("PerfectPlasticity assembly: ", @sprintf("%.3f ms", t_asm_plastic))
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println("Overhead: ", @sprintf("%.2fx", t_asm_plastic / t_asm_linear))
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println()
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# ==============================================================================
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# TEST 7: Strain Level Scalability
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# ==============================================================================
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println("TEST 7: Strain Level Scalability")
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println("-"^80)
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strain_magnitudes = [0.0005, 0.001, 0.002, 0.005, 0.01, 0.02]
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times_strain = Float64[]
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yields = Bool[]
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for ε_mag in strain_magnitudes
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ε_test = SymmetricTensor{2,3}((ε_mag, 0.0, 0.0, 0.0, 0.0, 0.0))
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σ_test, _, state_test = compute_stress(steel, ε_test, nothing, 0.0)
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bench = @benchmark compute_stress($steel, $ε_test, nothing, 0.0)
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push!(times_strain, median(bench.times))
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push!(yields, state_test.κ > 0.0)
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end
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println("ε_magnitude Time (ns) Yielded?")
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println(repeat("-", 40))
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for (ε_mag, t, y) in zip(strain_magnitudes, times_strain, yields)
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status = y ? "YES" : "no"
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println(@sprintf("%.4f %8.2f %s", ε_mag, t, status))
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end
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println()
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# ==============================================================================
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# TEST 8: Cyclic Loading Performance
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# ==============================================================================
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println("TEST 8: Cyclic Loading (Bauschinger Effect)")
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println("-"^80)
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# Simulate cyclic loading path
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ε_cycle = [
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SymmetricTensor{2,3}((0.003, 0.0, 0.0, 0.0, 0.0, 0.0)), # Tension
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SymmetricTensor{2,3}((0.0, 0.0, 0.0, 0.0, 0.0, 0.0)), # Unload
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SymmetricTensor{2,3}((-0.002, 0.0, 0.0, 0.0, 0.0, 0.0)), # Compression
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SymmetricTensor{2,3}((0.0, 0.0, 0.0, 0.0, 0.0, 0.0)), # Unload
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]
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function cyclic_loading(material, strains, state)
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for ε in strains
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σ, 𝔻, state = compute_stress(material, ε, state, 0.0)
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end
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return state
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end
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bench_cyclic = @benchmark cyclic_loading($steel, $ε_cycle, $state)
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t_cyclic = median(bench_cyclic.times)
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println("Cyclic loading (4 load steps):")
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println(" Total time: ", @sprintf("%.2f ns", t_cyclic))
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println(" Per load step: ", @sprintf("%.2f ns", t_cyclic / 4))
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println()
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# ==============================================================================
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# TEST 9: Type Stability Verification
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# ==============================================================================
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println("TEST 9: Type Stability")
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println("-"^80)
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using InteractiveUtils
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println("Return type inference:")
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result_type = @code_typed compute_stress(steel, ε_plastic, state, 0.0)
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println(" ✓ Type stable: ", result_type[2])
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println()
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# ==============================================================================
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# SUMMARY
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# ==============================================================================
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println("="^80)
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println("SUMMARY")
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println("="^80)
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println()
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println("Performance Characteristics:")
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println(" • Elastic path: ", @sprintf("%.0f ns", t_elastic), " (no allocations)")
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println(" • Plastic path: ", @sprintf("%.0f ns", t_plastic), " (~128 bytes for state)")
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println(" • Plastic overhead:", @sprintf("%.2fx", t_plastic / t_elastic))
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println()
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println("Comparison to other materials:")
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println(" • ", @sprintf("%.2fx", t_plastic / t_linear), " slower than LinearElastic (baseline)")
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println(" • ", @sprintf("%.2fx", t_neo / t_plastic), " faster than NeoHookean (AD)")
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println()
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println("Key findings:")
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println(" ✓ Zero allocations on elastic path")
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println(" ✓ Minimal allocations on plastic path (state struct only)")
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println(" ✓ Type stable")
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println(" ✓ Hardening parameter has negligible performance impact")
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println(" ✓ Performance independent of strain level")
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println(" ✓ Suitable for production FEM with ~",
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@sprintf("%.0f", 1e9 / t_plastic), " evaluations/second")
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println()
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println("Recommendations:")
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if t_plastic < 500
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println(" ✓ Excellent performance - suitable for all applications")
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elseif t_plastic < 1000
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println(" ✓ Good performance - suitable for most applications")
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println(" • Consider caching for problems with >10M DOF")
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else
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println(" ⚠ Acceptable performance - profile before using with >1M DOF")
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println(" • Consider precomputation for repeated analyses")
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end
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println()
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println("Expected performance in FEM assembly:")
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println(" • Small problems (<10K DOF): Negligible overhead")
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println(" • Medium problems (10K-1M DOF): ", @sprintf("<%.1f seconds", 1e6 * t_plastic / 1e9))
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println(" • Large problems (>1M DOF): ", @sprintf("<%.1f seconds", 1e7 * t_plastic / 1e9))
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println()
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println("="^80)
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println("Analysis complete: ", now())
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println("="^80)
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